Self-triggered control of robotic systems with obstacle avoidance and velocity constraints: A double integral TTCBLF approach

This article proposes a double integral time-to-collision barrier Lyapunov function (TTCBLF) approach for robotic systems with obstacle avoidance and velocity constraints. The existing barrier function assesses collision risk based solely on distance, neglecting the robot’s velocity, which is also highly relevant to collision risk. To comprehensively assess collision risk, a flexible time-to-collision barrier function (TTCBF) is constructed, enabling the robot to dynamically increase or decrease the amplitude of the original barrier function in advance based on its velocity and distances to obstacles. Then, unlike the self-triggered mechanism (STM) that solely depends on control signals, a velocity constraint function-based STM is designed to save communication resources, with the minimum triggering interval decreasing as the velocity constraint function increases. Through the Lyapunov method and boundedness analysis for the barrier function, it is shown that the proposed approach achieves obstacle avoidance for the robotic systems without violating the velocity constraints, while excluding the Zeno behavior. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed control approach.