# Research on the Path Planning Algorithm of a Manipulator Based on GMM/GMR-MPRM
## 1 Introduction
With the popularity of reinforcement learning, people began to study path planning based on reinforcement learning. [PERSON] used the modern proximal policy optimization algorithm to learn a grasping task [19]. However, the path planning algorithm based on reinforcement learning requires much training time, so it cannot realize online path planning. In addition, path planning algorithms based on sampling always start planning from the beginning, while the LfD method aims to generate task trajectories from human teaching paths. LfD uses demonstration paths to simulate the free space and optimize the objectives. The most famous one is the DMPS method. Generally, the reference trajectory of DMPS can be obtained from the suboptimal teaching path with noise by the GMM/GMR or reinforcement learning method [20]. [PERSON] presented a task-trajectory learning algorithm based on a few human demonstrations, and the demonstrated data were processed by a hidden Markov model approach. A Bayesian optimization-based algorithm has designed to autonomously optimize the robot control parameters. The proposed HMM algorithm can select the most reliable demonstrated task trajectory [21]. However, the HMM algorithm cannot deal with the inconsistency of the working environment between task demonstration and task reproduction. Aiming at the problem of the LfD method not being able to deal with new obstacles in the environment, many scholars have made efforts to solve such problems. [PERSON] used the coupling terms in DMPS to solve path planning problems, and the coupling term can allow avoiding obstacles of different sizes in a reactive manner after learning from human demonstrations [22]. By estimating an unknown reward function from the demonstration and using the quasi-Newton strategy to learn the parameters of the reward function, [PERSON] realized the path planning [23]. However, these algorithms are generally based on nonlinear optimization, which may fall into local minima. In order to use the prior knowledge of LfD, [PERSON] and [PERSON] proposed a method called the Attractor-Guided Planner (AGP), wherein each attractor point works as a replacement of the random sampling strategy in the original RRT. The results showed that the AGP planner is well suited for dynamic tasks in dynamic environments [24]. [PERSON] used Principal Component Analysis (PCA) to increase the probability of finding collision-free samples in a space with low clearance [25]. [PERSON] used the PCA algorithm to find the joint synergy of different areas in the configuration space according to the demonstration and used the joint synergy to determine the expansion of the tree based on the basic RRT [26]. [PERSON] presented a search-based planning method with experience graphs. The experience graphs can be generated in the configuration space by searching the search-space, and an effective path can be generated by searching the experience graphs with the weighted A-star algorithm [27; 28]. Although traditional motion planning algorithms have certain adaptive capabilities, they can only find a feasible path from the starting point to the target point. For complex tasks, they cannot guarantee that the planned path will pass through all key points, and the cost of designing a specific loss function for each task is high. Although LfD does not require defining the loss function manually, it cannot demonstrate all the possibilities of a task, so the adaptability is poor. Therefore, this paper proposes a path planning algorithm called the GMM/GMR-MPRM. The algorithm combines the advantages of the LfD algorithm and the motion planning to realize the path planning algorithm and uses the feasible space of the task trajectory obtained by the LfD as the sampling space of the MPRM algorithm. The algorithm can improve the success rate of path planning and maintain the similarity of the original task trajectory simultaneously.