MR-MPCC: Model Predictive Contouring Control for Robotic Manipulator Tracking under Moving Reference Frames

Chonghao Cheng; Tiancheng Li; Jonathan Woolfrey; Liang Zhao; Shoudong Huang

cs.ROOct 15, 2026

MR-MPCC: Model Predictive Contouring Control for Robotic Manipulator Tracking under Moving Reference Frames

Authors: Chonghao Cheng, Tiancheng Li, Jonathan Woolfrey, Liang Zhao, Shoudong Huang

Organizations: Robotics Institute, University of Technology Sydney, Sydney, NSW, Australia. · School of Informatics, University of Edinburgh, Edinburgh, UK.

Abstract

Maintaining small path-tracking errors under moving reference frames is essential for robotic manipulation tasks with tight execution tolerances, such as machining and surgical automation. Conventional time-indexed controllers, including tracking Model Predictive Control (MPC), rely on a fixed temporal correspondence with the reference trajectory and may therefore accumulate path-relative error under abrupt reference-frame motion or timing mismatch. This paper presents MR-MPCC, a Model Predictive Contouring Control (MPCC) framework for velocity-controlled robotic manipulators with 6-DoF end-effector pose regulation under Moving-Reference disturbances. A hierarchical control architecture is adopted, in which an upper-level MPCC optimizes path progress while penalizing contouring and orientation errors, and a constrained resolved motion rate control (RMRC) layer maps the commanded Cartesian twist to feasible joint velocities under joint-level and safety constraints. MR-MPCC is implemented in a ROS2--MuJoCo pipeline and validated on a UR5e platform under moving-reference disturbances, where the path frame is perturbed and tracked by electromagnetic sensors. Compared with PI control and time-indexed tracking MPC under matched disturbance, MR-MPCC achieves lower geometric path-following error and smaller deviations in the moving path frame, demonstrating improved path-following performance under reference-frame motion.

Figures & tables

Fig. 1 : MuJoCo simulation snapshot illustrating moving-reference disturbances applied to the path frame. An augmented figure shows a local disturbance segment, revealing reduced overshoot and faster return to the reference trajectory under our framework compared with PI and MPC.

Fig. 2 : Contouring/lag error and error estimation in MPCC. The reference path $\mathbf{p}^{d}(s)$ (black) is parameterized by arc length. The closest-point parameter $s_{k}^{\ast}$ defines the true errors with respect to the system position $\mathbf{p}_{k}$ : the contouring error $\mathbf{e}^{c}_{k}$ (green) and the lag error $\mathbf{e}^{l}_{k}$ (red). To avoid solving the closest-point projection at each step, MPCC propagates an estimated progress variable $\hat{s}_{k}$ , yielding approximate errors $\hat{\mathbf{e}}^{c}(\hat{s}_{k})$ and $\hat{\mathbf{e}}^{l}(\hat{s}_{k})$ computed at $\mathbf{p}^{d}(\hat{s}_{k})$ . The shaded plane $\pi(\hat{s}_{k})$ indicates the local linearization/projection neighborhood.

Control frequency $f_{c}$	500 Hz
Prediction horizon $N$	10
Contouring weight $\mathbf{Q}_{c}$	500 $\cdot\mathbf{I}_{3}$
Lag weight $Q_{\ell}$	20
Orientation weight $\mathbf{Q}_{o}$	40 $\cdot\mathbf{I}_{3}$
Input weight $\mathbf{R}_{u}$	0.01 $\cdot\mathbf{I}_{7}$

TABLE I : MPCC parameters used in both simulation and physical experiments.

Fig. 3 : Disturbance profiles used in the simulation. Each row corresponds to one disturbance configuration. Blue: translational component; orange: rotational component. The peak amplitudes for translation and rotation are on the left.

Scenario	ARMA $(p,q)$	Trajectory	Method	Contouring error [mm]			Lag error [mm]		Rotation error [mrad]
Scenario	ARMA $(p,q)$	Trajectory	Method	RMSE	MAE	MAX	RMSE	MAX	RMSE	MAX
RT	None	Spiral	PI	$5.3638$	$2.7572$	$52.613$	$4.5603$	$31.873$	$25.750$	$87.689$
			MPC	$5.5058$	$2.6372$	$52.692$	$4.5335$	$32.038$	$24.988$	$87.724$
			Ours	4.2794	2.3627	52.294	4.3819	31.446	24.778	87.65
	(1,1)	Spiral	PI	$5.5616$	$2.5324$	51.502	$5.5164$	42.456	$7.613$	$87.657$
			MPC	$4.7092$	$2.2240$	$51.968$	5.4503	$43.325$	$5.426$	87.655

TABLE II : Tracking errors under path frame evaluation.

Fig. 4 : Joint-velocity response (blue solid) and our MPCC formulation progress rate

v_{s}

(green dashed) after disturbance onset. MPCC suppresses the progress rate

v_{s}

during large deviations, which reduces transient deviation in contouring error at the cost of increased lag error.

Fig. 5 : Physical validation setup. A $200$ mm reference path is rigidly attached to a movable board defining the path frame $\mathcal{F}_{D}$ . Two EM sensors measure the board pose ${}^{W}\mathbf{T}_{S_{b}}(t)$ and the tool pose ${}^{W}\mathbf{T}_{S_{e}}(t)$ , enabling online estimation of ${}^{W}\mathbf{T}_{D}(t)$ and the end-effector pose ${}^{D}\mathbf{T}_{E}(t)$ for control and evaluation.

Fig. 6 : Trajectories used in physical experiment

Fig. 7 : Boxplot of the applied moving-reference disturbance magnitude and the resulting contouring error distributions for PI, MPC, and Ours (evaluated in the path frame

\mathcal{F}_{D}

Fig. 8 : Representative reconstructed end-effector trajectories in the board-attached frame under manually applied moving-reference disturbances. Orange and purple shaded regions indicate the first and second disturbance intervals, respectively. The translucent tolerance tube is defined by the tool diameter. The proposed MPCC-based framework remains closer to the reference path than PI and time-indexed tracking MPC.

Robotic Control

Robotic control studies how machines use sensing and computation to produce reliable movement and interaction in changing environments.

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VBT-MPC: Vision-Based Tactile MPC for Contour Following

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Vision-Based Tactile Sensing Tactile Sensing Model Predictive Control Tactile Sensing for Robotic Manipulation

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Tactile sensing plays a key role in robotic manipulation, particularly in tasks like surface inspection. Successful execution requires maintaining contact while accurately tracking object contours. In this work, we propose a Vision-Based Tactile Model Predictive Control (VBT-MPC) framework for robotic contour following using a Vision-Based Tactile Sensor (VBTS) mounted in an eye-in-hand configuration. The proposed controller operates directly in contour features space, thereby avoiding the need for separate pose-estimation modules or complex force-control architectures. We further compare our VBT-MPC with visual-servoing strategies adapted to tactile features, and evaluate contour tracking on objects with diverse geometries and materials in both simulation and real-world experiments.

Abstract

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