Path-following NMPC for serial-link robot manipulators using a path-parametric system reformulation

Abstract

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. *Niels van Duijkeren en Robin Verschueren are fellows of the TEMPO Initial Training Network. The work leading to these results has been carried out within the framework of FP7-ITN-TEMPO (607 957). This work also benefits from project G0C4515N of the Research Foundation-Flanders (FWO-Flanders), KU Leuven-BOF PFV/10/002 Centre of Excellence: Optimization in Engineering (OPTEC) and the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office (DYSCO).

Spline-Based Trajectory Generation for CNC Machines

“…The method aims at minimizing the tracking error and it is not possible to constrain it to a specific value. The authors of [13] propose a nonlinear model predictive path following method that uses a spatial reformulation to obtain simple geometric constraints. While this method allows explicitly constraining the tracking error, the corresponding optimization problem is strongly non-convex and very hard to solve.…”

Predictive joint trajectory scaling for manipulators with kinodynamic constraints

“…Path following control addresses the general problem of moving a dynamic system along a reference geometric curve using the velocity profile as an additional control variable [6,7,8,9,10]. These methods are intended to be implemented as feedback controllers.…”

“…Torque limits are considered via the inverse dynamics equations of the manipulator. The resulting non-linear constraints are then linearized at each iteration by using joint positions and velocities predicted at the previous cycle, similarly to [8,19,20]. The use of a zero-order linearization reduces the computational burden compared to standard SQP solvers.…”

A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control

“…Recently, both algorithmic and computational advances made NMPC applicable in real-time for systems with fast dynamics, e.g. in [2,23,27,29]. For an overview of computationally efficient methods for NMPC, we point the reader to [6,19].…”