Contact-implicit Model Predictive Control: Controlling diverse quadruped motions without pre-planned contact modes or trajectories

Gijeong Kim, Dongyun Kang, Joon-Ha Kim, Seungwoo Hong, Hae-Won Park

Abstract:

This paper presents a contact-implicit model predictive control (MPC) framework for the real-time discovery of multi-contact
motions, without predefined contact mode sequences orfoothold positions. This approach utilizes the contact-implicit differential
dynamic programming (DDP) framework, merging the hard contact model with a linear complementarity constraint. We
propose the analytical gradient of the contact impulse based on relaxed complementarity constraints to further the exploration of
a variety of contact modes. By leveraging a hard contact model-based simulation and computation of search direction through a
smooth gradient, our methodology identifies dynamically feasible state trajectories, control inputs, and contact forces while
simultaneously unveiling new contact mode sequences. However, the broadened scope of contact modes does not always ensure
real-world applicability. Recognizing this, we implemented differentiable cost terms to guide foot trajectories and make gait
patterns. Furthermore, to address the challenge of unstable initial roll-outs in an MPC setting, we employ the multiple shooting
variant of DDP. The efficacy of the proposed framework is validated through simulations and real-world demonstrations using a
45 kg HOUND quadruped robot, performing various tasks in simulation and showcasing actual experiments involving a forward
trot and a front-leg rearing motion.