Bayesian inference has many advantages in robotic motion planning over four perspectives: The uncertainty quantification of the policy, safety (risk-aware) and optimum guarantees of robot motions, data-efficiency in training of reinforcement learning, and reducing the sim2real gap when the robot is applied to real-world tasks. However, the application of Bayesian inference in robotic motion planning is lagging behind the comprehensive theory of Bayesian inference. Further, there are no comprehensive reviews to summarize the progress of Bayesian inference to give researchers a systematic understanding in robotic motion planning. This paper first provides the probabilistic theories of Bayesian inference which are the preliminary of Bayesian inference for complex cases. Second, the Bayesian estimation is given to estimate the posterior of policies or unknown functions which are used to compute the policy. Third, the classical model-based Bayesian RL and model-free Bayesian RL algorithms for robotic motion planning are summarized, while these algorithms in complex cases are also analyzed. Fourth, the analysis of Bayesian inference in inverse RL is given to infer the reward functions in a data-efficient manner. Fifth, we systematically present the hybridization of Bayesian inference and RL which is a promising direction to improve the convergence of RL for better motion planning. Sixth, given the Bayesian inference, we present the interpretable and safe robotic motion plannings which are the hot research topic recently. Finally, all algorithms reviewed in this paper are summarized analytically as the knowledge graphs, and the future of Bayesian inference for robotic motion planning is also discussed, to pave the way for data-efficient, explainable, and safe robotic motion planning strategies for practical applications.

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