Small-Gain Theorem Based Distributed Prescribed-Time Convex Optimization For Networked Euler-Lagrange Systems

In this paper, we address the distributed prescribed-time convex optimization (DPTCO) for a class of networked Euler-Lagrange systems under undirected connected graphs. By utilizing position-dependent measured gradient value of local objective function and local information interactions among neighboring agents, a set of auxiliary systems is constructed to cooperatively seek the optimal solution. The DPTCO problem is then converted to the prescribed-time stabilization problem of an interconnected error system. A prescribed-time small-gain criterion is proposed to characterize prescribed-time stabilization of the system, offering a novel approach that enhances the effectiveness beyond existing asymptotic or finite-time stabilization of an interconnected system. Under the criterion and auxiliary systems, innovative adaptive prescribed-time local tracking controllers are designed for subsystems. The prescribed-time convergence lies in the introduction of time-varying gains which increase to infinity as time tends to the prescribed time. Lyapunov function together with prescribed-time mapping are used to prove the prescribed-time stability of closed-loop system as well as the boundedness of internal signals. Finally, theoretical results are verified by one numerical example.

Hybrid Dynamics Modeling and Trajectory Planning for a Cable-Trailer System with a Quadruped Robot

Inspired by the utilization of dogs in sled-pulling for transportation, we introduce a cable-trailer system with a quadruped robot. The motion planning of the proposed robot system presents challenges arising from the nonholonomic constraints of the trailer, system underactuation, and hybrid interaction through the cable. To tackle these challenges, we develop a hybrid dynamics model that accounts for the cable's taut/slack status. Since it is computationally intense to directly optimize the trajectory, we first propose a search algorithm to compute a sub-optimal trajectory as the initial solution. Then, a novel collision avoidance constraint based on the geometric shapes of objects is proposed to formulate the trajectory optimization problem for the hybrid system. The proposed trajectory planning method is implemented on a Unitree A1 quadruped robot with a customized cable-trailer and validated through experiments.