Collision avoidance for multiple Lagrangian dynamical systems with gyroscopic forces

Abstract

This article introduces a novel methodology for dealing with collision avoidance for groups of mobile robots. In particular, full dynamics are considered, since each robot is modeled as a Lagrangian dynamical system moving in a three-dimensional environment. Gyroscopic forces are utilized for defining the collision avoidance control strategy: This kind of forces leads to avoiding collisions, without interfering with the convergence properties of the multi-robot system's desired control law. Collision avoidance introduces, in fact, a perturbation on the nominal behavior of the system: We define a method for choosing the direction of the gyroscopic force in an optimal manner, in such a way that perturbation is minimized. Collision avoidance and convergence properties are analytically demonstrated, and simulation results are provided for validation purpose.

Reactive Magnetic-Field-Inspired Navigation Method for Robots in Unknown Convex 3-D Environments

“…It is assumed that the robot only knows the surrounding environment as far as r l in all directions from the robot's position. We compare the performance of the proposed magnetic-field-inspired (MFI) algorithm with several reactive algorithms (particularly the APF [11], variable speed force field (VSFF) [12], circular field (CF) [18], and gyroscopic force (GF) method [24], [25]). These reactive methods are chosen since they do not rely on the availability of the environmental map, do not need the information regarding the obstacle's shape or geometry, and can be applied in a 3D environment with arbitrary-shaped obstacles.…”

“…There were also recent efforts to apply the concept of gyroscopic forces in 3D for fully-actuated and under-actuated system [22] but the method is limited to cylindrical and spherical obstacles with perfectly-known geometry. Gyroscopic-force-based algorithms were also used for multi-robot formation in 3D [23]- [25]. However, none of these works deals with the problem beyond the scope of collision avoidance among point-like agents for formation control.…”

“…Our approach also outperforms previous magnetic-field-inspired navigation methods [16]- [18] since it does not rely on prior knowledge of the obstacles' geometrical properties. Our approach also provides a clear improvement over gyroscopic force based approaches [19]- [25] as our method is designed to be generic so that it can be used not only for planar mobile robots but also for robots in 3D environments with an unknown arbitrarily shaped convex obstacle. This work extends our previous work which describes the preliminary formulation of the magnetic-field-inspired navigation method applied to mobile robot operating in planar environments only [26].…”

Interconnection and Damping Assignment Passivity–Based Control of an Underactuated 2–DOF Gyroscope

“…(b) The gyroscopic forces Γ(q)q, where Γ : R n → R n×n , are forces that conserve energy since they are perpendicular to the velocity of the mechanism, implying that they do not realize any work (Sabattini et al, 2017). Formally, a force…”

“…Property 2. The gyroscopic force is always perpendicular to the velocity of the mechanism, doing no work; this property guarantees that they do not modify the convergence characteristics of the desired control laws (Sabattini et al, 2017).…”