Variational point-obstacle avoidance on Riemannian manifolds
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In this paper, a variational point-obstacle avoidance problem on complete Riemannian manifolds is studied, which consists of minimizing an energy functional depending on the velocity, covariant acceleration and a repulsive potential function used to avoid an static obstacle.Abstract:
In this paper, we study variational point-obstacle avoidance problems on complete Riemannian manifolds The problem consists of minimizing an energy functional depending on the velocity, covariant acceleration and a repulsive potential function used to avoid an static obstacle given by a point in the manifold, among a set of admissible curves We derive the dynamical equations for stationary paths of the variational problem, in particular on compact connected Lie groups and Riemannian symmetric spaces Numerical examples are presented to illustrate the proposed methodread more
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Collision Avoidance of Multiagent Systems on Riemannian Manifolds
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Local minimizers for variational obstacle avoidance on Riemannian manifolds
TL;DR: In this paper , a variational obstacle avoidance problem on complete Riemannian manifolds is studied, where the goal is to minimize an action functional, among a set of admissible curves, which depends on an artificial potential function used to avoid obstacles.
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Variational Obstacle Avoidance with Applications to Interpolation Problems in Hybrid Systems
TL;DR: In this paper, the authors study variational obstacle avoidance problems on complete Riemannian manifolds and apply the results to the construction of piecewise smooth curves interpolating a set of knot points in systems with impulse effects.
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Riemannian cubics close to geodesics at the boundaries
TL;DR: In this article , the existence and uniqueness of Riemannian cubics under boundary conditions on position and velocity was investigated, where the boundary data in a neighborhood of geodesic boundary data was considered.
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Variational Obstacle Avoidance with Applications to Interpolation Problems in Hybrid Systems
TL;DR: In this article, the authors study variational obstacle avoidance problems on complete Riemannian manifolds and apply the results to the construction of piecewise smooth curves interpolating a set of knot points in systems with impulse effects.
References
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Real-time obstacle avoidance for manipulators and mobile robots
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.
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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.
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Nonholonomic mechanics and control
TL;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.
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Geometric control of mechanical systems
Francesco Bullo,Andrew D. Lewis +1 more
TL;DR: In this article, a comprehensive set of modeling, analysis and design techniques for a class of simple mechanical control systems is presented, that is, systems whose Lagrangian is kinetic energy minus potential energy.