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Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robots

Authors: Lorenzo Amatucci, Joao Sousa-Pinto, Giulio Turrisi, Dominique Orban, Victor Barasuol, Claudio Semini

Published: 2025 (Journal Paper)

Source: IEEE Robotics and Automation Letters

Algorithm: Primal-Dual iLQR (GPU)

arXiv: 2506.07823

DOI: 10.1109/LRA.2025.3559000

Summary

Implements Primal-Dual iLQR on GPU using parallel associative scans, reducing complexity from O(N(n+m)³) to O(log²(n)log(N)) per solve. Achieves up to 700% runtime improvement over acados and Crocoddyl for legged robot MPC, enabling centralized control of 16 robots and direct GPU-based learning-in-the-loop.

Abstract

This paper introduces a novel Model Predictive Control (MPC) implementation for legged robot locomotion that leverages GPU parallelization. Our approach enables both temporal and state-space parallelization by incorporating a parallel associative scan to solve the primal-dual Karush-Kuhn-Tucker (KKT) system. In this way, the optimal control problem is solved in O(log²(n)log(N) + log²(m)) complexity, instead of O(N(n + m)³), where n, m, and N are the dimension of the system state, control vector, and the length of the prediction horizon. We demonstrate the advantages of this implementation over two state-of-the-art solvers (acados and crocoddyl), achieving up to a 60% improvement in runtime for Whole Body Dynamics (WB)-MPC and a 700% improvement for Single Rigid Body Dynamics (SRBD)-MPC when varying the prediction horizon length. The presented formulation scales efficiently with the problem state dimensions as well, enabling the definition of a centralized controller for up to 16 legged robots that can be computed in less than 25 ms. Furthermore, thanks to the JAX implementation, the solver supports large-scale parallelization across multiple environments, allowing the possibility of performing learning with the MPC in the loop directly in GPU.

Primary

Paper arxiv.org

Standard

arXiv Abstract 2506.07823 arXiv PDF 2506.07823 arXiv HTML 2506.07823 DOI 10.1109/LRA.2025.3559000

Alternate

ieeexplore.ieee.org ieeexplore.ieee.org GitHub: iit-DLSLab/mpx github.com

Tags

  • GPU acceleration

  • Model predictive control

  • Legged robots

  • Primal-dual optimization

  • Trajectory optimization

  • Parallel computing

  • iLQR