Title: Convex strategies for trajectory optimisation: application to the Polytope Traversal Problem
Abstract: Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution.
Assuming that the total duration of the trajectory is given (ie time is a constant rather than a variable) is well-known to reduce significantly the complexity of the problem: a feasible guess can often be obtained by allocating an arbitrary large amount of time for the trajectory to complete. However for unstable dynamical systems such as humanoid robots, this ``quasi-static'' assumption does not always hold: sometimes only a dynamic motion can efficiently solve the problem. We propose a conservative formulation of the TO problem that simultaneously computes a feasible path and its time allocation. The problem is solved as an efficient convex optimisation problem guaranteed to converge to a locally optimal solution. The interest of the approach is illustrated with the computation of feasible trajectories that traverse sequentially a sequence of polytopes that represent the linear constraints that apply on the problem.
I will detail the simplifying assumptions that led to this efficient formulation and discuss how the approach advances the state of the art.