Organizations: Automation and Robotics Research Group, Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, 1855 Luxembourg, Luxembourg · School of Physics, Engineering and Computer Science (SPECS), and Robotics Research Group of the University of Hertfordshire, Hatfield, AL10 9AB, United Kingdom
Robot manipulators may start a new task with a tracking error larger than the prescribed tolerance. Conventional barrier controllers generally require the initial error to lie within this tolerance, which prevents their direct use under such conditions. This paper develops a progressive barrier controller that gradually contracts an initial error bound to the required value within a prescribed time. The robot can therefore start outside the final bound, while the direct joint-position error satisfies it after the transition. The closed-form control law combines progressive barrier feedback with an online adaptive torque term based on an actor--critic structure. A Lyapunov analysis establishes bounded closed-loop signals and gives sufficient conditions for satisfaction of the final tracking bound. Two-link simulations consider large initial errors, actuator saturation, dynamic variations, disturbances, and measurement errors. The adaptive term reduces the median root-mean-square tracking error by 45.1% compared with the zero-weight progressive barrier controller. The simulations also map the initial errors that can be handled at different transition times under fixed torque limits. Finally, an experiment on a Niryo Ned3 Pro illustrates tracking performance using measured position and motor-current data.
Figures & tables
Fig. 1: Progressive imposition of the joint tracking bound. The photograph at left shows the Niryo Ned3 Pro used in the single-joint experiment. The plot at right shows the nominal two-link simulation. The direct tracking error may initially lie outside the final bound, whereas the scaled error starts inside the barrier domain. The two errors coincide after the prescribed transition time.
Case
Link-2 mass increment (kg)
Friction scale
Disturbance scale
Measurement amplitude (rad)
Phase offset (rad)
Reference-speed scale
1
0.00
0.80
0.50
0.0000
0.00
0.80
2
0.25
0.95
1.25
0.0008
0.35
1.06
3
0.50
1.10
0.97
0.0016
0.70
0.89
4
0.00
1.24
0.68
0.0004
1.05
1.15
5
0.25
0.86
1.44
0.0012
1.40
0.99
6
0.50
1.01
1.15
0.0020
1.75
0.82
TABLE I: Fixed Paired Perturbation Cases
Fig. 2: Feasibility under the same torque limits. Each marker represents one proposed-controller run, and failed settings are retained. Longer transition times accommodate larger initial errors in this grid.
Fig. 3: Nominal two-link response from an initial tracking error outside the final bound: (a) joint tracking, (b) direct and scaled normalized tracking errors, and (c) applied joint torques under the fixed limits. The vertical dotted line marks Tc , and the shaded interval denotes the prescribed transition. The horizontal line in panel (b) marks ρ=1 , while those in panel (c) mark the two joint torque limits.
Fig. 4: Paired results for the 12 fixed perturbation cases: (a) vector-error RMS for t≥Tc , (b) largest normalized error for t≥Tc , and (c) last entry into the final envelope. Markers denote individual cases; boxes span the 25th–75th percentiles, center lines denote medians, and whiskers show the full range. CT denotes computed torque; lower values are better.
Fig. 5: Complete single-joint physical record without smoothing: reference and measured joint angle, error recomputed with the paper’s sign convention q−qd , and commanded and measured current in logged raw units.
This paper addresses the challenge of simultaneously compensating for state-dependent uncertainties and enforcing time-varying state constraints in Euler-Lagrange systems, a common requirement in robotics that remains underserved by existing control designs. A novel adaptive control framework is developed that combines an artificial time-delay-based uncertainty estimation strategy, also known as time-delay estimation, with a barrier Lyapunov function to enforce constraint-aware control design. Specifically, a state-dependent upper bound on the time-delay estimation approximation error is analytically formulated, and an adaptive law is constructed to estimate its parameters online, enabling real-time state-dependent uncertainty compensation without relying on prior model knowledge. To ensure constraint compliance, the barrier Lyapunov function-based controller enforces time-varying bounds on both position and velocity. The resulting architecture is provably stable via Lyapunov analysis. Experimental results on a five-degree-of-freedom robotic manipulator validate the framework's capability, compared with the state of the art, in maintaining strict adherence to safety-critical constraints under dynamic uncertainties.
Saksham Gupta, Rishabh Dev Yadav, Sarthak Mishra +5
Robotics Research Center, International Institute of Information Technology Hyderabad, India · Department of Computer Science, University of Manchester, UK · Autonomous Systems and Automatic Control in School of Engineering, Newcastle University, UK +1
Safe physical interaction is critical for deploying robotic manipulators in human-robot interaction and contact-rich tasks, where uncertainty, external forces, and actuator limitations can compromise both performance and safety. We propose an online adaptive impedance control framework that enforces joint-state safety while achieving compliant interaction under uncertain dynamics. The approach combines a quadratic-program-based safety filter with a novel composed position-velocity non-smooth control barrier function (NCBF), enabling joint position and velocity constraints to be enforced through a unified relative-degree-one barrier. Unknown dynamics are compensated online using an interval type-2 fuzzy logic system, while actuator torque limits are handled through soft constraints with exact penalty recovery of feasible solutions. A disturbance-observer-enhanced safety mechanism improves robustness against modelling errors and external interaction forces. Using composite Lyapunov analysis, we prove forward invariance of the safe set and the uniform ultimately boundedness of the impedance-tracking error. Simulations on a 7-DOF manipulator with severe parametric uncertainty and external interaction wrenches demonstrate safe constraint satisfaction and robust impedance tracking.
Faisal Lawan, Xiaoran Han, Joaquin Carrasco +2
Department of Electrical and Electronic Engineering, The University of Manchester, M13 9PL, United Kingdom
Control barrier functions are an effective model-based tool to formally certify the safety of a system. However, transferring their theoretical guarantees to real-world robotics systems requires high model fidelity. For example, payloads or wind disturbances can cause significant model perturbations to an aerial vehicle, leading to safety compromises. In this work, we propose a certifiable online learning-enhanced robust adaptive control barrier function, which adapts to disturbances using a Neural ODE and quantifies its adaptation uncertainty with conformal prediction. Our approach guarantees safety at all time under unknown time-varying model disturbances. It adopts a conservative strategy when the adaptation uncertainty is high; and efficiently adapts to reduce controller conservativeness as it receives more data. Our approach provides a provable safety guarantee with a probability bound under suitable Lipschitz smoothness assumptions on the underlying model and trajectory. These results demonstrate the potential of our method as a practical safety controller for robotics system operating under model perturbations.
Lishuo Pan, Mattia Catellani, An Cao +2
Department of Computer Science, Brown University, Providence, RI 02912 USA · Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, 41121 Modena, Italy · Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125 USA