A General Approach to Coordination Control of Mobile Agents With Motion Constraints

Abstract

Abstract-This paper proposes a general approach to design convergent coordination control laws for multi-agent systems subject to motion constraints. The main contribution of this paper is to prove in a constructive way that a gradient-descent coordination control law designed for single integrators can be easily modified to adapt for various motion constraints such as nonholonomic dynamics, linear/angular velocity saturation, and other path constraints while preserving the convergence of the entire multi-agent system. The proposed approach is applicable to a wide range of coordination tasks such as rendezvous and formation control in two and three dimensions. As a special application, the proposed approach solves the problem of distance-based formation control subject to nonholonomic and velocity saturation constraints.

Affine Formation Maneuver Control of Multiagent Systems

“…The stability of control law (29) can be analyzed similar to [30]. However, since the leader-follower affine formation control law was not specifically analyzed in [30], we present a proof here by fully considering the specific properties of this control law.…”

Adaptive estimator‐based formation maneuvering control of nonholonomic mobile robots

“…Remark Based on the virtual gradient control law in and the transformation in , linearization is realized by designing the linear and angular velocity as in and . Unlike the controller design without linearization in the works of Zhao et al, which can only ensure formation shape stabilization, distance‐based formation maneuvering in this work can be achieved with the modified gradient based controller design.…”

“…Based on the virtual gradient control law in (14) and the transformation in (16), linearization is realized by designing the linear and angular velocity as in (17) and (25). Unlike the controller design without linearization in the works of Zhao et al, 19,20 which can only ensure formation shape stabilization, distance-based formation maneuvering in this work can be achieved with the modified gradient based controller design. (1), under the control of designed linear and angular velocities respectively in (17) and (25) with the estimator (5), if (0) ∈ (r 0 ) with r 0 > 0 and the design parameters are according to the conditions that…”

On a hierarchical control strategy for multi-agent formation without reflection

“…with d * ij = d * jk = d * ki = d * , and the potential function V (i,j,k) is defined in (7). Then, (i) if K > 3/2 holds, p k converges globally to the unique correct equilibrium in P; (ii) if −2+2 √ 3 < K ≤ 3/2 holds, there exist a stable correct equilibrium in P and two unstable incorrect equilibria, and almost all trajectories of p k converge to the correct equilibrium formation in P; (iii) if 0 < K < −2+2 √ 3, there exist a locally stable correct equilibrium in P and one locally stable incorrect equilibrium not in P (as well as unstable saddle equilibrium points).…”