Whole-Body Nonlinear Model Predictive Control Through Contacts for Quadrupeds

Abstract

In this work we present a whole-body Nonlinear Model Predictive Control approach for Rigid Body Systems subject to contacts. We use a full dynamic system model which also includes explicit contact dynamics. Therefore, contact locations, sequences and timings are not prespecified but optimized by the solver. Yet, thorough numerical and software engineering allows for running the nonlinear Optimal Control solver at rates up to 190 Hz on a quadruped for a time horizon of half a second. This outperforms the state of the art by at least one order of magnitude. Hardware experiments in form of periodic and non-periodic tasks are applied to two quadrupeds with different actuation systems. The obtained results underline the performance, transferability and robustness of the approach.

STANCE: Locomotion Adaptation Over Soft Terrain

“…This approach relaxed the hard contact assumption in their WBC formulation by penalizing the contact interaction in the cost function rather than incorporating it as a hard constraint. For computational purposes, Neunert et al [12] and Doshi et al [13] proposed relaxing the rigid ground assumption. Neunert et al used a soft contact model in their nonlinear MPC formulation to provide smooth gradients of the contact dynamics to be more efficiently solved by their gradient based solver.…”

Trajectory Optimization With Implicit Hard Contacts

“…The main inspiration for our work is drawn from a formulation by Neunert et al [4] who introduce an explicit soft contact model in the system dynamics. Analogous to our approach, this allows the use of fast and unconstrained Riccati-style solvers for the OC problem while respecting the full body dynamics with contacts.…”

“…We evaluate our dynamics model against the soft contact model proposed by Neunert et al [4], which was also used for TO and is openly accessible in [27]. An important initial observation is that naively using soft contacts with default settings and a discretization of 10 ms yield a highly unstable behavior for our monopod.…”

“…The principal difficulty arises from complementarity conditions -contact forces may only act repulsively and only when bodies are in contact, furthermore bodies must not penetrate -which render the problem hard to solve numerically. Consequently, current approaches usually rely on prespecified contact configurations, computationally demanding combinatorial optimization problems, or coarse approximations of the forces arising during hard contacts [1]- [4]. Thus, most established methods suffer from at least one of the following: strongly nonlinear constraints leading to slow convergence, computationally expensive combinatorial search, necessity to predefine step sequence, unphysical contact models, or coarse approximations of physics.…”

Guided Constrained Policy Optimization for Dynamic Quadrupedal Robot Locomotion

“…2) Hard (κ) constraints cannot be violated and are included in the set of constrained cost functions C. These are directly included during policy updates. In case of aCPPO, these are included in (2), and for hCPPO these are included as a constraint, as shown in (1) for the objective L CLIP+V F+S t .…”