Adaptive Model Predictive Control for Differential-Algebraic Systems towards a Higher Path Accuracy for Physically Coupled Robots

TL;DR

The paper tackles the challenge of achieving high-precision path tracking for physically coupled robots under uncertain kinematics and non-circumventable built-in controllers. It combines a differential-algebraic equation (DAE) model of the coupled system with online Newton-Raphson parameter updates and a receding-horizon adaptive MPC that coordinates all robots while prioritizing tracking accuracy and load distribution. Key contributions include the DAE formulation with loop-closure constraints, a sensitivity-based parameter estimator, and a direct-collocation MPC that penalizes trajectory error and joint loads. Results from real-world experiments and simulations show substantial improvements in path accuracy (e.g., an 88.6% error reduction over a benchmark) and favorable load balancing, underscoring the potential for online high-precision manufacturing with off-the-shelf robots.

Abstract

The physical coupling between robots has the potential to improve the capabilities of multi-robot systems in challenging manufacturing processes. However, the path tracking accuracy of physically coupled robots is not studied adequately, especially considering the uncertain kinematic parameters, the mechanical elasticity, and the built-in controllers of off-the-shelf robots. This paper addresses these issues with a novel differential-algebraic system model which is verified against measurement data from real execution. The uncertain kinematic parameters are estimated online to adapt the model. Consequently, an adaptive model predictive controller is designed as a coordinator between the robots. The controller achieves a path tracking error reduction of 88.6% compared to the state-of-the-art benchmark in the simulation.

Figures (8)

• Figure 1: Two robots are coupled to a coupler. The spindle and TCP are mounted on the coupler to achieve a high stiffness while cutting the work-piece.
• Figure 2: The loop closure condition of a two-robot example
• Figure 3: Subfigure (a) shows the overall scenario of the experiment both in simulation and real execution. Subfig. (b) is the zoomed view of the enframed area in Subfig. (a). The modified reference trajectories $\boldsymbol{q}_\mathrm{ref}$ for robot $i=1$ and $i=2$ are transformed into TCP positions in Cartesian space with the forward kinematics. The TCP positions start with the arrow, move clockwise, and finish a loop in $14.69s$
• Figure 4: Reference Euler angles $\theta$ and angular velocities $\dot{\theta}$ of the coupler. The dash-dotted lines are the boundaries of segments where TCP comes to corners in Fig. \ref{['fig:path_trans']}.
• Figure 5: Comparing the sensor measurement $\boldsymbol{\tau}_\mathrm{m}$ and model prediction $\tilde{\boldsymbol{\tau}}_\mathrm{m}$. They converge after starting the estimation of uncertain kinematic parameters from $t=1s$. Joint movements start at $t=3s$. In the legends, the joint numbers are given in superscript brackets.