Sampling of Pareto-Optimal Trajectories using Progressive Objective Evaluation in Multi-Objective Motion Planning

In this paper, we introduce a Markov chain Monte Carlo (MCMC) method to solve multi-objective motion-planning problems. We formulate the problem of finding Pareto-optimal trajectories as a problem of sampling trajectories from a Pareto-optimal set. We define an implicit uniform distribution over the Pareto-frontier using a dominance function and then sample in the space of trajectories. The nature of MCMC guarantees the convergence to the Pareto-frontier, while the uniform distribution ensures the diversity of the trajectories. We also propose progressive objective evaluation to increase efficiency in problems with expensive-to-evaluate objective functions. This enables determination of dominance relationship between trajectories before they are entirely evaluated. We finally analyze the effectiveness of the framework and its applications in robotics.