Convex Data-Driven Model Predictive Control for Trajectory Tracking in Robotic Manipulators

Abstract

Accurate trajectory tracking is a fundamental control task in robotics, typically achieved using model-based methods. Computed Torque Control (CTC) is computationally efficient but struggles to handle system constraints, while Model Predictive Control (MPC) can manage constraints but often results in nonlinear formulations. This work introduces a convex Model Predictive Control (MPC) formulation that incorporates learned dynamics for a robot manipulator. A nonparametric model is used to learn the residual between a nominal model and the observed dynamics, using an inverse dynamics formulation. Convexification is achieved by applying implicit partial differentiation to linearize the inverse dynamics model augmented with the residual model along the reference trajectory, resulting in a Linear Time-Varying (LTV) system. Extensive simulations and hardware experiments on a Franka Emika Panda manipulator demonstrate that our convex MPC approach outperforms learning-based baselines in handling a broad range of model mismatches and constraints. Results also show that learning the residual in inverse dynamics form offers better tracking performance than learning the residual in forward dynamics.