Path-following NMPC for Serial-link Robot Manipulators Using a Path-parametric System Reformulation

This paper discusses path-following control for robotics, moving a manipulator along a path in Cartesian space, making a trade-off between tracking accuracy and the speed at which the path is followed. We present and validate a nonlinear model predictive control (NMPC) approach suitable for this nonlinear control task. This approach entails a method to model the position of the robot end-effector with respect to the path and, in addition, a reformulation of the robot prediction model in terms of an independent path parameter instead of time. This way, we obtain a convenient parameterization of path properties in the optimal control formulation and many geometric constraints, such as tracking tolerance, transform into simple linear or vector-norm constraints. Numerical simulations illustrate the benefits of this novel NMPC approach in an implementation that employs a direct multiple shooting discretization strategy and the real-time iteration scheme for fast computation of the control law. We show results of closed-loop simulations for a 6-DOF industrial robot executing a writing task, with computation times close to enabling real-time implementation.