A cross-validation approach to trajectory and shape reconstruction for rigid bodies

In this paper, a method is proposed for reconstructing the trajectory and shape of a rigid body in a damped environment from distributively collected, asynchronous data. In this problem setting, both the shape parameters of the rigid body and its trajectory are unknown. The shape/trajectory recovery problem is modeled as a minimization of energy dissipation under geometric and acceleration constraints. In order to solve this problem, a convex relaxation for the geometric constraint is introduced, and the geometric constraint is reinforced in a cross-validation stage to verify the parameters. In this manner the shape and the trajectory of the rigid body are reconstructed simultaneously. For simplicity, a two-dimensional ball is taken as the rigid body prototype and simulations demonstrate the efficacy of the algorithm.