  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.

Artificial Intelligence