Probabilistic Movement Primitives
Movement Primitives (MP) are a well-established approach for representing modular and re-usable robot movement generators. Many state-of-the-art robot learning successes are based MPs, due to their compact representation of the inherently continuous and high dimensional robot movements. A major goal in robot learning is to combine multiple MPs as building blocks in a modular control architecture to solve complex tasks. To this effect, a MP representation has to allow for blending between motions, adapting to altered task variables, and co-activating multiple MPs in parallel. We present a probabilistic formulation of the MP concept that maintains a distribution over trajectories. Our probabilistic approach allows for the derivation of new operations which are essential for implementing all aforementioned properties in one framework. In order to use such a trajectory distribution for robot movement control, we analytically derive a stochastic feedback controller which reproduces the given trajectory distribution. We evaluate and compare our approach to existing methods on several simulated as well as real robot scenarios.
The paper intends to unify several previously-achieved 
      characteristics of movement primitives (MP) in a single probabilistic 
      framework, while also describing new ways in which this framework allows 
      MPs to be modified or combined. This is accomplished through the 
      representation of trajectories by probability distributions of joint 
      location and velocity. The authors present the foundation for their 
      formulation by describing how standard MP features such as rhythmic and 
      stroke-based movements and temporal modulation are achieved in this new 
      framework. They also discuss how, due to the probabilistic nature of this 
      framework, they can modify position and velocity of a given trajectory 
      through conditioning as well as blend multiple MPs together by multiplying 
      distributions. The authors derive the necessary values for a robotic 
      controller and conclude the paper with experiments on both a real and 
      simulated robotic arm. The main contribution of this paper is 
      quite obviously the probabilistic characterization of movement primitives. 
      Through the authors' own citations we can see that prior works have 
      already noted the major contributions towards the flexibility and use of 
      MPs in robotic systems. However, as they state, this framework combines 
      several achievements in a single system and provides a new perspective of 
      how to view the theory behind MPs. A problem with their approach is that 
      the increased robustness comes at a cost: The system can no longer be 
      trained with a single demonstration. In their "robot hockey" experiment, 
      the authors state they use a total of 20 demonstrations to train their 
      robot. With such a significant number of demonstrations required, we start 
      to lose some of the benefits of MPs where instead other comparable 
      approaches might be used. Also, in the simulated experiment, the authors 
      state "[t]he ProMP could achieve an average cost value of a similar 
      quality as the optimal controller" yet the variance betwen via-points 
      seems fairly high. I would like to see more discussion as to how 
      optimality is maintained as well as how many samples must be taken from 
      the distribution in order to achieve decent results. A comparison to 
      related Gaussian process models should also be included.