Probability-Based Optimal Path Planning for Two-Wheeled Mobile Robots

Most dynamic systems show uncertainty in their behavior. Therefore, a deterministic model is not sufficient to predict the stochastic behavior of such systems. Alternatively, a stochastic model can be used for better analysis and simulation. By numerically integrating the stochastic differential equation or solving the Fokker-Planck equation, we can obtain a probability density function of the motion of the system. Based on this probability density function, the path-of-probability (POP) method for path planning has been developed and verified in simulation. However, there are rooms for more improvements and its practical implementation has not been performed yet. This paper concerns formulation, simulation and practical implementation of the path-of-probability for two-wheeled mobile robots. In this framework, we define a new cost function which measures the averaged targeting error using root-mean-square (RMS), and iteratively minimize it to find an optimal path with the lowest targeting error. The proposed algorithm is implemented and tested with a two-wheeled mobile robot for performance verification.