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

TL;DR

This paper presents a GPU-accelerated primal-dual iLQR algorithm for legged robot control, significantly reducing computation time and enabling real-time control and learning in complex multi-robot systems.

Contribution

It introduces a novel parallelized MPC solver leveraging GPU for efficient primal-dual KKT system solution, scalable to multiple robots and compatible with large-scale parallel learning.

Findings

Achieves up to 60% faster runtime than state-of-the-art solvers.

Enables control of up to 16 robots in less than 25 ms.

Supports large-scale parallelization for learning in GPU.

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 $\mathcal{O}(\log^2(n)\log{N} + \log^2(m))$ complexity, instead of $\mathcal{O}(N(n + m)^3)$, 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. The code associated with this work can be found at https://github.com/iit-DLSLab/mpx.