Performance-based Trajectory Optimization for Path Following Control Using Bayesian Optimization

TL;DR

The paper addresses the challenge of achieving fast and precise contour tracking in a 2D biaxial positioning system while tuning many controller parameters. It combines an MPCC-based trajectory planner with a cascade low-level controller and employs constrained Bayesian optimization with Gaussian-process surrogates to tune both MPCC and low-level gains using full-trajectory performance metrics. The results show that data-driven, joint tuning improves traversal time, tracking accuracy, and vibration suppression, with constrained BO offering substantial gains in contour error reduction at modest time penalties. The approach automates parameter tuning to accommodate model mismatch and geometry variations, enabling more productive and reliable machining operations.

Abstract

Accurate positioning and fast traversal times determine the productivity in machining applications. This paper demonstrates a hierarchical contour control implementation for the increase of productivity in positioning systems. The high-level controller pre-optimizes the input to a low-level cascade controller, using a contouring predictive control approach. This control structure requires tuning of multiple parameters. We propose a sample-efficient tuning algorithm, where the performance metrics associated with the full geometry traversal are modelled as Gaussian processes and used to form the global cost and the constraints in a constrained Bayesian optimization algorithm. This approach enables the trade-off between fast traversal, high tracking accuracy, and suppression of vibrations in the system. The performance improvement is evaluated numerically when tuning different combinations of parameters. We demonstrate that tuning the parameters of the MPC contour-controller achieves the best performance in terms of time, tracking accuracy, and minimization of the vibrations in the system.

Figures (5)

• Figure 1: The model predictive contouring control (MPCC)
• Figure 2: The error variables in the contouring MPC approach
• Figure 3: The scheme of data-driven tuning of MPCC based on Bayesian optimization
• Figure 4: Experimental results for the two geometries showing the tracking performance with the nominal controller, and with the MPC-based planner with manually tuned parameters.
• Figure 5: Position, velocity, acceleration, and maximal contour error resulting from optimization of the MPC parameters, comparing unconstrained BO optimization (solid lines) to BO optimization with additional constraint on the maximal tracking error, for infinity (left) and octagon(center) geometries. The right panel shows the evolution of BO iterations, until optimization terminates. The performance metrics evaluating infinitytracking accuracy and time are summarized in the table for unconstrained and constrained BO.