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

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 athttps://github.com/iit-DLSLab/mpx.