  Autonomous vehicles must often contend with conflicting planning
requirements, e.g., safety and comfort could be at odds with each other if
avoiding a collision calls for slamming the brakes. To resolve such conflicts,
assigning importance ranking to rules (i.e., imposing a rule hierarchy) has
been proposed, which, in turn, induces rankings on trajectories based on the
importance of the rules they satisfy. On one hand, imposing rule hierarchies
can enhance interpretability, but introduce combinatorial complexity to
planning; while on the other hand, differentiable reward structures can be
leveraged by modern gradient-based optimization tools, but are less
interpretable and unintuitive to tune. In this paper, we present an approach to
equivalently express rule hierarchies as differentiable reward structures
amenable to modern gradient-based optimizers, thereby, achieving the best of
both worlds. We achieve this by formulating rank-preserving reward functions
that are monotonic in the rank of the trajectories induced by the rule
hierarchy; i.e., higher ranked trajectories receive higher reward. Equipped
with a rule hierarchy and its corresponding rank-preserving reward function, we
develop a two-stage planner that can efficiently resolve conflicting planning
requirements. We demonstrate that our approach can generate motion plans in
~7-10 Hz for various challenging road navigation and intersection negotiation
scenarios.

Robotics;Systems and Control;Systems and Control