Trajectory optimization for domains with contacts using inverse dynamics

This paper presents an algorithm for direct trajectory optimization in domains with contact. Since contacts and other unilateral constraints may introduce non-smooth dynamics, many standard algorithms of optimal control and reinforcement learning cannot be directly applied to such domains. We use a smooth contact model that can compute inverse dynamics through the contact, thereby avoiding hybrid representation of the non-smooth contact state. This allows us to formulate an unconstrained, continuous trajectory optimization problem, which can be solved using standard optimization tools. We demonstrate our approach by optimizing a running gait for a 31-dimensional simulated humanoid. The resulting gait is demonstrated in a movie attached as supplementary material. The optimization result exhibits a synchronous motion of the arm and the opposite leg, eliminating undesired angular momentum; this is a key feature of bipedal running, and its emergence attests to the power of the optimization process.

Authors

• Tom Erez
• Emanuel Todorov

Keywords

• Trajectory
• Optimization
• Dynamics
• Computational modeling
• Heuristic algorithms
• Optimal control
• Legged locomotion
• Trajectory Optimization
• Inverse Dynamics
• Optimization Problem
• Angular Momentum
• Humanoid
• Contact Conditions
• Contact Model
• Smooth Model
• Continuous Trajectory
• Time Step
• Optimization Method
• Control Signal
• Search Space
• Current Control
• Reaction Force
• Hybrid Model
• Convex Optimization
• Contact Force
• Ground Reaction Force
• Inverse Form
• Minimal Representation
• Limit Cycle
• Presence Of Contact
• Contact Distance
• Flight Phase
• Compressed Representation
• Quadratic Cost
• Interpretation Of Dynamics
• Mass Matrix