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Optimal obstacle avoidance trajectory generation using the root locus principle

This paper details a framework to create a set of trajectories, all guaranteed to avoid known obstacles, using the generalized root locus (GRL). The creation of harmonic potential fields followed by generalized root locus analysis leads to a set of parameterized curves, whose gradient dynamics uniquely generate the curves. Next, the curve generation is addressed by considering three reparameterizations of the GRL which propagate at different speeds. After defining the set of admissible paths via the GRL, the paper covers a simpler method to solve the minimum time problem in the new framework with and without the state dependent speed constraints along the path. An example of the minimum time problem with two different constraints is included at the end.