Modeling and Analysis of Human Navigation with Crossing Interferer Using Inverse Optimal Control

The walking paths of humans in everyday life exhibit specific characteristics. Our investigation takes the well-established perspective that human locomotion approximately fulfills suitable optimality principles when walking from a starting position to a designated end position. Here, we address the special task of collision avoidance with a crossing interferer. While our model of the dynamics is quite simple, we focus on the task of determining the cost function out of a parametric family, that results in a best fit between the corresponding optimal control-based navigation and given recorded data of human navigation. The resulting bilevel optimization problem combines an optimal control problem on the lower level with a data fitting problem on the upper level. Our solution strategy uses the first-order optimality conditions of the (discretized) optimal control problem to transform the bilevel problem to a standard (one-level) optimization problem. Modeling aspects concerning the walking process and especially the interfering person are discussed. Since human walking motions with a crossing interferer do not seem to be globally optimal, an MPC-like approach distinguishing between obstacle avoidance and free motion is introduced and optimization results using recorded human data are presented.