Contact-Implicit Trajectory Optimization With Learned Deformable Contacts Using Bilevel Optimization

We present a bilevel, contact-implicit trajectory optimization (TO) formulation that searches for robot trajectories with learned soft contact models. On the lower-level, contact forces are solved via a quadratic program (QP) with the maximum dissipation principle (MDP), based on which the dynamics constraints are formulated in the upper-level TO problem that uses direct transcription. Our method uses a contact model for granular media that is learned from physical experiments, but is general to any contact model that is stick-slip, convex, and smooth. We employ a primal interior-point method with a pre-specified duality gap to solve the lower-level problem, which provides robust gradient information to the upper-level problem. We evaluate our method by optimizing locomotion trajectories of a quadruped robot on various granular terrains offline, and show that we can obtain long-horizon walking gaits of high qualities.

Authors

• Yifan Zhu 0020
• Zherong Pan
• Kris Hauser

Keywords

• Legged locomotion
• Deformable models
• Databases
• Dynamics
• Media
• Data models
• Trajectory
• Trajectory Optimization
• Bilevel Optimization
• Contact-implicit Trajectory Optimization
• Learning Models
• Quadratic Programming
• Contact Force
• Interior Point
• Physical Experiments
• Interior Point Method
• Contact Model
• Duality Gap
• Granular Media
• Quadruped Robot
• Time Step
• System Dynamics
• Optimal Control
• Performance Metrics
• Penetration Depth
• Cubic Spline
• Transportation Costs
• Linear Constraints
• Rigid Contact
• Strictly Convex
• Joint Velocity
• Path Planning
• Coulomb Friction
• Robot Dynamics
• Legged Robots
• Proportional-integral-derivative
• Radial Basis Function