Accelerating Model Predictive Control for Legged Robots through Distributed Optimization

Lorenzo Amatucci, Giulio Turrisi, Angelo Bratta,

Victor Barasuol, Claudio Semini

GitHub

arXiv

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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.

Distributed Optimization

Our approach partitions the robot into multiple independent subsystems, significantly speeding up computation while ensuring coherence among their solutions through a parallelized implementation of ADMM. Essentially, we run separate MPCs in parallel for each subsystem, with ADMM maintaining consistency across them. This makes our algorithm highly scalable, virtually independent of system complexity. For instance, integrating an articulated arm onto a quadruped involves adding a new subsystem and incorporating it into the consensus framework. This method effectively handles complex whole-body motions, overcoming the challenges associated with full dynamic models.

( Convergence of the two subsystems to a common optimal solution )

Results

Reduced Computational Time: Our method achieved up to a 75% reduction in computational time compared to traditional centralized approaches.
Scalability: The system efficiently integrated additional components like a 6-DoF arm on a quadruped without affecting computation time

(The robot is split into three difference section highlighted in different colors)

Whole Body MPC:

Thanks to the Whole-Body formulation we can stabilize agile maneuvers like a handstand, without any need for a complex predefined trajectory. Indeed, for the emergence of the biped walking behavior, it was sufficient a step function for the robot's desired base pitch equal to 90deg and a 90deg increase in the front HFE (Hip Flexion Extension) reference joint position.