  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.
