Fast Contact-Implicit Model Predictive Control

In this article, we present a general approach for controlling robotic systems that make and break contact with their environments. Contact-implicit model predictive control (CI-MPC) generalizes linear MPC to contact-rich settings by utilizing a bilevel planning formulation with lower level contact dynamics formulated as time-varying linear complementarity problems (LCPs) computed using strategic Taylor approximations about a reference trajectory. These dynamics enable the upper level planning problem to reason about contact timing and forces, and generate entirely new contact-mode sequences online. To achieve reliable and fast numerical convergence, we devise a structure-exploiting interior-point solver for these LCP contact dynamics and a custom trajectory optimizer for the tracking problem. We demonstrate real-time solution rates for CI-MPC and the ability to generate and track nonperiodic behaviors in hardware experiments on a quadrupedal robot. We also show that the controller is robust to model mismatch and can respond to disturbances by discovering and exploiting new contact modes across a variety of robotic systems in simulation, including a pushbot, planar hopper, planar quadruped, and planar biped.