Practical Approaches for Time-Optimal MPC: Dual Stage and Artificial Reference Methods

This paper introduces and compares two model predictive control (MPC) formulations for time-optimal point-to-point motion planning that are tailored to facilitate reaching distant points. The formulations overcome the need for a large number of decision variables and result in an invariant structure of the underlying nonlinear programming problem, both facilitating the deployment process. The first approach, a dual stage method, divides the prediction horizon into two stages: a time-optimal one with constant system sampling intervals and a free-time stage with variable sampling to reach distant points while ensuring terminal state compliance. The second approach uses an artificial reference with exponential error weighting, guiding the reference toward the target as the system’s motion progresses. Both strategies reduce the computational complexity associated with traditional time-optimal MPC by maintaining a consistent problem structure and minimizing the required sampling points. This makes them well-suited for real-time applications and practical hardware implementation. The effectiveness of each approach is demonstrated through simulations of a unicycle performing point-to-point motion in obstacle-laden environments.