Robust MPC for tracking of nonholonomic robots with additive disturbances

TL;DR

This paper introduces two robust MPC strategies, tube-MPC and NRMPC, for nonholonomic robot tracking under disturbances, ensuring stability and feasibility through constraint tightening and feedback mechanisms.

Contribution

The paper presents novel robust MPC schemes specifically designed for nonholonomic systems with disturbances, including stability proofs and simulation validation.

Findings

Both strategies maintain trajectory within desired bounds.

Recursive feasibility and stability are theoretically guaranteed.

Simulation results confirm effectiveness of the proposed methods.

Abstract

In this paper, two robust model predictive control (MPC) schemes are proposed for tracking control of nonholonomic systems with bounded disturbances: tube-MPC and nominal robust MPC (NRMPC). In tube-MPC, the control signal consists of a control action and a nonlinear feedback law based on the deviation of the actual states from the states of a nominal system. It renders the actual trajectory within a tube centered along the optimal trajectory of the nominal system. Recursive feasibility and input-to-state stability are established and the constraints are ensured by tightening the input domain and the terminal region. While in NRMPC, an optimal control sequence is obtained by solving an optimization problem based on the current state, and the first portion of this sequence is applied to the real system in an open-loop manner during each sampling period. The state of nominal system model is updated by the actual state at each step, which provides additional a feedback. By introducing a robust state constraint and tightening the terminal region, recursive feasibility and input-to-state stability are guaranteed. Simulation results demonstrate the effectiveness of both strategies proposed.