Formation control of multiple elliptical agents with limited sensing ranges

Abstract

This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptical shape and with limited sensing ranges to perform a desired formation. The controllers guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on an algebraic separation condition between ellipses, Lyapunov's method, and smooth or p-times differentiable step functions. These functions are introduced and incorporated into novel potential functions to solve the collision avoidance problem without the need of switchings under the agents' limited sensing ranges.

Formation Tracking for Nonlinear Multi‐Agent Systems with Delays and Noise Disturbance

“…Let the noise perturbation term be for some noise intensity constants σ i j ≥0. Then the noise‐perturbed time‐varying consensus protocol can be designed as where { w i j , i , j = 1,2,…, N } are independent standard white noise, a (·):[0,+ ∞ )→(0,+ ∞ ) is a time‐varying tracking consensus‐gain function as defined in , which is piecewise continuous and nonincreasing. The consensus‐gain function a (·) also satisfies , called the convergence condition, and , called the robustness condition.…”

“…where {w ij , i, j = 1, 2, … , N} are independent standard white noise, a(⋅) ∶ [0, +∞) → (0, +∞) is a time-varying tracking consensus-gain function as defined in [22,24], which is piecewise continuous and nonincreasing. The consensus-gain function a(⋅) also satisfies ∫ +∞ 0 a(s)ds = +∞, called the convergence condition, and ∫ +∞ 0 a 2 (s)ds < +∞, called the robustness condition.…”

Transverse function control with prescribed performance guarantees for underactuated marine surface vehicles

“…A transverse function approach was proposed to construct smooth feedback control laws that guarantee practical stabilization of any (feasible or infeasible) reference trajectory (ie, stabilization of system output in a small neighborhood of the reference trajectory) for a controllable driftless nonlinear system. 7 Recently, the transverse function control approach has been effectively applied to practically stabilize any smooth reference trajectory, whether this trajectory is feasible or not, for underactuated mobile robots 8 and marine surface vehicles, 9,[27][28][29] where the calculations of transverse functions or/and stability analysis usually require an accurate vehicle model (see Remarks 4 and 5 presented in this paper for detailed discussions and technical analyses). In an uncertain maritime environment, however, an accurate model may not be obtained a priori, eg, the hydrodynamic damping effects, [30][31][32][33] and the vehicle model usually suffers from external disturbances induced by ocean currents, winds, and waves (winds generated).…”

Containment control of continuous-time linear multi-agent systems with aperiodic sampling

“…The material in this paper was partially presented at the 33rd Chinese Control Conference, July 28-30, 2014, Nanjing, China. This paper was recommended for publication in revised form by Associate Editor Tamas e.g., consensus (Jadbabaie, Lin, & Morse, 2003;Liu, Xie, & Wang, 2010;Olfati-Saber & Murray, 2004;Ren & Beard, 2005), formation control (Ding, Yan, & Lin, 2010;Do, 2012;Lin, Francis, & Maggiore, 2005), rendezvous (Cortes, Martinez, & Bullo, 2006;Dong & Huang, 2013), flocking (Olfati-Saber, 2006;Zhang, Zhai, & Chen, 2011), and coverage control (Cortés, Martínez, Karatas, & Bullo, 2004;Zhai & Hong, 2013). As a kind of cooperative behavior, containment control of multiagent systems has been investigated a lot in recent years.…”