Planning with Spatial-Temporal Abstraction from Point Clouds for Deformable Object Manipulation

Effective planning of long-horizon deformable object manipulation requires suitable abstractions at both the spatial and temporal levels. Previous methods typically either focus on short-horizon tasks or make strong assumptions that full-state information is available, which prevents their use on deformable objects. In this paper, we propose PlAnning with Spatial-Temporal Abstraction (PASTA), which incorporates both spatial abstraction (reasoning about objects and their relations to each other) and temporal abstraction (reasoning over skills instead of low-level actions). Our framework maps high-dimension 3D observations such as point clouds into a set of latent vectors and plans over skill sequences on top of the latent set representation. We show that our method can effectively perform challenging sequential deformable object manipulation tasks in the real world, which require combining multiple tool-use skills such as cutting with a knife, pushing with a pusher, and spreading the dough with a roller.

Introduction
Consider a typical cooking task of making dumplings from dough. People plan over which piece of dough to manipulate and which tool to use in sequence, incorporating both spatial and temporal abstractions. A spatial abstraction reasons about objects, parts, and their relations to each other, such as reasoning about pieces of dough instead of reasoning about individual dough particles; such a spatial abstraction enables efficient planning and compositional generalization. On the other hand, a temporal abstraction incorporates abstract actions represented as a set of skills. With abstract actions, the agent plans for the types and parameters of the skills to execute over a period of time, instead of making plans for low-level actions such as joint torques at each time step. Temporal abstractions allow planning at the skill level, enabling more efficient optimization for solving long-horizon tasks. An autonomous robot that operates in unstructured environments should be able to reason about world dynamics using high-level spatial and temporal abstractions instead of reasoning only over the physical state, raw sensory observation, or low-level robot actions.
The research community is making rapid progress towards developing state abstractions for manipulating deformable objects, including key points [1,2], graphs [3,4], dense object descriptors [5], or implicit functions [6,7]. However, most of these approaches do not make abstractions at the temporal level, limiting their use to short-horizon tasks. Methods are also being developed with temporal abstractions, planning over a set of skills to solve long-horizon tasks [8,9,10]. However, the lack of spatial abstraction severely limits their generalization ability. Therefore, it remains a key question in robot learning on how to learn spatial and temporal abstractions within a unified framework for complex and long-horizon manipulation tasks.
In this work, we focus on the challenging task of sequential deformable object manipulation, as shown in Figure 1. We consider a set of dough manipulation tasks that require sequentially applying different skills using multiple tools to manipulate dough, such as spreading using a roller, cutting using a knife and pushing using a pusher, where the longest task requires applying 6 skills in sequence. Deformable objects like dough have nearly infinite degrees of freedom. As such, in this work, we dynamically cluster points in a point cloud into different groups and learn a point cloud encoder to map each element in the group into a latent vector. In this way, we obtain a compositional 3D set representation of the state space. Given an observation and a target point cloud, we then sample skill sequences with subgoals generated in this latent space. We learn skill abstraction modules to determine the feasibility and score of each skill sequence and use them for planning.
Our contribution of this paper is a framework that PlAns with Spatial and Temporal Abstraction (PASTA) by learning a set of skill abstraction modules over a 3D set representation. Our framework can compose a set of skills to solve complex tasks with more entities and longer-horizon than what was seen during training. We show that PASTA significantly outperforms an ablation that performs planning with a flat representation without a spatial abstraction (e.g. without a set representation). Finally, our planner can be trained in simulation and transferred to the real world.

Related Work
Model-based Planning for Sequential Manipulation. One line of research for sequential manipulation is Task and Motion Planning (TAMP). TAMP systems typically assume known object states and known effects for the action operators [11,12,13,14,15]. However, it is difficult to estimate states and dynamics for unknown objects or from partial observations. While recent works have made progress in learning certain components of the system, such as the logical states [16] from high dimensional observations or learning action models [17,18,19] from interactions, they still require either known states or known action operators. In contrast, we do not assume known states or action operators, and learn a 3D set representation as well as the action model with the representation.
Another approach learns dynamics directly from visual observations [3,20,21]. Most of these works focus on learning a one-step dynamics model for planning short-horizon tasks. A few works learn the dynamics model over a set of skills and use it for sequential manipulation of rigid objects [22,23] or deformable objects [8]. However, these works do not use an object-centric representation and thus cannot easily generalize to more complex scenes. In contrast, our framework unifies both temporal and spatial abstraction and can perform long-horizon manipulation for complex tasks with more objects than in previous work, as we will show.
Planning with Spatial Abstraction. Prior works leverage spatial abstraction to facilitate solving tasks that involve complex dynamics and high-dimensional observations. These works either model a compositional system with Graph Neural Networks (GNN) [3,4,7,24,25] or learn policies directly from object-centric representations [26,27]. These works demonstrate compositional generalization, but they learn policies or one-step dynamics models for planning, which can be difficult for solving long-horizon tasks. In contrast, our framework connects temporally extended spatial abstractions with a feasibility predictor to plan over a longer time horizon. Xu et al. [28] learns a planner grounded Step 1 Step 2 Step 3 Enumerate attention structures goal pc < l a t e x i t s h a 1 _ b a s e 6 4 = " q 3 a 5 t F d R x J p g 1 7 j L v + 1 f 9 + n 9 w c j g a T 0 e T j 8 G 4 C d l g j z w j z 8 l L M i a v y R F 5 T 4 7 J j F D y n f w g P 8 m v 6 E N U R 6 t o v S m N e p c 9 T 8 g 1 R N / + A K V A 4 W 4 = < / l a t e x i t > u obs 0 < l a t e x i t s h a 1 _ b a s e 6 4 = " 7 J i d 2 C b 9 t R M a 2 X 5 r f W Q 5 k I w e v q c = " < l a t e x i t s h a 1 _ b a s e 6 4 = " J / g 5 j 7 W v l J X U k C 1 z S N 2 j 2 I 8 y k r o = " < l a t e x i t s h a 1 _ b a s e 6 4 = " K S Z 1 W v 0 k y P L H L A U 4 R l 9 4 k 3 4 J k 0 q I 3 g S r a u z n 3 4 + J y 8 5 s z Y J P n Z i 6 5 c v X b 9 x s 7 N / q 3 b d + 7 e G + z e P z K q 0 R S m V H G l T 3 J i g D M J U 8 s s h 5 N a A x E 5 h + P 8 9 F V b P 1 6 C N k z J 9 3 Z V Q y Z I J V n J K L E B m g 9 G L u 2 W z H S V Z 2 4 U J 1 0 M k / h l i M l k u E F 8 M 3 f j I U 6 8 n w / 2 N i D e t O G / y C b Z O 3 j 4 9 t f v r 9 G H w / l u 7 A V 9 Q 9 / R j + h 1 J C I b L d e t U e 9 8 5 g G 6 F N H n P x R Y 4 A k = < / l a t e x i t > u 2,0 < l a t e x i t s h a 1 _ b a s e 6 4 = " r l 7 < l a t e x i t s h a 1 _ b a s e 6 4 = " 2 p C 8 G 9 C q m A R a V X F F U 5 H d h U 0 5 G w k = " > A A A C y X i c d V F N b x M x E H W W r x K + U h A n L i s K U g 9 R t K n a 0 N 4 q c U H i U i T S V s q G a N Y 7 u 7 H q j 8 X 2 t g 3 G J / 4 D F 3 4 K J 6 7 0 x J F / g z d p U B v B S L Z G 7 8 2 M n + d l F W f G J s n v V n T j 5 q 3 b d 9 b u t u / d f / D w U W f 9 8 a F R t a Y 4 p I o r f Z y B Q c 4 k D i 2 z H I 8 r j S A y j k f Z y e u G P z p F b Z i S 7 + 2 s w r G A U r K C U b A B m n R 2 X D o f M t J l N n b 9 X j K P b t L b C z E Y d J e I r z + 4 U g H 3 E 5 d 4 P + l s L I l 4 W R r / R Z b J x v 7 T 7 1 8 3 L 3 6 9 O J i s t z 6 n u a K 1 Q G k p B 2 N G / a S y Y w f a M s r R t 9 P a Y A X 0 B E o c h V S C Q D N 2 c 2 k + f h m Q P C 6 U D k f a e I 5 e 7 X A g j J m J L F Q K s F O z y j X g P 7 k s U z z 3 K 5 C 4 r k b X H P P u a b P g P A j m p d L M T s X W q m h b 7 I 4 d k 1 V t U d K F 5 q L m s V V x s / c 4 Z x q p 5 b O Q A A 0 T G I 3 p F D R Q G 9 x p p z k W 4 Y H 5 z 5 z S I E v 0 L l j i G 0 u 6 Y c c 7 z Z W E J y W e U S U E y N y l o E s B 5 9 6 l q k I N V u l m b W d B H W e C W e M u e d + + 6 t f / k 8 O t X n / Q 2 3 4 X j N s m i 1 g j z 8 h z s k n 6 5 B X Z J 2 / I A R k S S r 6 R H + Q n u Y j e R h + j 8 + j T o j R q X f Y 8 I d c i + v I H W X 3 i r Q = = < / l a t e x i t > u goal 0 < l a t e x i t s h a 1 _ b a s e 6 4 = " h e i E H x I E U + U D k f a e I 5 e 7 X A g j J m J P F Q K s F O z y j X g P 7 k 8 V 7 z w K 5 C 4 r k b X H I v u a b P g I g j m p d L M T s X W q m g 7 2 R 0 5 J q v a o q Q L z Z O a x 1 b F z d 7 j g m m k l s 9 C A j R M Y D S m U 9 B A b X C n n R U 4 C Q / M f + a U B l m i d 8 E S 3 1 j S D T v e a a 4 k P C n x j C o h Q B Y u A 1 0 K O P c u U x V q s E o 3 a z s L 6 j g T z B p 3 y f v 2 V b / + n x x u 9 d J + b / t d M G 6 b L G K N P C P P y S Z J y S u y T 9 6 Q A z I g l H w j P 8 h P c h G 9 j T 5 G 5 9 G n R W n U u u x 5 Q q 5 F 9 O U P W 6 7 i r g = = < / l a t e x i t > u goal e E H w m M / A A q d g d z 8 r s A w D F j / z x o K u s P W 2 y l s f z N w O 1 r 7 p r i S M 1 H j B j V K g C 5 + B r R R 8 a 3 1 m a r R A x n a 2 X Q R 1 U i h B z q / y b T / s K 1 3 f z k 1 w t D N M 3 w 5 3 v y S D v V 2 2 j A 3 2 n L 1 k r 1 n K 3 r E 9 d s B G b M w 4 k + w 7 + 8 l + R S + i / e h T 9 H l Z G v V W P c / Y t Y g O / w K j Z 9 R 7 < / l a t e x i t > P goal < l a t e x i t s h a 1 _ b a s e 6 4 = " R q X c s s B x M Z p 6 Z H z g m T 8 Y 7 l n + W J Y = " > A A A C m X i c b V F N b 9 N A E N 2 Y j 5 b w 1 c K x F 4 s I i U M V 2 V W B 3 i j i U n E K g j S V 6 l C N 1 2 N n l f 2 w d s c t 0 e I f w Z H y S / g p / B v W S Q 4 0 Z a R d P b 2 Z 2 X n 7 J q + l c J Q k f 3 r R n b v 3 7 m 9 t P + g / f P T 4 y d O d 3 W e n z j S W 4 5 g b a e x Z D g 6 l 0 D g m Q R L P a o u g c o m T f P 6 h y 0 8 u 0 T p h 9 B d a 1 D h V U G l R C g 4 U q M n o q z e 5 a y 9 2 B s k w W U Z 8 G 6 R r M H j 3 + 2 c X 1 6 O L 3 d 7 3 r D C 8 U a i J S 3 D u P E 1 q m n q w J L j E t p 8 1 D m v g c 6 j w P E A N C t 3 U L / W 2 8 We then sample point clouds (pc) from the demonstration trajectories to train our set skill abstraction modules. (c) We map point clouds into a latent set representation and plan over tool-use skills to perform long-horizon deformable object manipulation tasks. P obs , P goal are the observation and target pc; ui,j denotes component j at step i. The example shows our method performs the CutRearrange task, which requires cutting the dough into two pieces with a knife and transporting each piece to its target location. on object-centric visual observation and can solve long-horizon tasks. However, its planner takes a symbolic goal and plans in a predefined symbolic domain to output symbolic subgoals. In contrast, our method does not require defining a symbolic planning domain.
Deformable Object Manipulation. Deformable objects have nearly infinite degrees of freedom and complex dynamics, making them very challenging to manipulate. Previous works have explored pouring liquid [6,29,30], rope manipulation [31,32], and cloth manipulation [33,34,4,35,36]. Other papers have also explored manipulating elasto-plastic objects such as deforming them by grasping [3,37], rolling [38,39,40], or cutting [41]. However, these works mostly only consider manipulation with one skill at a time. In contrast, we consider the task of sequential manipulation using multiple tools. The one exception is DiffSkill [8], where multiple skills are chained together. However, DiffSkill uses RGB-D images to represent the scene. In contrast, we use a 3D set representation that separately encodes each entity in the scene, enabling compositional generalization to tasks with more objects and longer-horizon. Furthermore, we use point clouds as the input and we are able to transfer our planner from simulation to the real world.

Method
Given a point cloud of the dough P obs and a goal point cloud P goal , our objective is to execute a sequence of actions a 1 , ..., a Ttot that minimizes the distance between the final observed point cloud and the goal D(P obs Ttot , P goal ) where P obs Ttot is the observation point cloud at time T tot . We aim to solve long-horizon tasks that require chaining multiple skills in novel scenes with more objects than training. To do so, we present a general framework that incorporates spatial and temporal abstractions, as summarized in Figure 2. We use point clouds as input to all our modules to enable easier transfer from simulation to the real world and to enable robustness to changes in viewpoint.
We assume access to an offline dataset of demonstration trajectories D demo from K skills, where each trajectory demonstrates one of the skills using one tool. We can learn skill policies by imitation learning from these demonstrations. To chain these skills to solve long-horizon tasks, we train a set of skill abstraction modules (Sec. ) which can be used for planning in the latent space (Sec. ).

Spatial Abstraction from Point Clouds
Scene Decomposition: First, we describe our spatial abstraction of the point cloud observation. Given a point cloud P ∈ R N ×3 , we first cluster the points into different components based on their proximity in space. In this paper, we apply DBSCAN [42] to P and group points into a set of entity point clouds {P i ∈ R Ni×3 } i=1...C by separating points from high-density regions into different clusters. While other works on scene decomposition can also be used [43], we find this simple method to be sufficient for our tasks.
Entity Encoding: Planning directly in the high-dimensional space of point clouds is inefficient. To enable efficient planning in a latent space, we train a point cloud variational autoencoder (VAE) [44]. The VAE model includes three modules: A point cloud encoder φ : R Ni×3 → U that maps each entity point cloud to a latent vector, a decoder ψ : U → R Ni×3 that maps from a latent space back into a point cloud, and a prior distribution over the latent space p u : U → [0, 1] which can be used to generate samples from the latent space during planning. We can then encode the point clouds {P i } into a set of latent vectors: {u i } i=1...C as our set latent representation. We further achieve translation invariance by separating the translation from its shape embedding. See the Appendix for details.

Learning Skills by Imitation
Given the demonstration trajectories D demo of K skills, we first distill these trajectories into K closed-loop policies. The input to the policy for the k th skill π k is a subset of the observed point clouds {P o i } and goal point clouds {P g j }, and a tool point cloud P tool k . The policy only sees a subset of the dough point cloud and goal point cloud in the scene to enable compositional generalization to scenes with more objects. For example, a dough-spreading policy will only see the dough being spread. To achieve this, we train each set point cloud policy with behavior cloning and hindsight relabeling [45] on the demonstration dataset with an attention mask that filters out the non-relevant entity point clouds. During planning, this attention mask will be provided by the planner. The policy outputs an action at each timestep to control the tool directly.

Neural Spatial and Temporal Abstraction
We assume that each skill learned from the demonstration is only capable of performing a single-stage task with a single tool for a single object. To solve longer-horizon tasks, we further learn a feasibility predictor and a cost predictor. They can be used to plan subgoals that chain the skills into a sequence, such that each subgoal is feasible for the corresponding policy to reach and the final subgoal reaches a given goal. Additionally, all these modules take in the set representation {P 1 . . . P C } as input to achieve compositional generalization.
Set Feasibility Predictor Similar to DiffSkill [8], we train a feasibility predictor ...Ng are latent set representations of an observation and goal point cloud respectively. The feasibility predictor outputs a value in [0, 1] denoting if the goal can be reached from the observation by executing the k th skill. In DiffSkill, the feasibility predictor uses a flat representation that takes in a single latent vector for all objects in the scene as input. However, as our skills such as cutting or spreading only need to take in a subset of the objects as input, we use the same attention method for the feasibility and assume that the feasibility predictor only takes as input a subset of the full set Here, N k and M k are the number of components in the observation and goal for skill k. The number of components in the observation and goal can be different since the number of components can change before and after executing a skill; for example, the cut skill takes one component as observation and cuts it into two components. As another example for robot assembly [46], the number of entities increases when a piece is disassembled into parts and the number of entities decreases when the parts are assembled. In this work, we manually define the number of entities N k , M k per skill. Determining which subset to attend to when executing each skill can be difficult; we make this decision during planning and defer the details to Sec. . We parameterize f k to be invariant to permutation using max-pooling layers. See Appendix for details.
We train the feasibility predictor of skill k with positive examplesÛ o ,Û g , where the goalÛ g can be reached from the observationÛ o within T timesteps by executing skill k. The negative examples are goalÛ g that cannot be reached from the observationÛ o using skill k. During training, we obtain positive pairs for the feasibility predictor by sampling two point clouds (P obs , P goal ) from the same trajectory in the demonstration set. To findÛ o ,Û g , we first cluster the observation and goal point clouds into two sets {P o i }, {P g j } respectively. Then, we match point clouds in the observation set to those in the goal set by finding the pairs of point clouds that are within a Chamfer distance of : We then remove these point clouds from the corresponding set, since these are the point clouds that have already been moved to the target location in the goal. We can then encode the remaining point clouds intoÛ o ,Û g as explained above. We generate hard negative samples by replacing one entity in the positive examples with a random latent vector.
Set Cost Predictor As we do planning in a latent space, we train a set cost predictor as our planning objective which determines how close a plan is to a given goal. The set cost predictor C takes two latent set representation as input U o , U g . Since our tasks focus on matching each entity in the observation with one in the goal, we assume they have the same number of components, i.e.
To compute the cost, we try to find the matching entity with the minimal where σ is a permutation and c θ is a cost prediction network parameterized by an MLP trained to predict the Chamfer Distance between the point clouds corresponding to the two latent vectors. This allows faster planning compared to first decoding latent vectors to point clouds and then computing their distance. Finally, optimization of the cost is done by performing Hungarian matching between the two sets containing latent vectors.

Planning with Set Representation
Given an observation and a goal point cloud P obs , P goal , we plan for the types of skills to apply in sequence, the attention for each skill (i.e. findÛ o ⊆ U o ), and the latent subgoals for each skill (i.e. the exact value for each latent vector inÛ o ). As the simplest approach, we run a three-level nested optimization: In the top level, we exhaustively search over the combinations of skills to apply at each step, i.e. k 1 . . . , k H , where k h indexes the skill applied at the high-level step h. We only keep the sequences that end with the same set cardinality as the goal by ensuring that In the second-level optimization, we search over different attention structures. Denote the latent set at the high level step h to be U h . We formally define the attention structure at step h to be I h , which consists of a list of indices, each of length N k h , such that I h selects a subset from U h−1 to be the input to the feasibility predictor, i.e.Û h−1 = U h−1 I h ⊆ U h−1 . Assume that we have N h components before applying skill k h , i.e. |U h−1 | = N h and skill k h takes K h components as its observation. We can search over all C K h N h combinations of attention structures. For components not considered by the skill, its latent vector will remain the same at step h. The combination of each skill attention yields an attention structure I for the whole plan, as illustrated in Fig. 2(c). For this level of optimization, we use a sampling-based procedure to avoid an exhaustive search over topologically equivalent attention structures. See the Appendix for how we do this efficiently.
In the low-level optimization, for each attention structure I, we follow the optimization in DiffSkill [8]. We first sample multiple initializations for the set of latent subgoals U, where each latent vector in the set is initialized from our generative model. We can then perform gradient descent to further optimize the latent subgoals on the following objective: where k is the skill sequence, I is the attention structure of the plan, U is the set of all latent subgoals, Optimize latent subgoalsÛ 1 , . . .Û H according to Sec. to obtain cost J(k, I, U) ; 5 Choose skill sequence k, attention structure I, and subgoals U that minimizes J(k, I, U) ; 6 for h ← 0 to H − 1 do 7 Decode the subgoal fromÛ h using the decoder ψ ; 8 Execute policy π ki following the subgoal ; and U g is the goal set. Finally, we can use our policy to execute our plan by following each subgoal. A summary of our method can be found in Algorithm 1.

Experiments
Our experiments are categorized into three parts: In Sec. 8, we describe the experimental setups and the baselines we consider. In Sec. 8 and Sec. 8, we show that PASTA outperforms the baselines and ablate different components in our framework. In Sec. 8, we demonstrate that PASTA can be effectively transferred to the real world without any fine-tuning.

Simulation Tasks and Baselines
Environment setups We consider several long-horizon dough manipulation tasks and divide them into two categories. First, we consider the three tasks from Diffskill [8]: LiftSpread, GatherTransport, and CutRearrange. These tasks require the agent to sequentially compose at most two skills to spread, cut or transport the dough. We further propose two new generalization tasks: CutRearrangeSpread (CRS) and CRS-Twice, where there are more entities during testing than during training. Similar to prior work [8], we specify the minimal planning horizon required for each task. Our approach also succeeds when we increase the horizon up to twice as long. See the Appendix, Sec 4.5 for details.

Generalization tasks
The CRS task provides a number of demonstration trajectories performing one of the three skills: Cutting with a knife, pushing with a pusher, and spreading with a roller. The demonstration of each skill only shows a tool manipulating a single piece of dough. During testing, the agent needs to cut a dough into two, transport one piece to a spreading area and then spread it. Generalization to more entities is required as there will be two entities in the scene, whereas during training there was only one entity. Can we do even more generalization? In the CRS-Twice task, we use the same agent trained on the CRS dataset and ask it to cut two pieces of dough from a chunk, transport both of them to a spreading area, and spread them both. This is a 6-horizon task with up to 3 entities in the scene, much more complex than the skill demonstrations the agent is trained on. Due to the long-horizon nature of CRS-Twice, we specify the skill skeleton and use receding horizon planning for all the planning-based methods. See the Appendix for details.
Baselines We consider several baselines in simulation: First, a gradient-based trajectory optimizer with oracle information (Traj-Opt), which can solve single-stage tasks for deformable object manipulation as shown in prior works [47]. Second, a model-free RL with Soft Actor Critic [48] with RGB-D image input (SAC-Image). Third, a SAC agent that takes in the dough, target dough, and tool point clouds as input, the same as our method (SAC-Point). Fourth is DiffSkill, a model-based planning method from Lin et al. [8], which takes RGB-D images as input and has no spatial abstraction. The last one is Flat 3D, which extends DiffSkill to use 3D point clouds as input, with a "flat" 3D representation that encodes the whole scene to a single latent vector without any spatial abstraction.
Metric We specify goals as 3D point clouds of different geometric shapes such as boxes and spheres at specific locations. We report the normalized decrease in the Earth Mover Distance (EMD) approximated by the Sinkhorn diverge [49] computed as s(t) = s0−st s0 , where s 0 , s t are the initial and current EMD. We additionally set a threshold for the score to determine the success of a trial.

Comparison with Baselines in Simulation
Method Task (Horizon) DiffSkill tasks Generalization tasks LiftSpread (2) GatherMove (2) CutRearrange (3) CRS (3) CRS-Twice (6) Traj-Opt (Oracle) [   Effectively using spatial abstraction to model the scene, PASTA achieves 100% success rate in CRS and retains a good performance in CRS-Twice. All the baselines, especially the planning baselines (DiffSkill, Flat 3D) fail dramatically, as they can only produce plans that consist of scenes seen in training. Impressively, PASTA is the only approach that reaches a non-zero success rate on these tasks that require compositional generalization. PASTA has a computational complexity of O(K H · |I| · T G ), where K is the number of skills, H is the planning horizon, |I| is the number of attention structures and T G is the time it takes to solve each gradient-based optimization. We discuss more efficient planning algorithms in the limitation section as well as in the Appendix, Sec. 5.   Table 2 shows the quantitative performance of each ablation and PASTA in CutRearrange. First, we consider a variant of feasibility predictor's training, which removes the hard negative samples and only uses random negative sampling (No Hard Negatives), which halves the success rate. Second, we consider two variants of the planner, one without gradient-descent (No Gradient Planning) and one without sampling (No Sampling Planning). The results show that both components are crucial to planning. We provide more ablations on the policy and the planner in the Appendix. Figure 3 shows our real world setup. We use a Franka robot with an Azure Kinect camera capturing the RGB-D observation of the workspace. The robot is equipped with a tool station [50] that allows an automatic change of tools. For real world "dough", we use Kinect Sand as a proxy because of its stable physical property. We transfer the feasibility predictor and cost predictor of PASTA directly from simulation and define heuristic controllers for the skills. For evaluation, we first generate a desired target point cloud and then reset the dough to its initial shape and record its point cloud. We then plan using PASTA and then use the heuristic controllers to follow the plan. Finally, we report the normalized improvement EMD. We compare with the Flat3D method and also with human.

Real World Experiments
We evaluate three of the simulation tasks: CutRearrange, CRS, and CRS-Twice. For each task, we evaluate the same four initial and target shapes for all methods and report the performance in Table 3. Figure 3 shows the keyframes from the execution of PASTA. We overlay the planned subgoals as well

Observation
Step 1 Step 2 Step 3 Final 3D view

Observation
Step 1 Step 2 Step 3 Final 0.820 CutRearrange CRS-Twice Observation Step 1 Step 2 Step 3 Step 4 3D view Step 5 Step  Figure 3: Real world setup and execution with planned subgoals. Our workspace consists of a Franka robot, a top-down camera, and a novel tool changer behind the robot that allows the robot to automatically switch tools.
For each task, we show frames after executing a skill overlaid with the decoded point cloud subgoal; we report the final performance in red and overlay the ground truth target in green in the final frame. Additionally, we include a 3D view of the last generated subgoal to show the shape variations.
as the final goal. PASTA performs on par with human in the real world, highlighting the robustness of our planner and the advantage of using 3D representation for sim2real transfer.  Table 3: Normalized improvement on real world tasks. Each entry shows the mean and std of the performance over 4 runs. Flat 3D does not produce any meaningful plan for CRS, so we do not evaluate it on CRS-Twice.

Conclusions and Limitations
In this work, we propose a planning framework named PASTA that incorporates both spatial and temporal abstraction by planning with a 3D latent set representation with attention structure. We demonstrate a manipulation system in the real world that uses PASTA to plan with multiple tool-use skills to solve the challenging deformable object manipulation tasks, and we show that it significantly outperforms a flat 3D representation, especially when generalizing to more complex tasks.
Limitations: First, we only transfer the planner to the real world and use heuristic controllers instead of the policy trained in simulation. This is due to the sim2real gap caused by the differences in dough's physical parameters, table friction, and occlusions from the robot arm. Prior work [38] shows promising results in transferring a closed-loop policy taking partial point clouds as input, and future work can explore better sim2real methods. Second, our planner exhaustively searches overall skill combinations and attention structures and does not scale well to longer sequences with more skills. Future work can incorporate more efficient search algorithms or priors to prune the search space. Finally, we rely on an unsupervised clustering method for entity decomposition and a point cloud VAE for mapping an observation to our latent set representation. Future work can incorporate self-supervised methods for learning the decomposition. For further discussion on the limitations and future work, please see Sec. 5 of the Appendix.
1 Implementation Details

Entity Encoding
To train our point cloud variational autoencoder [44], we normalize the point cloud of each entity P i to be centered at the origin, i.e.P i = P i − t i , where t i is the mean of all points in P i . We then encode each centeredP i into a latent encoding: consists of the encoding of the point cloud's shape z i and the position of the center of the point cloud t i . We model the point cloud's position t i explicitly such that the learned latent embedding z i can focus on shape variation alone and the model that plans over u i can still reason over point clouds at different spatial locations. During training, we record the 3D bounding box of all training data t min , t max ∈ R 3 , and we sample from [t min , t max ] during planning. We denote this combined distribution of u = [z, t] as P u .

Details on Training Set Feasibility Predictor
Hard Negative Samples Suppose skill k takes N k latent vectors from observationÛ o and M k latent vectors from goalÛ g as input.
To generate random pairs of observations and goals as negative samples for the feasibility predictor, we can sample each latent point cloud representation u i by sampling the shape z i from the VAE prior p z and sampling the position t i from the distribution of positions in the training dataset. Such random negative samples are used similarly in DiffSkill [8]. However, as the combined dimension of the set representation becomes larger compared to a flat representation, we need a way to generate harder negative samples. To do so, for a positive pair of set representation ({u o i }, {u g j }), we randomly replace one of the entities u o i or u g j with a random sample in the latent space and use it as a negative sample. Our ablation results show that this way of generating hard negative samples is crucial for training our set feasibility predictor.
Noise on Latent Vectors During training of the feasibility predictor, for each of the input latent vector u = [z, t], where z ∈ R Dz is the latent encoding of the shape and t ∈ R 3 is the 3D position of the point cloud, we add a Gaussian noise to each part, i.e.ẑ = z + σ z andt = t + σ t , where ∼ N (0, I). The amount of noise determines the smoothness of the feasibility landscape. Without any noise, planning with gradient descent with the feasibility function becomes much harder.

Details on the Attention Structure for Planning with Set Representation
Given the initial latent set observation U obs with N o components, and the skill sequences k 1 , . . . , k H , in this section we describe how to generate the attention structure. We denote the latent set representation at step h as U h , h = 1 . . . H and define U 0 = U obs . As skill k h takes in N k h components as input and M k h components as output, by calculation we know that U h has N o + h i=1 M ki − N ki components. From now on, we denote |U h | = N h and U h = {u h,1 , . . . , u h,N h }. As the skill k h only applies to a subset of the input U h−1 , we now formally define the attention structure at step h to be I h , which consists of a list of indices, each of length N k h , such that I h selects a subset from U h−1 to be the input to the feasibility predictor, i.e.
However, enumerating all I h is infeasible, as there are C N k h N h combinations for each step. Fortunately, we do not have to enumerate all different structures. The insight here is that, for each attention structure I 1 , . . . I H , we will perform a low-level optimization. In this low-level optimization, we will first initialize all the latent vectors to be optimized from P u and then perform gradient descent on them. As many of the attention structures yield topologically equivalent tree structures (An example of such a tree is illustrated in Figure 2c of the main paper), and each latent vector in the tree is sampled independently from the same distribution P u , these topologically equivalent tree structures result in the same optimization process. As such, we do not need to exhaust all of such attention structures.
Instead of enumerating each topologically different structure and then sampling multiple initializations for the low-level optimization, we randomly sample sequences (I 1 , . . . I H ) and perform low-level gradient-descent optimization on all the samples. In this way, with enough samples, we will be able to cover all attention structures. Now, we can sequentially build up the subgoals latent set representation during planning. Specifically, assuming that we have constructed the previous latent set representation U h−1 , we will now describe the procedure for constructing U h , as well as the predicted feasibility for the current skill k h , i.e. f k h (Û o,h ,Û g,h ), whereÛ o,h ,Û g,h are the subset of U h−1 and U h attended by the feasibility predictor. First, we generate I h by randomly choosing the index of a subset from U h−1 . U h are composed of two parts: The first part is the latent vectors generated by applying the skill k h . For this part, we will create a set of new vectors u h,0 , . . . u h,M h k . This part of the latent vectors will be attended by the feasibility predictor asÛ g,h = {u h,0 , . . . u h,M h k }. The second part of U h comes from the previous latent set vectors that are not modified by the skill, i.e. U h−1 \ U h−1 I h , and U h is the addition of both parts, i.e.
In this way, we can sequentially build up U h from U h−1 , and U 0 is simply U obs . At the same time, we have determined our attention structure and the feasibility prediction. Our objective can thus be written as arg min where U is the set union of all latent vectors to be optimized.

Network Architectures
Set Feasibility Predictor We use a Multi-Layer Perceptron (MLP) with ReLU activations for our feasibility predictor. We apply max-pooling to the transformed latent vectors ofÛ o andÛ g to achieve permutation invariance. Below is our architecture: Set Policy The set point cloud policy for the k th skill π k takes in an observed point cloud P obs , a goal point cloud P goal , and a tool point cloud P tool k and outputs an action at each timestep to control the tool directly. The tool point cloud P tool is obtained by sampling points on the mesh surface of the tool and then transforming these points to the same camera frame as the P obs and P goal , assuming the pose of the tool is known from the robot state. Instead of taking latent vectors as input, the policy functions directly in point cloud space, which allows it to handle times when spatial abstraction is ambiguous. For instance, during cutting and merging, the number of dough components gradually increases or decrease, during which the latent set representation is not changing smoothly while the point clouds change smoothly during the process. We later show the advantage of using point clouds directly as the policy input. We concatenate each point's (x, y, z) coordinates with a one-hot encoding to indicate whether the point belongs to the observation, tool, or goal, and we input the points into a PointNet++ [51] encoder followed by an MLP which outputs the action. We use a point cloud for the tool to allow the PointNet encoder to reason about the interaction between the tool and the dough in the same space. We use PyTorch Geometric's [52] implementation of PointNet++ and with the following list of modules in our encoder.  200  200  1500  1200  # of target configurations  200  200  1500  1200  # of training trajectories  1800  1800  1350  1080  # of testing trajectories  200  200  150  120  # of total trajectories  2000  2000  1500  1200  # of total transitions  1e5  1e5 7.5e4 6e4

Training Details
Training data. We inherit the data generation procedure from DiffSkill [8]: first, we randomly generate initial and target configurations. The variations in these configurations include the location, shape, and size of the dough and the location of the tool. We then sample a specific initial configuration and a target configuration and perform gradient-based trajectory optimization to obtain demonstration data. For each task, the demonstration data consists of all the transitions from executing the actions outputted by the trajectory optimizer. We perform a train/test split on the dataset and select 5 configurations in the test split for evaluating the performance for all the methods. More information about training and testing data can be found in Table 4.
Point cloud VAE. We train our point cloud VAE by maximizing the evidence lower bound (ELBO). For a dataset of observations P (X), which consists of the segmented point cloud of each entity in the scene, we optimize the following objective: where Q φ (z|X) is the encoder modeled as a diagonal Gaussian, P ψ (X|z) is the decoder, and p(z) is standard Gaussian. The VAE is pretrained, and we fix its weights prior to training the other modules.
Point cloud policy. We train our point cloud policy with standard behavioral cloning (BC) loss, i.e. for the k-th skill, we sample a transition from the demonstration data, which contains the observed point clouds {P o i }, goal point clouds {P g j }, a tool point cloud P tool k , and the action of the tool a. Then, we match point clouds in the observation set to those in the goal set by finding the pairs of point clouds that are within a Chamfer Distance of : {(P o i , P g j ) | D Chamf er (P o i , P g j ) < } and filter out the non-relevant point clouds. Last, we pass the filtered point clouds into the policy and minimize the following loss: Feasibility predictor. We train the feasibility predictor for the k-th skill by regressing to the groundtruth feasibility label using mean squared error (MSE) as loss, i.e.
During training, we obtain positive pairs for the feasibility predictor by sampling two point clouds (P obs , P goal ) from the same trajectory in the demonstration set. To findÛ o ,Û g , we first cluster the observation and goal point clouds into two sets {P o i }, {P g j } respectively. Then, we match point clouds in the observation set to those in the goal set by finding the pairs of point clouds that are within a Chamfer Distance of : {(P o i , P g j ) | D Chamf er (P o i , P g j ) < }. We then remove these point clouds from the corresponding set, since these are the point clouds that have already been moved to the target location in the goal. We can then encode the remaining point clouds intoÛ o ,Û g using our VAE.
Cost predictor. We train the cost predictor by simply regressing to the Chamfer Distance (CD) between two entities represented by their latent vectors, i.e.  where P i and P j are point clouds of a single entity sampled from the dataset and φ is the encoder.
There are two reasons that we train a cost predictor on latent vectors instead of directly computing the Chamfer Distance between two point clouds. For one, decoding each latent vector would greatly bottleneck the planning speed. Experiments on CutRearrange show that with our learned cost predictor, the planning takes 35s; on the other hand, if we decode the latent vectors and use the Chamfer Distance, even with a subsampled point cloud of 200 points, the planning takes 37200s (around 10 hours), which is impractical to use. Moreover, using a cost predictor can also offer us the flexibility to incorporate more complex reward functions in the future.
Finally, We train our policy, feasibility predictor, and cost predictor with the following loss: We use λ π = 1, λ f = 10, and λ c = 1 for all of our experiments.

Hyperparameters for Simulation Dough
We use PlasticineLab [47] for evaluating our simulation experiments. We provide the hyperparameters that are relevant to the properties of the dough in simulation to enhance the replicability of our results. See Table 5 for details.

Hyperparameters for DBSCAN
To cluster a point cloud, we use Scikit-learn's [53] implementation of DBSCAN [42] with eps=0.03, min_samples=6, min_points=10 for all of our environments. Further, we assign each noise point identified by DBSCAN to its closest cluster. Table 6 shows the hyperparameters used for PASTA in our simulation tasks. Planning for CRS-Twice requires a large amount of samples. Therefore, we modify the planner to improve sample efficiency. See Sec. 2.4 for details.

Receding Horizon Planning for CRS-Twice
As the planning horizon increases, the number of possible skill sequences as well as the number of possible attention structures increases exponentially. The task of CRS-Twice has a planning horizon of 6 and is a much more difficult task to solve. As such, for this task, we specify the skill sequences and use Receding Horizon Planning (RHP). Starting from the first time step, we follow the procedure in Algorithm 1 but only optimize for H RHP steps into the future and compare the achieved subgoal with the final target to compute the planning loss. After optimization, we take the first subgoal from the plan and discard the rest of the plan. We then repeat this process until we reach the overall planning horizon H. In our experiments, we use H RHP = 3. While we can perform model predictive control and execute the first step before planning for the second step, we find this open-loop planning and execution to be sufficient for the task.

Heuristic Policies
Transferring the learned policies from simulation to the real world can be more difficult than transferring the planner itself, as the policies are affected more by the sim2real gap, such as the difference in friction and properties of dough in the real world. To sidestep this challenge, for our real world experiments, we design three heuristic policies: cut, push, and roll to execute the generated plans in the real world.
Just like our learned policies in simulation, each heuristic policy takes in the current observation and the generated subgoal in point clouds and outputs a sequence of desired end effector positions used for impedance control. In addition, each policy takes in the attention mask provided by the planner indicating the components of interest. The same DBSCAN procedure is used for this. The cut policy first calculates the cutting point by computing the length ratio of the resulting components. Then it cuts the dough and separates it such that the center of mass of each resulting component matches the one in the subgoal. For the push policy, given a component and a goal component, the policy pushes the dough in the direction that connects the two components' center of mass. The roll policy first moves the roller down to make contact with the dough. Then, based on the goal component's length, the policy calculates the distance it needs to move the roller back and forth when making contact with the dough.

Procedure for Resetting the Dough
To compare different methods with the same initial and target configurations, we first use a 3D-printed mold to fit the dough to the same initial shape. We then overlay the desired initial location on the image captured by the top-down camera and place the dough at the corresponding location in the workspace to ensure different methods start from the same initial location.

Procedure for the Human Baseline
Following the same procedure in section 3.2, we first reset the dough to the initial configuration. Then, we overlay the goal point cloud on the image captured by the top-down camera. The overlay image is shown on a screen and presented to the human in real-time when the human is completing the task.

Procedure for Making the Real Dough
Material Quantity(g) Baker's percentage(%) Flour 300 100 Water 180 60 Yeast 3 1 We follow the recipe shown in Table 7 to make the real dough. Following the tradition of baking, we use the backer's percentage, so that each ingredient in a formula is expressed as a percentage of the flour weight, and the flour weight is always expressed as 100%. First, we take 300 grams of flour, 3 grams of yeast, and 180 grams of water into a basin. Then, we mix the ingredients and knead the dough for a few minutes. Next, we use a food warp to seal the dough in the basin and put them in the refrigerator to let the dough rest for 4-5 hours. Finally, we take out the dough from the refrigerator and reheat it with a microwave for 30-60 seconds to soften it.  Ablations on feasibility predictor. Following the discussions in Sec 1.2, we train a feasibility predictor without adding any noise to show that adding noise helps with the optimization landscape during planning. We call this ablation No Smoothing Feasibility. As shown in Table 8, this variant only achieves half of the success rate of PASTA, suggesting the importance of noise during training.
Ablations on policy. We consider two ablation methods for our set policy. First, we consider a Shared Encoder Policy that takes in the latent vectors from the encoder and uses a max pooling layer followed by an MLP to produce the action. The architecture is very similar to our Set Feasibility Predictor. Our results in Table 8 show that this architecture has zero success in our task. We hypothesize that this is because the entity encoding can be unstable during the skill execution. For example, during cutting, the dough slowly transitions from one piece to two pieces, making the input to the policy unstable.
Second, we compare with a Tool Concat Policy that takes in the observation and goal point cloud of the dough, passes them through a PointNet++ [51] encoder to produce a feature, and then concatenates the tool state to the feature. The concatenated feature is passed through a final MLP to output the action. In comparison, the set policy in PASTA takes the point cloud of the tool and concatenates it with the dough in the point cloud space before passing it to the PointNet. We hypothesize that this way allows PointNet to reason more easily about the spatial relationships between the tool point cloud and the dough point cloud. Results in Table 8 highlight the advantage of using a point cloud to represent the tool.
Ablation on set representation. We consider a variant of PASTA Set without Filtering, which uses the same set representation as PASTA, but does not filter entities that are approximately the same both during training and testing. This filtering is only possible with a set representation and we want to show the advantage of this filtering. For this ablation, during training, the feasibility predictor takes in all the entities in the scene in set representation, and the policy takes in the concatenation of point clouds from each entity. During planning, we do not enumerate attention structures but  instead optimize for all the entities. As shown in Table 8, without filtering, this ablation performs significantly worse than PASTA, showing that filtering is an important advantage enabled by our set representation.

Visualization of the Latent Space
We visualize the latent space of PASTA in CutRearrange in Figure 6 and visualize the latent space of Flat 3D baseline in Figure 7 for comparison. Since we use a latent dimension of 2 for all of our environments, we can visualize the original latent space without applying any dimensionality reduction techniques. PASTA only encodes the shape of each entity and thus can better model the variations in shapes. On the other hand, Flat 3D couples the shape variation with the relative position of two entities. This makes a flat representation difficult to generalize compositionally to scenes with different numbers of entities or scenes with entities that have novel relative spatial locations to each other.

Runtime of PASTA
We implement the planning in the latent set representation in an efficient way, which can plan with multiple different structures in parallel on a GPU. To demonstrate the efficiency of PASTA, we vary the number of samples used for planning and record the planning time and final performance. We conduct the experiments in CutRearrange. Figure 5a shows that the planning time scales approximately linearly with the number of samples, and Figure 5b shows the planning performance versus the number of samples. As the result suggests, PASTA can achieve its optimal performance with a very short amount of planning time (under 1 minute) for the majority of our tasks. Finally, we summarize the planning time for all of our tasks in simulation in Table 9.
LiftSpread GatherMove CutRearrange CRS CRS-Twice* Planning time (seconds) 58 35 35 307 7810 Table 9: Summary of planning time of PASTA in all of the simulation tasks. CRS-Twice uses Receding Horizon Planning, which results in an increase in planning time.

Additional metrics for real world experiments
We also quantitatively computed the action error v.s. subgoal error for our real world trajectories. The results are shown in Table 10. From the results in the table, our planned goal is closer to the ground truth goal than the achieved goal, measured by the Earth Mover's Distance (EMD), which shows that the controller does not compensate for the error of the planner.

Robustness of PASTA
We show that PASTA is robust to two types of variations and can retain high performance.
Robust to planning horizon First, we increase the planning horizon from the minimal length for the task (3) to twice the minimal length (6), and we observe that PASTA retains a high performance across all horizons. The results are shown in Table 11. This suggests that in practice, one can specify a maximum planning horizon for PASTA when the exact horizon is unknown.
Robust to distractors Second, we show that PASTA is robust to distractors in the scene. We add 2 distractor objects in CRS (which makes the scene have 4 objects in total). We observe that PASTA retains a normalized performance of 0.879 and 100% success rate (without distractor: 0.896/100%) using the same amount of samples to plan. Our planner is able to ignore the distractors using our attention structure at every step to only attend to the relevant components in the scene. We also added an example trajectory with distractor dough pieces to our website under "CRS with distractors".

Further Discussion on Limitations and Future Work
More Efficient Planning Planning skill sequences with a large search space is a challenging problem by itself but much progress has been made by the task and motion planning community to obtain a plan skeleton [54,55,56]. For example, Caelan et al. [54] propose two methods, the first one is to interleave searching the skill sequence with lower-level optimization and the second one is to have lazy placeholders for some skills. Danny et al. [56] propose to predict skill sequences from visual observation. Recent works have also explored finding skill sequences using pre-trained language models [57,58].
Sim2Real Transfer for Real Dough One possible approach is to train with domain randomization to make the policy more robust to changing dynamics (e.g. stickiness) of dough. Another option is to perform online system identification of the dough dynamics parameters [59,60] or real2sim methods [61,62]. In future work, we can also integrate our method with other works that perform low-level dough manipulation in the real world, such as recent work from Qi et al. [63].
Goal Specification Our planner requires specifying the goal with a point cloud and coming up with a point cloud goal is not always easy. However, rapid progress are being made with languageconditioned manipulation and future work can combine language to specify more diverse tasks.  Figure 6: Latent space of PASTA in CutRearrange. We sample coordinates on a grid from the 2D latent space encoding the shapes and then decoding each latent vector into a point cloud. We then rearrange the decoded point cloud into the grid based on the corresponding coordinates in the latent space.  Figure 7: Latent space of Flat 3D in CutRearrange. We sample coordinates on a grid from the 2D latent space encoding the shapes and then decoding each latent vector into a point cloud. We then rearrange the decoded point cloud into the grid based on the corresponding coordinates in the latent space.


Improving urban bicycle infrastructure-an exploratory study based on the effects from the COVID-19 Lockdown

Introduction During the COVID-19 lockdown significant improvements in urban air quality were detected due to the absence of motorized vehicles. It is crucial to perpetuate such improvements to maintain and improve public health simultaneously. Therefore, this exploratory study approached bicycle infrastructure in the case of Munich (Germany) to find out which specific bicycle lanes meet the demands of its users, how such infrastructure looks like, and which characteristics are potentially important. Methods To identify patterns of bicycle infrastructure in Munich exploratory data is collected over the timespan of three consecutive weeks in August by a bicycle rider at different times of the day. We measure position, time, velocity, pulse, level of sound, temperature and humidity. In the next step, we qualitatively identified different segments and applied a cluster analysis to quantitatively describe those segments regarding the measured factors. The data allows us to identify which bicycle lanes have a particular set of measurements, indicating a favorable construction for bike riders. Results In the exploratory dataset, five relevant segment clusters are identified: viscous, slow, inconsistent, accelerating, and best-performance. The segments that are identified as best-performance enable bicycle riders to travel efficiently and safely at amenable distances in urban areas. They are characterized by their width, little to no interaction with motorized traffic as well as pedestrians, and effective traffic light control. Discussion We propose two levels of discussion: (1) revolves around what kind of bicycles lanes from the case study can help to increase bicycle usage in urban areas, while simultaneously improving public health and mitigating climate change challenges and (2) discussing the possibilities, limitations and necessary improvements of this kind of exploratory methodology.

Introduction
The COVID-19 pandemic has fundamentally changed how movement and interaction take place in urban areas. As social distancing is the new norm in public spaces all over the world ( De Vos, 2020 ) people change their transport behavior with immediate effect. Despite the rise of new formats of interaction and remote working, transport is and will remain a fundamental aspect of daily life ( Brooks et al., 2020 ;Laverty et al., 2020 ). Nonetheless, new challenges are imposed on the way people move around cities, encouraging new and innovative solutions for major challenges such as urban health and climate change adaptation.
Many studies have shown that a strong immune system is an indicator for a mild course of infection ( Taghizadeh-Hesary & Akbari, 2020 ). At the same time, Gupta et al. (2020) observe a positive correlation between air pollution and the lethality of a COVID-19 infection. Against City, but also other major cities have witnessed similar developments. De Vos (2020) frames cycling as a way to maintain public health while Hammami et al. (2020) highlight the importance of sufficient physical activity, especially during lockdown situations. An increase in bicycle traffic is, therefore, a possibility to face two challenges at the same time -mild courses of infection for COVID-19 patients and adaptation for climate change in urban areas -as this mode of transport does not only reduce emissions, improve air quality, and has environmental as well as public health benefits ( Cole-Hunter et al., 2015 ), but cycling is also a vital part in building up a strong immune system to fight infectious diseases ( Aman & Masood, 2020 ).
The situation caused by the pandemic needs to be framed as a public health opportunity ( Brooks et al., 2020 ). It requires long-overdue infrastructural change, as infrastructure is a leading factor that influences individual decisions for cycling as a preferred mode of transport ( Boss et al., 2018 ). As bicycles constitute an important part of a community's transportation system, the increasing pressure of individual transport ( Dewulf et al., 2015 ) is an obstacle for cyclists, due to increased interaction with motorized traffic and associated safety concerns ( Bagloee et al., 2016 ). Bao et al. (2017) argue that bicycle traffic has the potential to reduce the challenges imposed by too much motorized individual traffic. King and Krizek (2020) argue that changes in street design can rapidly increase access by individual modes of transport ( Barros et al., 2020 ), but as financial means for such changes are usually limited they need a thorough evaluation to have the expected effect ( Boss et al., 2018 ).
The global lockdown provided a test scenario with little individual motorized traffic in urban areas. Therefore, the aim of this exploratory study is the following: How are bike lanes perceived from a bicycle rider's perspective and what do they need to look like so that increasing individual traffic (triggered by the COVID-19 pandemic) will shift towards cycling? As cycling infrastructure should be based on the users' needs and not spatial constraints, such as existing road networks or limitations by buildings ( Guerreiro et al., 2018 ) a rider-related approach is chosen. This may help to identify potential bike lanes that meet those demands and do not hinder the usage of bicycles as a sustainable mode of transport in urban areas. The exploratory case study was conducted in the city of Munich (Germany). Future COVID-19 policies will have a strong effect on the development of public spaces ( Honey-Rosés et al., 2020 ) and the global lockdowns are an opportunity to change the previous state of traffic infrastructure ( Laverty et al., 2020 ). This paper is structured as follows: First, the lockdown is framed against (a) the background of 'Geographies of Health' with a special focus on air pollution development as well as the accompanying barriers to cycling at the same time and (b) the connection of bicycle infrastructure and bicycle usage. We document the exploratory methods used to identify types of bicycle lanes that enable cyclists to perform best and enjoy the ride at the same time and explain how their clustering was carried out. The case study investigates an exploratory dataset, that shows the analysis for a selected route in Munich. Based on this case study we discuss (1) aspects that revolve around what kind of bicycles lanes can help to increase bicycle usage in urban areas, while simultaneously improving public health and mitigating climate change challenges and (2) the possibilities, limitations, and necessary improvements of this kind of exploratory methodology.

Theoretical background & previous research
For this study, concepts originating from 'Geographies of Health' provide valuable insights into the analysis and choice of factors to identify how bike lanes need to be designed to enable the shift from motorized individual traffic towards human-scale individual carbon-neutral bicycle traffic. Health is not only about the absence of sickness in a person, but also the social and cultural construct of health, wellness, identity within the environment, and spatial experience ( Giesbrecht et al., 2014 ). As societies will probably continue to face public health issues after the COVID-19 pandemic, knowledge about how cities can address those challenges needs to be deepened. Cities that encourage active transport can address such challenges more efficiently and profoundly ( Giles-Corti et al., 2016 ).
Public transport systems are potential sources of infection, as social distancing cannot be upheld at all times. Long-lasting effects such as mistrust against public transport, as pointed out by Conway et al. (2020) can therefore be directly incorporated into the future planning of urban transport systems and be enriched by knowledge about other communicable or non-communicable diseases, e.g. cardiovascular diseases (CVD) ( Giles-Corti et al., 2016 ). Many studies have shown a strong correlation between bicycle usage and health indices (e.g. Bagloee et al., 2016 ). Furie and Desai (2012) state that insufficient physical activity may result in CVD as well as obesity, diabetes, and blood-pressure-related health problems. Therefore, cycling is among the modes of transport that add to the daily amount of recommended physical activity ( Panik et al., 2019 ). Celis-Morales et al. (2017) describe in their case study that 90% of active commuters meet the minimum of recommended daily physical activity which is a factor for a lower risk of CVD mortality. Additionally, even on a psychological level bicycle transport has positive effects: According to Avila-Palencia et al. (2017) ) people who cycle to work experience positive effects for their self-esteem coupled with a positive environmental impact and significantly feel less stress. Those positive effects are among the motivations of people to use bicycles instead of other modes of transport -consciousness, pro-health, and the cyclist lifestyle ( Biernat et al., 2018 ).
To incorporate those positive public health effects into individual daily schedules, Cole-Hunter et al. (2015) highlight the importance of urban environments to facilitate such changes. A proof of the positive development of less motorized traffic in cities was not the rise of bicycle traffic but the global lockdown situation that forced many people to work at home instead of daily commuting to work. Liu et al. (2020) have shown that during the lockdown and the following reduction in human activities there was a decrease of 8,8% in global CO 2 emissions (less individual motorized transport cannot account for this as a whole, but passenger transport accounts for 45,1% of all CO 2 emissions caused by transport ( Ritchie, 2020 )). In the 1940s up to 85% of trips in European cities were taken by bike, however, the development of cheap oil favored motorized individual transport ( Larsen, 2017 ), although the distances are amenable to cycling: Rissel et al. (2013) state that for the case of Sydney 25% of distances traveled by car are below 2 kms and even half are less than 5 kms.
Many cities have experienced significant improvements in air quality during the lockdown. In Wuhan (China) the lockdown had a substantial effect on the ozone and nitrogen oxide (NO x ) concentration. As NO x decreased by 53,3% the concentration of ozone increased by 116,6% ( Lian et al., 2020 ). Kerimray et al. (2020) measured similar values for Almaty (Kazakhstan, − 35% NO x concentration). Forster et al. (2020) estimate that the global NO x concentration decreased by approximately 30%. For the city of Munich, where the empirical study took place, similar observations were made, regarding the NO x concentration in the city. Fig. 1 shows the differences in the NO x concentration in Munich for three different periods (2019, 2020 1st quarter, 2020 2nd quarter). The strongest difference is noticeable between the first and second quarters of 2020 when the lockdown was imposed, and traffic was significantly reduced. This figure backs up the findings of Laverty et al. (2020) investigating NO x measures in urban areas and shows that transportation has direct and indirect impacts on public health. This is not only based on the decrease of NO x but also less carbon dioxide and noise, resulting in higher air quality and a better urban atmosphere ( Zambrano-Monserrate et al., 2020 ). Nonetheless, such developments might not be permanent: Chang et al. (2020) have shown for the case of Taiwan that post-lockdown the NO x concentration rose between 5 and 12%, due to the shift from public transport to individual motorized transport -as a way to enable safe transport in pandemic times.  (2020) . Conway et al. (2020) state, based on a US survey, that some behavioral changes initiated by the lockdown will persist, especially when it comes to cycling and walking more often. Although this study was carried out with highly educated US citizens only, the authors conclude that it is unlikely to fully return to pre-pandemic transportation habits. Especially health is a reason to frequently travel by bicycle but it is still outweighed by factors revolving around physical effort and the lack of a safe cycling network ( Félix et al., 2019 ).
Although cycling already is the default choice of transport for many cyclists in urban areas ( Kuhnimhof et al., 2010 ) there seems to be a connection between the individual choice to cycle and the built environment. Piras et al. (2021) provide an empirical example stating that there is a positive correlation between perceived cycling benefits, perceived comfort, and perceived importance of bicycle infrastructure and the propensity to cycle. In addition, they identified a connection between socio-demographic factors (e.g. age, gender), structures in urban areas, and bicycle usage and therefore conclude to focus on the built environment and behavioral and perceptional factors equally ( Piras et al., 2021 ). Lanzendorf and Busch-Geertsema (2014) conclude that cycling is intertwined with infrastructural improvements. Buehler and Pucher (2021) reviewed the difference between urban traffic in the US as well as European countries but reach the same verdict: They explain differences in cycling and walking fatalities in Europe by better infrastructure and lower urban speeding limits.
Of course, infrastructural change has been intensely analyzed by scholars. Blitz et al. (2020) demonstrate by drawing from a case study in the German Rhine-Main Metropolitan Region that infrastructural improvements of bicycle streets have positive impacts, especially for frequent bicycle users. Nonetheless, they emphasize including individual urban travel behavior in future studies. Ghekiere et al. (2014) focused on cycling safety for children and conducted qualitative interviews about cycling infrastructure. They identified wide and even cycle tracks, a good overview of traffic, and traffic density as key factors for perceived safety. Although they reached those results by interviewing children, their findings seem to apply to a broader range of cyclists. For the German city of Münster, Schröder (2021) suggests that significant improvements of the built environment result in more safety, comfort, and shorter travel times. She demonstrates this by drawing from empirical evidence from improved bicycle streets. Further studies focused on barriers to using bicycles in urban infrastructure (e.g. traffic and too few bike lanes) (e.g. Dill & McNeil, 2016 ).
Although infrastructural improvement seems to be omnipresent in most studies, Assunçao-Denis and Tomalty (2019) name factors that cannot be influenced by infrastructural planning, such as cultural, demographic, or economic settings. Despite the importance, they emphasize the effect of local measures by expanding bicycle infrastructure. In a statistical study, Haustein et al. (2020) describe the model of perceived ease derived from cycling safety and security, autonomy, and priority in planning. This model explains 65% of the variance of the individual cycling perception ( Haustein et al., 2020 ). Other authors analyze behavior and perception from different angles: Aletta et al. (2018) describe how the sound level is a factor to the cycling comfort but highly dependent on personal perception. van Cauwenberg et al. (2012) assign the personal perception of safety to gender differences and Pooley et al. (2011) draw attention to the individual perception of safety. In this context, Schwedes, Wachholz, & Friel (2021) support this thesis and state that safety cannot be understood as a number but needs to be analyzed from a qualitative point of view.
Abdai and Hurwitz (2018) analyzed the perceived level of comfort during a bicycle ride when overtaking truck loading zones as a factor to increase or decrease the share of cyclists. They analyzed ambient traffic (volume and truck traffic) as well as pavement markings and traffic signs as factors that influence the comfort during a ride, thus affecting future decisions to choose the bicycle as an adequate mode of transport. Other studies, such as Cho et al. (2009) argue similarly.
While Pooley et al. (2011) show that cyclists are especially concerned about risks that stem from interaction with motorized traffic), Dill and McNeil (2016) characterize four types of cyclists as not all cy- clists have the same perception of safety, risk, or comfort. Nonetheless, not only the perception of cyclists is important but also of motorized vehicle users. Huemer and Strauß (2021) present an empirical experiment showing that car drivers feel more confident to overtake cyclists when those travel in lanes segregated by a marking. As the presented studies have shown the analysis of behavioral and perceptional rider-related data (e.g. level of sound or level of comfort) in connection with bicycle infrastructure (e.g. type of bicycle lane) is necessary to expand bicycle infrastructure as a medium to combat health and environment-related crises. In the following section, we, therefore, present our exploratory approach for this case study.

Methods & case study
The case study is carried out in Munich, Germany's third-biggest city and home to one of the country's biggest car manufacturers. Cycling is a popular trend in the city, leading to an increase of cyclists in the modal split: While only 10% of inner-city travelers used bicycles in 2002, the share increased to 18% in 2017 ( BMDV 2019 ). As Table 1 shows, the share of cyclists of all traffic participants in Munich is higher than the German average, while there is also comparatively less motorized individual traffic.
Drawing from literature and studies about behavioral, perceptional, and individual perspectives while cycling in urban areas, we use bicyclerider-related data as a way to obtain data on how riders experience a route by bicycle and as a possibility to focus on multiple factors that influence a ride at the same time. This honors the critique formulated by Ryu et al. (2015) . We include different aspects that depend on the rider, such as velocity or pulse as well as environmental data (temperature, humidity, and level of sound (as an indicator of nearby-motorized traffic and the traffic situation)). This data is held against the background of the status of the bicycle lanes, and segments are identified depending on their design (type of bike lane, interaction with traffic, structural condition) and qualitative evaluation of the rider's comfort after each ride (perceived safety, perceived quality of bike lanes, perceived comfort of infrastructure, perceived flow of the ride, perceived interferences with other traffic participants). To enable a comparison between different segments the data is spatially obtained: Most of the data is obtained using free apps on an Android smartphone fixed to the handlebar of the bicycle. The route is agreed upon beforehand and one bicycle rider carries out test routes. Table 2 gives an overview of the measurement devices and which apps are used to measure.
The bicycle trips are carried out on weekdays between 8 and 9 am during the morning commute and between 4 and 6 pm during the evening commute. All trips follow the agreed-upon route and all traffic rules are strictly obeyed. The chosen route consists of a cross-section of Munich from the West to the South-East and represents a commutable distance that is amenable to average bicycle users (6-10 km). Additionally, the route contains different kinds of bicycle lanes: segregated and shared lanes as well as no bicycle lanes; lanes that range from interaction with motorized traffic (in motion or parked) or pedestrians to no interactions; and bicycle lanes that have a high quality down to lanes that are consistently inter-or disrupted by sidewalks or other structural features. As the route is mostly flat (except for one short uphill segment, 300 m distance, elevation gain 14 m) the influence of altitude can be neglected.
To receive information on the identified segments a cluster analysis is carried out. Data was collected for defined time intervals (10 s) which concluded in 5.424 data points along the route, including all information mentioned in Table 2 . A hierarchical cluster analysis is carried out as beforehand no structures were existent in the dataset ( Janssen & Laatz, 2017 ). We select the squared Euclidean distance as a proximity measure and the Ward method as a merging algorithm to keep the variance within a group to a minimum ( Backhaus et al., 2016 ;Bortz & Schuster, 2010 ). It is possible to simplify the multiple and complex relations between the single data points to detect spatial relations. To calculate the different clusters, we utilize personal (velocity, pulse) and environmental factors (level of sound). The environmental factors humidity and temperature are excluded from the analysis as they do not add to the differentiation of the clusters. As the case study is carried out in August, temperature and humidity do not significantly differ during the single rides. The decision for the exact number of clusters is made, using the elbow criteria as well as the dendrogram. The attribution of a feature to a cluster is made using standardized residuals. Additionally, we run a discriminant analysis to categorize waypoints that are lacking information due to measurement errors ( Backhaus et al., 2016 ). In the last step, the spatial data is enriched by the information gained from the cluster analysis, and implications for bike lanes are derived.

Results
The cluster analysis sheds light on which type of bicycle lanes enables cyclists to perform best, move the most efficiently and safely between two destinations, and enjoy the ride at the same time. Those are the most important factors to decide for or against the usage of bicycles as a mode of transport ( Bagloee et al., 2016 ;Félix et al., 2019 ). The following section presents the five identified clusters: viscous, slow, inconsistent, accelerating, and best-performance . Table 3 shows the five different clusters along the personal and environmental factors used for the cluster analysis. The number in brackets indicates the standardized residuals. When the standardized residual is > 2,0 it is interpretable and the higher it is, the stronger the attribute is linked to the corresponding cluster ( Backhaus et al., 2016 ). Fig. 2 represents the spatial distribution of the clustered segments, including the position of traffic lights along the routes. Three of the identified clusters represent data points that are characterized by nonoptimal comfort of bicycle usage: viscous, slow, and inconsistent . The cluster viscous is characterized by a (very) slow velocity ( < 10 km/h to 10-15 km/h) and a (very) high pulse at the same time (115-130 to > 130 bpm). The level of sound is ranging from quiet (75-80 dB) to normal (80-85 dB). The assigned bicycle lanes are usually intensely used by motorized traffic, such as cars or buses, and there is always plenty of interaction between all traffic participants. As the level of sound is quite low, motorized traffic is most of the time not in full motion but congested. Usually, bicycle riders can overtake but always have to be alerted to not cause any damage to cars (in motion or stopping) as well as not have any damage caused to themselves. Viscous segments usually have little to no coverage of bicycle lanes.
Another segment that is distinguished by a high level of interaction with other traffic participants is the slow segment. Bicycle riders cannot accelerate to a comfortable fast velocity as the segment is often disrupted by motorized vehicles or construction sites (although this is mostly a temporal phenomenon). Although the traffic lights are usually controlled to be in a series there are long waiting times to be expected as soon as a series is missed, resulting in a slow overall velocity. Based on all the forced stops the pulse is within a normal range (100-115 bpm).   The last cluster that is assignable to the non-optimal bicycle ride performance segments is inconsistent : The velocity ranges from slow ( < 10 km/h) up to very fast ( > 25 km/h) -this suggests a very uneven and non-consistent riding dynamic. Despite the fast velocity, the pulse is usually in a (very) low range. It is significant that the level of sound is very loud ( > 90 dB), which indicates that surrounding traffic is omnipresent, either accelerating or in full motion. Such segments tend to feature strong interactions with other traffic participants, e.g. motorized vehicles or pedestrians. The quality of bicycle lanes varies strongly from segregated lanes to narrow lanes that are embedded between shops and parked vehicles. The intensity of interaction varies accordingly by the time of the day.
The first cluster that is assigned to a more optimal riding and performance experience is accelerating . Segments that are marked accelerating can be traveled fast or very fast, resulting in a high pulse ( > 130 bpm). The level of sound is very loud which indicates traffic in motion in the vicinity of the segment. The traffic light is usually controlled to be synchronized but another factor responsible for disruptions and braking maneuvers are pedestrians and motorized vehicles. The main difference between accelerating and inconsistent is therefore the possibility of higher velocity on accelerating segments.
The optimal bicycle riding performance is possible on segments labeled as best-performance . The velocity ranges from normal (15-20 km/h) and fast (20-25 km/h) to very fast ( > 25 km/h). Accordingly, pulse ranges between 100 and 115 bpm (normal) up to 115-130 bpm (high). Best-performance segments offer the highest quality of bicycle lanes: wide, evenly paved lanes with little to no interaction with accompanying traffic. Along such lanes, some segments are even segregated through the construction of barriers, giving bicycle riders protection, and hindering interaction that would result in dangerous breaking maneuvers or physical injury. Besides, traffic lights are often in favor of bicycle riders, giving them the smoothest and most efficient bicycle riding experience of all identified cluster segments. Taking the research question into the account, what kind of bicycle lanes are needed to prevent the shift of individualization in urban transport towards motorized vehicles, lanes that fit the best-performance description are most likely to make people decide in favor of bicycles instead of cars. Those are the factors that result in positive associations with bicycle paths, as described Fig. 3. Overview of bicycle paths on the test route related to pictures at selected sites -the numbers in the pictures correspond to the segments in the map above.
by Fraser and Lock (2011) . Such segments are mostly found outside of densely used city centers towards residential areas where space is less contested ( Fig. 2 ). Fig. 3 compares the quality and the differences between the different bicycle lanes that occur along the route. The numbers in the pictures correspond to the segments on the map. Picture 21 is an example of the best-performance segment. There is no interaction with the traffic on the left side of the bicycle lane and no parking, shops, or any other source of possible interaction with pedestrians on the right side of the bicycle lane. Additionally, the bicycle lane is constructed differently than the pedestrian lane, adding up to the clear border, enhancing the safe usage for both cyclists on the left side and pedestrians on the right side. Accelerating segments are best represented by picture 8. The bicycle lane is quite narrow and motorized vehicles are often crossing into the bicycle lane as there is only an overlookable marking between the car and bicycle lane on this shared street. The non-optimal performance segment inconsistent is shown in picture 14. Parking is possible on the left side of the bicycle lane and shops are found on the right side. Additionally, there is the possibility to park and lock bicycles on the right side which is another possibility that bicycle riders will need to abruptly stop their bicycle. Slow segments are presented in picture 13, despite the difference that such segments are characterized by very dense traffic (mostly made up by motorized vehicles). Picture 17 represents an example of the viscous segment. The bicycle lane is quite narrow and there is a constant interference of the bicycle ride by opening car doors and people walking on the bicycle lane as the pedestrian lane is narrow. Additionally, people crossing the road are not easily spotted between cars, so bicycle riders on this viscous segment need to ride more carefully than on open bicycle lanes to avoid physical injury.
As the empirical survey was carried out in August the environmental weather conditions did not vary fundamentally. There was a slight difference in the daytime of the commute as the temperature was usually lower in the morning than in the evening, but no significant correlation was detected. For this study, it can be concluded that the influence of the environmental factors weather and humidity can be neglected for the summer months. This supports several studies' findings' ( Bagloee et al., 2016 ;Félix et al., 2019 ): The main reasons to decide for or against bicycles as a suitable mode of transport is determined by the quality of bicycle lanes and the resulting implications for safety and comfort.

Discussion
We engage in two discussions: (1) What kind of bicycle lanes can help to increase bicycle usage in urban areas as means to improve public health in times of crisis and mitigating to climate change challenges? (2) What are the possibilities, limitations, and necessary improvements of this kind of exploratory methodology?

Improved bicycle lanes as means to combat environmental challenges in urban areas
As the COVID-19 pandemic has shown, the prevention of crises is a cheaper solution than a cure. This applies to the climate crisis as well ( Manzanedo & Manning, 2020 ). At the moment there are two scenarios for transportation in urban areas possible: business as usual or significant change to decrease the number of motorized vehicles in cities by either increasing the attractiveness of working from home ( Hensher, 2020 ) or increasing the attractiveness of bicycles as a preferred mode of transport.
This exploratory study shows that only a share of all segments in an urban area meet the demands that cyclists have for best-performance segments. This supports the findings of Bagloee et al. (2016) as well as Parkin and Koorey (2012) : The authors suggest that bicycle infrastructure cannot be simply added to an existing road network that is primarily used by motorized traffic but has to be promoted by separate networks. Although Cole-Hunter et al. (2015) suggest that bicycle lanes that are embedded in urban green areas are increasingly frequented, our findings cannot reproduce this correlation. This needs further differentiation as Aletta et al. (2018) focused on the relationship between the comfort of a bicycle ride and green areas contrasted by the perception of sound. In our case especially the separation as mentioned by Bagloee et al. (2016) and Schröder (2021) has a positive effect on the rider's perception of comfort and performance on the segment (see the comparison in Fig. 3 ). This also supports the findings by Ghekiere et al. (2014) although they focused on children's comfort while cycling.
The best-performance segment is characterized by an efficient mode of traveling by bicycle. This finding is in accordance with Dewulf et al. (2015) arguing that lost time is a major factor for dissatisfaction in commuters as well as Wild and Woodward (2019) stating that bicycle traffic can diminish transport-related uncertainties, such as congestions.
While the implementation of bicycle infrastructure that fits the characterization of best-performance segments seems necessary, there are barriers: Although the positive effects for urban health and climate change mitigation are obvious, urban developments have to be taken into account: Larsen (2017) argues that urban sprawl poses a threat to bicycle commuting as distances will not be amenable to most bicycle riders anymore, thus resulting in higher use of motorized vehicles and additional implications for the environment that cannot be subsidized by constructional improvements buy only by a strong link between public transport and bicycle usage. While this study only covered amenable distances between 5 and 10 km, further evidence from longer distances is necessary to generate reliable insights. This is especially necessary, as the course of COVID-19 infections remains unpredictable and the increase in individual motorized traffic continues to pressure urban transportation systems.
To promote cycling as one of the few carbon-neutral forms of urban transport ( Fraser & Lock, 2011 ) while simultaneously increasing physical activity for public urban health ( Perez et al., 2015 ;Zambrano-Monserrate et al., 2020 ), the cluster analysis shows, that infrastructure enabling such positive changes is already partly available in urban areas but needs further spread. It is essential to improve bicycle infrastructure in the sense of best-performance segments as they contain the highest perceived feeling of safety, which is necessary for the choice of transportation ( Ghekiere et al., 2014 ;Marshall & Ferenchak, 2019 ).

Possibilities, limitations, and necessary adaptations of this exploratory methodology
We present a new approach for analyzing bicycle lanes in an urban area. Especially, the usage of bicycle-rider-centric data bears the poten-tial of new insights for future analysis of bicycle networks. In addition, the qualitative identification of segments with similar perceptions of safety, comfort, interaction, and quality of bike lanes offers insights that are detached from purely quantitative approaches and therefore focus on the personal perception of bicycle riders.
To further consolidate the findings of this exploratory study a few improvements are necessary: As only one bicycle rider carried out the measurement rides and gave qualitative insights that led to the identification of segments, the perspectives of additional riders are necessary. Therefore, it is important to create a sample that covers a large share of the population, e.g. from younger to older people, all genders, as well as regular and irregular bicycle riders. Especially the latter is important to include the different types of cyclists as shown by Dill and McNeil (2016) . By enhancing the sample of riders, personal effects can be bypassed, resulting in a more neutral and nuanced analysis.
Another point for improvement is the length of the study. Although this study was carried out in August, probably the busiest month for cyclists in German cities due to favorable weather conditions, cycling infrastructure will need to be sufficient all year long during all kinds of weather conditions (especially during colder seasons or rainy conditions). New analyses can focus on the effect of weather conditions on different kinds of bicycle lanes. For this sample, the weather conditions did not differ sufficiently.
While this study contains the most direct factors that influence a bicycle ride, an addition of qualitative urban data might generate interesting insights: For example, the proximity to urban green spaces ( Aletta et al., 2018 ;Cole-Hunter et al., 2015 ), congestions (e.g. data from GoogleMaps), airflow within the city or shadow and direct sunlight situations can add to complex but more in-depth findings to the comfort and performance of bicycle riders.
As a novelty, this study used qualitative data to identify segments based on the perception of the bicycle rider. Although this is a new approach, it should be used directly within the cluster analysis, so that such effects can be directly compared to the average velocity and infrastructural occurrence on site. Finally, a comparison of different cities will be interesting. In Germany, Berlin can be an insightful example, as during the COVID-19 lockdown a lot of new pop-up bicycle lanes have been instated ( Kraus & Koch, 2020, 2021.

Conclusion
This exploratory study raises several questions: How are bike lanes perceived from a bicycle rider's perspective? How do they need to look like, that the rise in individual traffic (triggered by the COVID-19 pandemic) will shift towards cycling? By using a bicycle-rider-centric approach, we can identify bicycle lane segments that fulfill riders' wishes for safety and efficient travel between two destinations in urban areas as well as a distinction between desirable and non-desirable bicycle infrastructure. The clusters viscous, slow, inconsistent, accelerating, and best-performance are identified and spatially applied to the empirical example of Munich. Following the study's result, we agree with Parkin and Koorey (2012) that cycling has to be treated as a distinct mode of transport instead of a side-product that can be added to existing road networks. Following Harms et al. (2014) we confirm that there is a need for a differentiated approach to analyze cycling infrastructure adequately. We conclude that the improvement of bicycle infrastructure bears the potential to tackle environmental or health-related challenges in urban areas, such as climate change or the spread of infectious diseases like COVID-19.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
The datasets generated during the study are available at GitHub via the following link: https://github.com/schwal95/floatingbikedata

Funding
We acknowledge support by the Open Access Publication Fund of the Freie Universität Berlin.