Hybrid control trajectory optimization under uncertainty

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.

Authors

• Joni Pajarinen
• Ville Kyrki
• Michael C. Koval
• Siddhartha S. Srinivasa
• Jan Peters 0001
• Gerhard Neumann

Keywords

• Trajectory optimization
• Uncertainty
• Planning
• Robot sensing systems
• Hybrid Control
• Trajectory Control
• Friction
• Dynamic Programming
• Control Sequence
• Differentiation Program
• Discrete Action
• Trajectory Planning
• Car Drivers
• Discrete Control
• Time Step
• Cost Function
• Second Derivative
• Nonlinear Dynamics
• Continuous Action
• Inequality Constraints
• Equality Constraints
• Quadratic Programming
• Linear Parameters
• Hard Limit
• Rapidly-exploring Random Tree
• Greedy Approach
• Linear Feedback Control
• Mixed-integer Nonlinear Programming
• Nominal Trajectory
• Observational Uncertainty
• Linear Quadratic Regulator
• Forward Pass
• Extended Kalman Filter