Hybrid control trajectory optimization under uncertainty
This work addresses the challenge of optimizing hybrid controls in robotics, which is incremental as it builds on existing DDP methods to handle discrete actions and uncertainty.
The paper tackles the problem of hybrid control trajectory optimization under uncertainty by extending Differential Dynamic Programming to incorporate discrete actions and handle partially observable Markov decision processes, achieving successful validation in car driving and box pushing scenarios.
Trajectory optimization is a fundamental problem in robotics. While optimization of continuous control trajectories is well developed, many applications require both discrete and continuous, i.e., hybrid, controls. Finding an optimal sequence of hybrid controls is challenging due to the exponential explosion of discrete control combinations. Our method, based on Differential Dynamic Programming (DDP), circumvents this problem by incorporating discrete actions inside DDP: we first optimize continuous mixtures of discrete actions, and, subsequently force the mixtures into fully discrete actions. Moreover, we show how our approach can be extended to partially observable Markov decision processes (POMDPs) for trajectory planning under uncertainty. We validate the approach in a car driving problem where the robot has to switch discrete gears and in a box pushing application where the robot can switch the side of the box to push. The pose and the friction parameters of the pushed box are initially unknown and only indirectly observable.