Accelerating Model Predictive Control for Legged Robots through Distributed Optimization

TL;DR

The paper tackles the challenge of real-time whole-body MPC for legged robots with complex nonlinear dynamics by introducing a distributed optimization framework based on consensus ADMM. The robot is partitioned into subsystems that solve local optimal control problems in parallel, with coupling maintained through a consensus mechanism and a shared interaction wrench. Empirical results show convergence toward the centralized solution and substantial speedups (approximately $2$–$4\times$) when adding subsystems like a 6-DoF arm, with a horizon of $N=50$ and $dt=0.01$ s, executed at $50$ Hz. This approach enables scalable online planning on modern hardware, facilitating more capable and larger-scale legged robot systems, and sets the stage for hardware validation and integration with alternative nonlinear solvers.

Abstract

This paper presents a novel approach to enhance Model Predictive Control (MPC) for legged robots through Distributed Optimization. Our method focuses on decomposing the robot dynamics into smaller, parallelizable subsystems, and utilizing the Alternating Direction Method of Multipliers (ADMM) to ensure consensus among them. Each subsystem is managed by its own Optimal Control Problem, with ADMM facilitating consistency between their optimizations. This approach not only decreases the computational time but also allows for effective scaling with more complex robot configurations, facilitating the integration of additional subsystems such as articulated arms on a quadruped robot. We demonstrate, through numerical evaluations, the convergence of our approach on two systems with increasing complexity. In addition, we showcase that our approach converges towards the same solution when compared to a state-of-the-art centralized whole-body MPC implementation. Moreover, we quantitatively compare the computational efficiency of our method to the centralized approach, revealing up to a 75% reduction in computational time. Overall, our approach offers a promising avenue for accelerating MPC solutions for legged robots, paving the way for more effective utilization of the computational performance of modern hardware.

Figures (6)

• Figure 1: Simulation snapshots of robotic systems controlled by the proposed MPC with distributed optimization, performing different agile motions. On the top, a quadruped standing up on two feet and walking forward. On the bottom, a quadruped manipulator following a triangular spiral with the manipulator end-effector, the reference is highlighted in blue while the actual trajectory is in green.
• Figure 2: Schematic of a quadruped robot with an articulated arm on top split into three separate subsystems. Each section of the robot sees the dynamic effect of the other parts through the interaction wrench $\boldsymbol{F}$.
• Figure 3: Block scheme of the proposed control framework highlighting the communication bus between the decomposed Subsystem Optimizations.
• Figure 4: The two plots on the left show the trend of the $l_2$ norm of the residuals along the iteration of Algorithm \ref{['algo:dwmpc']}. On top is the residual for the quadruped with no arm, while on the bottom are the residuals for the quadruped manipulator. The right side plots show the time plot of the residual norm while the robot is trotting in simulation. Again, the top plot is for the robot with no arm, and the bottom one is for the quadruped manipulator.
• Figure 5: Phase plots of the robot trotting with the centralized (dashed blue line) and distributed (orange line) solutions. The plot shows a recording of the robot trotting in simulation at a desired speed of 0.3 $m/s$. Where RF-LF-LH-RH stands for Right Front, Left Front, Left Hind, Right Hind and, HAA, HFE, KFE stand for Hip Abduction/Adduction, Hip Flexion/Extension, and Knee Flexion/Extension.