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Variational collision and obstacle avoidance of multi-agent systems on Riemannian manifolds
11 Oct 2019-
TL;DR: In this paper, a path planning problem from a variational approach to collision and obstacle avoidance for multi-agent systems evolving on a Riemannian manifold is studied, which consists of finding non-intersecting trajectories between the agent and prescribed obstacles on the workspace, among a set of admissible curves, to reach a specified configuration, based on minimizing an energy functional that depends on the velocity, covariant acceleration and an artificial potential function used to prevent collision with the obstacles and among the agents.
Abstract: In this paper we study a path planning problem from a variational approach to collision and obstacle avoidance for multi-agent systems evolving on a Riemannian manifold. The problem consists of finding non-intersecting trajectories between the agent and prescribed obstacles on the workspace, among a set of admissible curves, to reach a specified configuration, based on minimizing an energy functional that depends on the velocity, covariant acceleration and an artificial potential function used to prevent collision with the obstacles and among the agents. We apply the results to examples of a planar rigid body, and collision and obstacle avoidance for agents evolving on a sphere.
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01 Jul 2020
TL;DR: A variational approach for decentralized collision avoidance of multiple agents evolving on a Riemannian manifold is introduced, and the global existence of extrema for the energy functional is shown.
Abstract: We introduce a variational approach for decentralized collision avoidance of multiple agents evolving on a Riemannian manifold, and we derive necessary conditions for extremal. The problem consists of finding non-intersecting trajectories of a given number of agents sharing only the information of relative positions with respect to their nearest neighbors, among a set of admissible curves, such that these trajectories are minimizers of an energy functional. The energy functional depends on covariant acceleration and an artificial potential used to prevent collision among the agents. We show the global existence of extrema for the energy functional. We apply the results to the case of agents on a compact and connected Lie group. Simulation results are shown to demonstrate the applicability of the results.
6 citations
27 Nov 2020
TL;DR: Two control forces, formation keeping force and generalized Lorentz force, are proposed to adaptively maintain the formation pattern while avoiding obstacles and result in a flexible overall obstacle avoidance effect for formation systems demonstrated by numerical simulations.
Abstract: We consider the obstacle avoidance problem of formation vehicles in an obstacle laden environment. Two control forces, formation keeping force and generalized Lorentz force, are proposed to adaptively maintain the formation pattern while avoiding obstacles. The methods result in a flexible overall obstacle avoidance effect for formation systems demonstrated by numerical simulations.
1 citations
TL;DR: The objective is to enable multiple UAVs to collaborate toward a common goal, as one would find in a remote sensing setting, using an agreement protocol carried out by the multi-agents using local information, and without external user input.
Abstract: Unmanned Aerial Vehicles (UAVs) have been increasingly used in the context of remote sensing missions such as target search and tracking, mapping, or surveillance monitoring. In the first part of our paper we consider agent dynamics, network topologies, and collective behaviors. The objective is to enable multiple UAVs to collaborate toward a common goal, as one would find in a remote sensing setting. An agreement protocol is carried out by the multi-agents using local information, and without external user input. The second part of the paper focuses on the equations of motion for a specific type of UAV, the quadcopter, and expresses them as an affine nonlinear control system. Finally, we illustrate our work with a simulation of an agreement protocol for dynamically sound quadcopters augmenting the particle graph theoretic approach with orientation and a proper dynamics for quadcopters.
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TL;DR: In this article, an optimal control of robotic systems with a Riemannian geometric view is given, and a formulation of the PMP using the intrinsic geometry of the configuration space.
Abstract: The aim of this paper is to give some existence results of optimal control of robotic systems with a Riemannian geometric view, and derive a formulation of the PMP using the intrinsic geometry of the configuration space. Applying this result to some special cases will give the results of avoidance problems on Riemannian manifolds developed by A. Bloch et al. We derive a formulation of the dynamic programming approach and apply it to the quadratic costs and extend the linear quadratic regulator to robotic systems on Riemannian manifolds and giving an equivalent Riccati equation. We give an optimisation aspect of the Riemannian tracking regulator of F. Bullo and R.M. Murray. Finally, wee apply the theoretical developments to the regulation and tracking of a rigid body attitude.
References
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TL;DR: This paper reformulated the manipulator con trol problem as direct control of manipulator motion in operational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and geometric transformation.
Abstract: This paper presents a unique real-time obstacle avoidance approach for manipulators and mobile robots based on the artificial potential field concept. Collision avoidance, tradi tionally considered a high level planning problem, can be effectively distributed between different levels of control, al lowing real-time robot operations in a complex environment. This method has been extended to moving obstacles by using a time-varying artificial patential field. We have applied this obstacle avoidance scheme to robot arm mechanisms and have used a new approach to the general problem of real-time manipulator control. We reformulated the manipulator con trol problem as direct control of manipulator motion in oper ational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and kine matic transformation. Outside the obstacles' regions of influ ence, we caused the end effector to move in a straight line with an...
6,515 citations
Book•
01 Jul 1990
TL;DR: This paper reformulated the manipulator control problem as direct control of manipulator motion in operational space-the space in which the task is originally described-rather than as control of the task's corresponding joint space motion obtained only after geometric and kinematic transformation.
Abstract: This paper presents a unique real-time obstacle avoidance approach for manipulators and mobile robots based on the artificial potential field concept. Collision avoidance, tradi tionally considered a high level planning problem, can be effectively distributed between different levels of control, al lowing real-time robot operations in a complex environment. This method has been extended to moving obstacles by using a time-varying artificial patential field. We have applied this obstacle avoidance scheme to robot arm mechanisms and have used a new approach to the general problem of real-time manipulator control. We reformulated the manipulator con trol problem as direct control of manipulator motion in oper ational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and kine matic transformation. Outside the obstacles' regions of influ ence, we caused the end effector to move in a straight line with an...
3,063 citations
Book•
01 Jan 1975
TL;DR: In this article, the authors present a revised edition of one of the classic mathematics texts published in the last 25 years, which includes updated references and indexes and error corrections and will continue to serve as the standard text for students and professionals in the field.
Abstract: This is a revised printing of one of the classic mathematics texts published in the last 25 years. This revised edition includes updated references and indexes and error corrections and will continue to serve as the standard text for students and professionals in the field.Differential manifolds are the underlying objects of study in much of advanced calculus and analysis. Topics such as line and surface integrals, divergence and curl of vector fields, and Stoke's and Green's theorems find their most natural setting in manifold theory. Riemannian plane geometry can be visualized as the geometry on the surface of a sphere in which "lines" are taken to be great circle arcs.
1,929 citations
Book•
01 Jan 2003TL;DR: In this paper, the authors propose energy-based methods for stabilizing nonholonomic systems using non-holonomic control theory based on geometric properties of the system's properties. But they do not discuss the energy-independent methods of stabilisation.
Abstract: Introduction.- Mathematical Preliminaries.- Basic Concepts in Geometric Mechanics.- Introduction to Aspects of Geometric Control Theory.- Nonholonomic Mechanics.- Control of Mechanical and Nonholonomic Systems.- Optimal Control.- Stability of Nonholonomic Systems.- Energy-Based Methods for Stabilization.- References.- Index.
1,328 citations