## 1 Introduction
Generally speaking, when a potential field is constructed, the robot in this field suffers the corresponding repellent force both from the goal and the obstacle simultaneously so as to prevent the robot from colliding with the obstacle. During this process, the goal generates the attractive field and the obstacle generates the repulsive field. The two fields act together on robots located in the artificial potential field to generate the desired motion trajectory [25; 35]. This approach has the characteristics of a simple structure and real-time underlying control. For these above reasons, this approach has been extensively used in mobile robotics [36; 37] and robotic manipulators [38] to achieve real-time obstacle avoidance and smooth trajectory control. Recently, new discoveries have been found in this research direction. According to [PERSON] and [PERSON]'s study, DMPs can combine with the artificial potential fields to avoid the related obstacles [13; 16; 23]. The artificial potential field can be seen as a coupling term added to the differential equation of DMPs directly, with the purposes to offer related direct feedback of the environment. Additionally, in [PERSON]'s study, he found that the static potential cannot generate a smooth trajectory, especially when the end effector moves towards the obstacle directly. To solve this problem, he used the dynamic potential field in conjunction with DMPs to avoid obstacles. This approach has been successfully used to avoid the point obstacles [13] and many static obstacles [23]. However, the obstacles in these papers are all considered as single points individually, without considering the spatially extended obstacles. Additionally, we have not found any paper systematically describing DMPs' generalization ability and its obstacle avoidance function in the autonomous manipulation of service robots. In this paper, we have detailed a general framework for WMRA to learn demonstrated motion and generalize it to a new environment even where existing obstacles are located on its motion path so as to help the elderly and disabled to live independently in an unstructured home environment. This framework is mainly based on the DMPs-DPF approach, which is an approach of dynamic movement primitives combined with dynamic potential fields. The main achievement of this paper is that it systematically describes the whole realization process of WMRA's autonomous manipulation, including learning, generalization, and obstacle avoidance with any shape and size obstacles. Unlike the traditional path planning method, this approach can quickly generate a new path that conforms to the user's operating habits without tedious programming process and heavy consumption of time. This characteristic is particularly suitable and preferred by the users of WMRA to accept the assistive help from WMRA without any panic and fear. It is worth highlighting that the users of WMRA are just located in the operating space of the robotic arm, which is obviously different from other service robots. Additionally, this approach can also be used in the field of human-robot collaboration [39; 40], which has similar work scenes with the WMRA. The rest of this paper is organized as follows. In Section 2, we described the dynamic system framework for movement generation, mainly including the introduction of the dynamic movement primitives model and the learning and generalization process of DMPs. In Section 3, we introduced the overall framework of the DMPs-DPF approach and mainly described the coupling term for obstacle avoidance. In Section 4, we carried out a set of experiments of placing a cup on the table, including without obstacle, with a small spherical obstacle, and with a large cuboid obstacle. We concluded and briefly introduced the future research trends in Section 5.