Most computational models of protein-ligand interactions consider only the energetics of the final bound state of the complex and do not examine the dynamics of the ligand as it enters the binding site. We have developed a novel technique for studying the dynamics of protein-ligand interactions based on motion planning algorithms from the field of robotics. Our algorithm uses electrostatic and van der Waals potentials to compute the most energetically favorable path between any given initial and goal ligand configurations. We use probabilistic motion planning to sample the distribution of possible paths to a given goal configuration and compute an energy-based "difficulty weight" for each path. By statistically averaging this weight over several randomly generated starting configurations, we compute the relative difficulty of entering and leaving a given binding configuration. This approach yields details of the energy contours around the binding site and can be used to characterize and predict good binding sites. Results from tests with three protein-ligand complexes indicate that our algorithm is able to detect energy barriers around the true binding site that distinguish this site from other predicted low-energy binding sites.