2018/09/10 by Anthony M. Bloch, Bloch, Anthony, Margarida Camarinha +3
Computer Science · Engineering · #Control and Dynamics of Mobile Robots #FOS: Electrical engineering #FOS: Mathematics #Guidance and Control Systems #Optimization and Control (math.OC) #Robotic Path Planning Algorithms #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1809.03168
openalex publication_date 2018/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This work is devoted to studying dynamic interpolation for obstacle avoidance. This is a problem that consists of minimizing a suitable energy functional among a set of admissible curves subject to some interpolation conditions. The given energy functional depends on velocity, covariant acceleration and on artificial potential functions used for avoiding obstacles. We derive first-order necessary conditions for optimality in the proposed problem; that is, given interpolation and boundary conditions we find the set of differential equations describing the evolution of a curve that satisfies the prescribed boundary values, interpolates the given points and is an extremal for the energy functional. We study the problem in different settings including a general one on a Riemannian manifold and a more specific one on a Lie group endowed with a left-invariant metric. We also consider a sub-Riemannian problem. We illustrate the results with examples of rigid bodies, both planar and spatial, and underactuated vehicles including a unicycle and an underactuated unmanned vehicle.