C-space Entropy: A Measure for View Planning and Exploration for General Robot-Sensor Systems in Unknown Environments

Abstract

We consider the view planning problem where a range sensor is mounted on a robot mechanism with non-trivial geometry and kinematics. The robot-sensor system is required to explore the environment for obstacles and free space. We present an information theoretical approach in which the sensing action is viewed as reducing ignorance of the planning space, the C-space of the robot. The concept of C-space entropy is introduced as a measure of this ignorance. The next view in the planning process is so chosen that it maximizes the expected reduction of C-space entropy, called the maximal (expected) entropy reduction (MER) criterion. We derive closed-form expressions for expected entropy reduction for an idealized point field-of-view sensor under a Poisson point process model of the environment. We show via simulations and real experiments that the MER criterion is significantly more efficient in sensor-based path planning and exploration tasks than other purely physical space based criteria previously used in the literature.