Distributed Observer-Based Prescribed Performance Control for Multi-Robot Deformable Object Cooperative Teleoperation

In this paper, a distributed observer-based prescribed performance control method is proposed for using a multi-robot teleoperation system to manipulate a common deformable object. To achieve a stable position-tracking effect and realize the desired cooperative operational performance, we first define a new hybrid error matrix for both the relative distances and absolute positions of robots and then decompose the matrix into two new error terms for cooperative and independent robot control. Then, we improve the Kelvin-Voigt (K-V) contact model based on the new error terms. Because the center position and deformation of the object cannot be measured, the object dynamics are then expressed by the relative distances of robots and an equivalent impedance term. Each robot incorporates an observer to estimate contact force and object dynamics based on its own measurements. To address the position errors caused by biases in force estimation and realize the position-tracking effect of each robot, we improve the barrier Lyapunov functions (BLFs) by incorporating the errors into system control. which allows us to achieve a predefined position-tracking effect. We conduct an experiment to verify the proposed controller’s ability in a dual-telerobot cooperative manipulation task, even when the object is subjected to unknown disturbances. Note to Practitioners—This article is inspired by the limitations of multi-telerobot manipulation with a deformable object, where the deformation of the object cannot be measured directly. Meanwhile, force sensors, especially 6-axis force sensors, are very expensive. To realize the purpose that objects manipulated by multiple robots match the same state as operated on the leader side, we propose an object-centric teleoperation framework based on the estimates of contact forces and object dynamics and the improved barrier Lyapunov functions (BLFs). This framework contributes to two aspects in practice: 1) propose a control diagram for deformable object co-teleoperation of multi-robots for unmeasurable object’s centre position and deformation; 2) propose an improved BLFs controller based on the estimation of contact force and robot dynamics. The estimation errors are considered and transferred using an equivalent impedance to be integrated into the Lyapunov function to minimize both force and motion-tracking errors. The experimental results verify the effectiveness of the proposed method. The developed framework can be used in industrial applications with a similar scenario.