Collision avoidance based on separating planes for feet trajectory generation

In this paper, we present a formulation of the collision avoidance constraints that relies on the use of separating planes instead of a distance function. This formulation has the advantage of being defined and continuously differentiable in every situation. Because it introduces additional variables to the optimization problems, making it bigger and potentially slowing down its resolution, we propose a different resolution method that takes advantage of the independence of the variables, to form two subproblems that can be solved efficiently in an alternate problem fashion. We present some preliminary results using this approach in order to highlight its potential and promises in terms of convergence speed and robustness.