A control Lyapunov function approach to multi-agent coordination

Abstract

Abstract-In this paper, the multiagent coordination problem is studied. This problem is addressed for a class of robots for which control Lyapunov functions can be found. The main result is a suite of theorems about formation maintenance, task completion time, and formation velocity. It is also shown how to moderate the requirement that, for each individual robot, there exists a control Lyapunov function. An example is provided that illustrates the soundness of the method.

Cascade design for formation control of nonholonomic systems in chained form

“…& Remark 5.1. Theorem 5.1 shows that the proposed cooperative control laws robustly solved the objectives (16) and (17) in the presence of communication delay. The time delay t is assumed to be finite constant.…”

“…To set up the reference trajectories appropriately, we generate the desired trajectory for the center of the group then the six real trajectories are constructed based on the offsets (L xi , L yi ) defined in Eqs. (16) and (17). The center of the group's trajectory is given by…”

“…There have been many different control strategies for mobile robot formation reported in the literature, such as the behavior-based approach [9][10][11], the virtual-structure [7,[12][13][14][15], the leader-follower approach [16][17][18][19][20][21], artificial potential [22][23][24][25], graph theory [26,27] and other relevant techniques like consensus algorithms in which a group of vehicles try to negotiate with their neighbors to reach an agreement on a common state. This type of algorithm has been studied extensively for single integrator [28,29] as well as for double integrator [6].…”

Robust formation control of electrically driven nonholonomic mobile robots via sliding mode technique

“…Various approaches have been proposed for the formation control of multiple robots in the literature. These are largely categorized as behaviorbased [2][3][4], virtual structure [5][6][7], and leader-following [8][9][10][11][12]. Each approach has its own characteristics.…”

Multi-robot formation control and object transport in dynamic environments via constrained optimization

“…Examples of typical approaches for formation control include Lyapunov functions (Ogren et al, 2001), model predictive control (Dunbar and Murray, 2002), flocking (Dimarogonas and Kyriakopoulos, 2005) and leader-follower control (Ren and Sorensen, 2008), each one with its own advantages and disadvantages. For a short review on this topic we refer the reader to Chen and Wang (2005).…”