We present a probabilistic method for path planning that considers trajectories constrained by both the environment and an ensemble of restrictions or preferences on preferred motions for a moving robot. Our system learns constraints and preference biases on a robot޲s motion from examples, and then synthesizes behaviors that satisfy these constraints. This behavior can encompass motions that satisfy diverse requirements such as a sweep pattern for floor coverage, or, in particular in our experiments, satisfy restrictions on the robot޲s physical capabilities such as restrictions on its turning radius. Given an approximate path that may not satisfy the required conditions, our system computes a refined path that satisfies the constraints and also avoids obstacles. Our approach is based on a Bayesian framework for combining a prior probability distribution on the trajectory with environmental constraints. The prior distribution is generated by decoding a Hidden Markov Model, which is itself is trained over a particular set of preferred motions. Environmental constraints are modeled using a potential field over the configuration space.

This paper poses the requisite theoretical framework and demonstrates its effectiveness with several examples.