Trajectory optimization for continuous ergodic exploration on the motion group SE(2)

Autonomous active sensing presents the need for control of sensor motion in both position and orientation. This paper presents a method of planning continuous search trajectories over the Euclidean motion group SE(2): The method allows one to calculate an optimal search trajectory with respect to a distribution representing probable information gain over the search space. The ergodicity of a trajectory with respect to the information distribution is used to formulate an objective function for a projection-based optimal control strategy. Results from previous work on ergodic trajectory optimization are extended to consider trajectories and information densities defined on SE(2).