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