Hierarchical Incremental MPC for Redundant Robots: A Robust and Singularity-Free Approach

This article presents a model predictive control (MPC) method for redundant robots controlling multiple hierarchical tasks formulated as multilayer constrained optimal control problems (OCPs). The proposed method, named hierarchical incremental MPC (HIMPC), is robust to dynamic uncertainties, untethered from kinematic/algorithmic singularities, and capable of handling input and state constraints such as joint torque and position limits. To this end, we first derive robust incremental systems that approximate uncertain system dynamics without computing complex nonlinear functions or identifying model parameters. Then, the constrained OCPs are cast as quadratic programming problems which result in linear MPC, where dynamically-consistent task priority is achieved by deploying equality constraints and optimal control is attained under input and state constraints. Moreover, hierarchical feasibility and recursive feasibility are theoretically proven. Since the computational complexity of HIMPC drastically decreases compared with nonlinear MPC-based methods, it is implemented under the sampling frequency of 1 kHz for physical experiments with redundant manipulator setups, where robustness (high tracking accuracy and enhanced dynamic consistency), admissibility of multiple constraints, and singularity-avoidance nature are demonstrated and compared with state-of-the-art task-prioritized controllers.