Stabilization of a Hierarchical Formation of Unicycle Robots with Velocity and Curvature Constraints

Abstract

Abstract-The paper proposes a new geometric approach to the stabilization of a hierarchical formation of unicycle robots. Hierarchical formations consist of elementary leader-follower units disposed on a rooted tree: each follower sees its relative leader as a fixed point in its own reference frame. Robots' linear velocity and trajectory curvature are forced to satisfy some given bounds. The major contribution of the paper is to study the effect of these bounds on the admissible trajectories of the main leader. In particular, we provide recursive formulas for the maximum velocity and curvature allowed for the main leader, so that the robots can achieve the desired formation while respecting their input constraints. An original formation control law is proposed and the asymptotic stabilization is proved. Simulation experiments illustrate the theory and show the effectiveness of the proposed designs.

A dϕ-Strategy: Facilitating Dual-Formation Control of a Virtually Connected Team

“…Formation control can be defined as controlling the configuration or state of a team of agents en route to a target, normally maintaining constant their relative locations, hence maintaining the formation type and pattern [8][9][10][11]. Indeed, scalable formations with increased heterogeneity are evidently deployed to satisfy stringent time, labor, and cost demands.…”

“…While the leadcarrier approach is known for its poor disturbance rejection properties [15] and dependence placed upon a single agent, it is commonly utilized in literature because of its simplicity, scalability, and ability to contain an array of formations with richer specifications and complexities [3,9,11,[15][16][17]. This work deploys a new lead-carrier scheme to establish and control a team fixed in a dual-formation, for the first time.…”

Saturated control of time-varying formations and trajectory tracking for unicycle multi-agent systems

“…Theorem 1: Consider a group of unicycle agents with the kinematics of the agent , ∈ 1,2, … , , described by (6). Suppose that the reference trajectory of agent is given by (9), and this trajectory satisfies the non-holonomic constraint , sin , + , cos , 0.…”

“…Formation control with saturation constraints on control signals, as studied in [6], is less often in the literature, although such constraints are present in practice, hampering stability and performance of formation control. Control of time-varying formations of unicycles is rarely found in the literature; reference [2] is just an exception.…”

Consensus of Fractional-Order Multiagent Systems with Nonuniform Time Delays

“…During recent years, consensus problems of multiagent systems have attracted a great deal of attention due to their enormous potential applications in many areas such as the formation control of multirobot systems [1], cooperative control of unmanned aerial vehicles [2], and distributed information filtering [3]. In the past decade, research results have been continuously springing up about consensus problems of various multiagent systems.…”