Position and Orientation Tunnel-Following NMPC of Robot Manipulators Based on Symbolic Linearization in Sequential Convex Quadratic Programming

Abstract

The tunnel-following nonlinear model predictive control (NMPC) scheme allows to exploit acceptable deviations around a path reference. This is done by using convex-over-nonlinear functions as objective and constraints in the underlying optimal control problem (OCP). The convex-over-nonlinear structure is exploited by algorithms such as the generalized Gauss-Newton (GGN) method or the sequential convex quadratic programming (SCQP) method to reduce the computational complexity of the OCP solution. However, the modeling effort and engineering time required to implement these methods is high. We address the problem of reducing the modeling effort in the implementation of SCQP, focusing on a standard sequential quadratic programming (SQP) implementation where symbolic linearization is applied to the nonlinear part of the convex-over-nonlinear functions in the objective and constraints. The novelty of this letter is twofold. It introduces a novel operator that applies symbolic linearization in a transparent and easy way to solve nonconvex OCPs with the SCQP method, and introduces a meaningful representation of an orientation-tunnel for robotic applications by means of a convex-over-nonlinear constraint, which preserves the convexity exploitation by the SCQP method. The proposed technique is demonstrated in a tunnel-following task for a 7-degrees-of-freedom manipulator.