Contact-Implicit Trajectory Optimization

接触隐式轨迹优化Advanced

Letting the optimizer decide, on its own, when and where to contact the environment, instead of fixing the contact order in advance.

Traditional trajectory optimization treats events like ‘foot touches down’ or ‘hand touches object’ as discrete modes, requiring a human to specify the mode order in advance (left foot first, then right), then optimizing within each segment. For tasks like multi-finger manipulation, where contact changes constantly, there's simply no way to write that order down beforehand. MIT's Posa, Cantu, and Tedrake proposed a direct method (WAFR 2012, journal version in IJRR 2014) that makes contact force itself a decision variable, describing contact with complementarity constraints: distance φ ≥ 0, normal force λ ≥ 0, and φ·λ = 0 — meaning ‘no contact, no force; force means touching’ — solved with sequential quadratic programming, so the contact schedule and the trajectory come out together. These constraints originate from the linear complementarity problem used in physics engines. The cost is that the problem is non-convex and hard to converge, often needing relaxation or smoothing; later work developed contact-implicit MPC that can run online.

ExamplePosa et al. used the same method to plan a finger rotating a fixed-axis object, simple grasping and manipulation tasks, planar walking for Spring Flamingo, and high-speed bipedal running for FastRunner, all without specifying a contact order in advance; Le Cleac'h et al. (2021) proposed a fast contact-implicit MPC that generated non-periodic motions in real time on a real quadruped robot.

Also called: Contact-Implicit MPC, CI-MPC, Through-Contact Trajectory Optimization
Related: Trajectory Optimization · Linear Complementarity Problem · Sequential Quadratic Programming · Direct Collocation · Multi-contact Planning · Gait Planning
Sources: Posa, Cantu, Tedrake: A Direct Method for Trajectory Optimization of Rigid Bodies Through Contact
Le Cleac'h et al., Fast Contact-Implicit Model-Predictive Control (arXiv:2107.05616)