Holistic vision of Inverse Optimal Control

Inverse Optimal Control (IOC) is a problem that exists in many fields. In the context of human motion analysis, many methods for solving this problem have been proposed. This paper presents the Projected Inverse Optimal Control (PIOC) approach which puts forward a simple and complete vision of the problem. PIOC is composed of several independent elements allowing to cover problems of dimensioning, measurement noise and reliability of solution. The first element is the parameterization of the data, allowing to reduce the dimensions of the problem. The second element corresponds to the decoupling of the conditions including the conditions of identifiability of the parameters, singularity of the problem and feasibility of the solution. The last element refers to the choice of solution. We show with this approach that the classical solution methods are in fact projections in the space of trajectories. PIOC also allows us to propose a simple algorithm for the choice of basis, a recurrent problem in IOC