Adaptive Artificial Time-Delay Control with Barrier Lyapunov Constraints for Euler-Lagrange Robots

2026-05-29

AI Summary

This work addresses the joint challenge of state-dependent uncertainties and time-varying state constraints in Euler–Lagrange robotic systems by proposing a model-free adaptive control approach. By introducing an artificial time-delay estimation technique, the study derives, for the first time, an analytical upper bound on the state-dependent time-delay estimation error. This bound is integrated with a barrier Lyapunov function to formulate a constraint-aware adaptive law that simultaneously enforces strict satisfaction of time-varying safety constraints on both position and velocity while compensating for dynamic uncertainties in real time. The closed-loop system’s stability is rigorously established via Lyapunov stability theory, and experimental validation on a five-degree-of-freedom robotic manipulator demonstrates superior safety-critical control performance under strong dynamic disturbances compared to existing methods.

Abstract

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.

Problem

• state-dependent uncertainties
• time-varying state constraints
• Euler-Lagrange systems
• robotic control
• safety-critical constraints

Innovation

• adaptive time-delay estimation
• barrier Lyapunov function
• state-dependent uncertainty
• time-varying constraints
• Euler-Lagrange systems