MR-MPCC: Model Predictive Contouring Control for Robotic Manipulator Tracking under Moving Reference Frames
When the workpiece under a UR5e robot arm was knocked mid-path, a contouring controller from the University of Technology Sydney held the tool 20 to 22% closer to the drawn path on average than standard PI control or time-indexed MPC (4.28 mm against 5.36 mm and 5.51 mm RMS error in simulation), the researchers report in a preprint. Peak errors, set by the jolt itself, stayed about the same for all three.
How should a robot arm follow a precise path when the object that carries the path moves unexpectedly, as a patient's bone or a clamped part might during milling?
Most arm controllers track a reference that is indexed by time: at second t the tool should be at point p(t). If the frame holding the path is shoved, a time-indexed controller keeps chasing the clock and can build up sideways error from the path, which is what matters in machining or surgical milling. Joint-level control can look stable while the tool is off the line.
PI and PID loops are cheap and well understood but do not predict ahead or handle constraints. Robust, tube-based and learning-augmented model predictive control (MPC) add constraints and disturbance handling, but stay time-indexed. Model predictive contouring control (MPCC), which measures error along and across the path and lets the controller choose how fast to progress, is established for machine tools and drones; on manipulators it has mainly been used for obstacle and singularity avoidance on a 7-axis Panda.
MR-MPCC runs two layers at 500 Hz. The upper layer is a task-space MPCC over a 10-step horizon that expresses errors in a frame attached to the moving path, splits position error into a cross-path contouring part and an along-path lag part, adds an orientation error for full 6-DoF pose, and optimises a virtual progress speed alongside the end-effector twist. Contouring is weighted 25 times more than lag (500 against 20). The lower layer is a constrained resolved-motion-rate quadratic program that turns the twist into joint velocities while enforcing joint position, speed and acceleration limits, a manipulability barrier against singularities and self-collision distances. The system runs in a ROS 2 and MuJoCo pipeline; on hardware an NDI Aurora electromagnetic tracker at 40 Hz measures both the board carrying the path and the tool.
In MuJoCo simulation with five matched trials per case, MR-MPCC had the lowest contouring RMS error in every disturbance setting. For combined translation and rotation of the path frame on a spiral path it scored 4.28 mm against 5.36 mm for PI (20.2% lower) and 5.51 mm for MPC (22.3% lower); with one correlated disturbance model it beat MPC by 21.0% (3.72 against 4.71 mm). The edge was largest for translation-only jolts (0.70 against 0.97 mm for MPC, 27.3% lower) and smallest on harder geometries: 3.1% on a flower path and 1.3% on a helix. Maximum contouring error was similar for all controllers at about 50 to 53 mm. The mechanism is visible in the logs: after a jolt the controller slows its progress along the path to recover the line, trading temporary lag for cross-path accuracy. On a physical UR5e following straight, sine and spiral paths on a board pushed by hand, the method showed a lower median and a narrower spread of contouring error than both baselines (MEKAWIRE computed the simulation percentages from the paper's table).
The hardware results are given only as box plots, with no numeric errors and no count of tolerance violations against the 16 mm ring gauge, and the text gives both three and ten runs per controller. Disturbances were applied by hand. The path-frame pose is held constant over the prediction horizon and measured at 40 Hz, and the authors leave sensing delay, uncertainty and contact forces to future work. Peak error, the number that decides a scrapped part or a safety stop, did not improve. It is a preprint.
The setting maps onto tasks where the target moves under the tool: robotic bone milling (the work is funded by an Australian NHMRC grant), deburring on fixtures that flex, and machining with collaborative arms such as Universal Robots' UR5e. A velocity-level controller that plugs into ROS 2 is easy for integrators to try. Our reading: a 20% cut in average error is useful for surface quality, but buyers in surgery and machining will judge it on peak deviation and on measured hardware numbers, which this paper does not yet supply.
The full text is not republished here because the paper's license does not allow it. Read the original on arXiv.