Contact-Implicit MPC: Controlling Diverse Quadruped Motions Without Pre-Planned Contact Modes

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Contact-Implicit MPC: Controlling Diverse Quadruped Motions Without Pre-Planned Contact Modes or Trajectories.
Gijeong Kim, Dongyun Kang, Joon-Ha Kim, Seungwoo Hong, and Hae-Won Park.
Under-review
Preprint: doi.org/10.48550/arXiv.2312.0...
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 or foothold 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.
00:00 - Extension 1 "Experiment of front-leg rearing motion"
01:00 - Extension 2 "Experiment of real-time trot motion discovery"
02:28 - Extension 3 "Effect of relaxation variable"
03:15 - Extension 4 "3D simulation: Various reference configurations"
04:22 - Extension 5 "3D simulation: Discovery of gait"
05:36 - Extension 6 "3D simulation: Random rotation task"
06:24 - Extension 7 "Comparison with MuJoCo MPC"
08:37 - Extension 8 "Additional result of 2D case"
09:26 - Extension 9 "3D simulation: Re-planning in response to slippage"

[@chalkchalk2283]

really impressive work!!

[@jungillkang4497]

Outstanding🎉

[@user-fn3zm1yk4f]

Fancy algorithm!

[@junnykim5200]

Wow amazing!! It can even do handstand?????

[@Cian-_-]

planche is a difficult exercise, welcome to calisthenics lil buddy