Bounded Coordination Control of Second-order Dynamic Agents

Khac Duc Do

doi:10.4172/2168-9695.1000105

Abstract

This paper presents a constructive design of distributed and bounded coordination controllers that force mobile agents with second-order dynamics to track desired trajectories and to avoid collision between them. The control design is based on the new bounded control design technique for second-order systems, and new pairwise collision avoidance functions. The pair wise collision functions are functions of both the relative position and velocity of the agents instead of only the relative position as in the literature. Desired features of the proposed control design include: 1) Boundedness of the control inputs by a predefined bound despite collision avoidance between the agents considered, 2) No collision between any agents, 3) Asymptotical stability of desired equilibrium set, and 4) Instability of all other undesired critical sets of the closed loop system. The proposed control design is then applied to design a coordination control system for a group of vertical take-off and landing (VTOL) aircraft.

Highlights

Coordination control of multiple agents has received a lot of attention from researchers in the control community due to its various applications to search, rescue, coverage, surveillance, reconnaissance and cooperative transportation
Since this paper focuses on designing bounded coordination controllers for the agents with second-order dynamics, we do not consider the case where the shape of the virtual structure is time-varying, i.e., the vectors li are time-varying, to avoid complication of the presentation
We summarize the results of the proposed coordination control design for VTOL aircraft in the following theorem: Theorem 7.1: Under Assumption 5.1, the smooth controls

Summary

Introduction

Coordination control of multiple agents has received a lot of attention from researchers in the control community due to its various applications to search, rescue, coverage, surveillance, reconnaissance and cooperative transportation. Since this paper focuses on designing bounded coordination controllers for the agents with second-order dynamics, we do not consider the case where the shape of the virtual structure is time-varying, i.e., the vectors li are time-varying, to avoid complication of the presentation. We present saturation functions, a technique for designing bounded controllers for a second-order system, and nonzero convergent lemma for a differential inequality, smooth step functions, pairwise collision avoidance functions, and Barbalat-like lemma These preliminary results will be used in the control design and stability analysis later. Property 4) allows us to use control design and stability analysis methods found in [40] for continuous systems instead function βij are given in Definition 5.3, and is the set of all the agents except for the agent i. We present an application of the proposed coordination control design in the previous section to design a coordination control system for a group of VTOL aircraft

Related work

Conclusions