Abstract
We develop a set of novel autonomous controllers for multiple point-mass robots or agents in the presence of wall-like rectangular planes in three-dimensional space. To the authors’ knowledge, this is the first time that such a set of controllers for the avoidance of rectangular planes has been derived from a single attractive and repulsive potential function that satisfies the conditions of the Direct Method of Lyapunov. The potential or Lyapunov function also proves the stability of the system of the first-order ordinary differential equations governing the motion of the multiple agents as they traverse the three-dimensional space from an initial position to a target that is the equilibrium point of the system. The avoidance of the walls is via an approach called the Minimum Distance Technique that enables a point-mass agent to avoid the wall from the shortest distance away at every unit time. Computer simulations of the proposed Lyapunov-based controllers for the multiple point-mass agents navigating in a common workspace are presented to illustrate the effectiveness of the controllers. Simulations include towers and walls of tunnels as obstacles. In the simulations, the point-mass agents also show typical swarming behaviors such as split-and-rejoin maneuvers when confronted with multiple tower-like structures. The successful illustration of the effectiveness of the controllers opens a fertile area of research in the development and implementation of such controllers for Unmanned Aerial Vehicles such as quadrotors.
Highlights
(LbCS), essentially an APF method, for the control and stability of a system point-mass mobile robots that, in theory, can take on reasonably high velocities. e Lyapunov-based control scheme (LbCS) has been employed to warrant point and posture stabilities in the sense of Lyapunov for MPC for various robotic systems, such as car-like mobile robotic systems [4], mobile manipulators [16], tractor-trailer systems [12, 17], and swarming [18]
Contributions. e novelty of this paper is the ease in developing autonomous controllers for the avoidance of three-dimensional wall-like rectangular planes by a mobile robot or agent while it is in motion using a technique known as the Minimum Distance Technique (MDT). e ability to do this opens up many possibilities
For instance, with autonomous Unmanned Aerial Vehicles (UAVs), it is possible to model a drone’s performance in the face of such obstacles as buildings and tunnel walls, and its maneuverability inside buildings clustered with rectangular objects and exited
Summary
We construct the components of the Lyapunov function. We assume that Pi has a priori knowledge of the entire workspace. e principle objective is to construct the Lyapunov function from which we derive the nonlinear velocity control inputs vi(t), wi(t), and ui(t) for i 1, . . . , n such that Pi navigates and reaches its target configuration, avoiding any obstacle, whether fixed, moving, or artificial, while it is in motion. e design of the nonlinear control inputs is captured in Figure 3, clearly illustrating the roles of the individual components in the design of the control scheme. All obstacles, whether it is fixed or moving, with respect to the kinodynamic constraints that are tagged with the robotic system including the constraints on velocity and angles before reaching its objective target. Once it has reached the target, it essentially means that it has accomplished the task that was given to the robot, and it needs to stop at the target configuration. This means that the energy of the robotic system needs to be zero at the target configuration; that is, the nonlinear controllers need to vanish at the target To achieve this and to ensure the convergence of Pi to its target configuration, we consider the auxiliary function of the form
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