Approximate Time-Optimal Model Predictive Control of a SCARA Robot: A Case Study

Abstract

This paper investigates, based on a case study of a SCARA robot, how time-optimal point-to-point motion can be approximately realized using a model predictive control formulation that has low computational complexity. Time-optimality is realized by an indirect formulation and different objective functions are compared. Using the ℓ1-norm instead of a quadratic penalty mimics time-optimality, however, to reduce computational complexity and evade some of its disadvantages, the Huber-norm is introduced as a velocity penalty while the position is penalized quadratically. The contribution of the sampling rate and the length of the prediction horizon is also examined, as the sampling rate poses a limit on the available computation time, while the prediction horizon influences computational complexity. Simulations were carried out in a MATLAB environment using the CasADi toolbox.