# Path Planning Based on NURBS for Hyper-Redundant Manipulator Used in Narrow Space
## 1 Introduction  
With the development of aerospace technology, the demand for on-orbit services such as maintenance of space equipment and fuelling has become more and more urgent. In order to reduce costs and improve the efficiency of astronauts working outside the cabin, many countries or communities have adopted space robots [1] as an important development direction of spacecraft on-orbit services. In European and American, the space robotic arm is mainly carried in the extravehicular environment to assist astronauts to check and repair some space station faults, which reduces the workload of astronauts to a certain extent and avoids the hidden dangers of astronauts' operations in outer space [2; 3; 4]. Orbiting service robots for aerospace applications are generally divided into multi-footed crawling robots [5; 6; 7] and space-operating manipulators [8; 9; 10; 11]. For the routine operation tasks of the space station, such as surface wiping, target detection and grabbing, the space operation robot arm is generally used to complete the task. With the complexity of its operating environment and the narrowing of its working space, many researchers have set their sights on the research of continuous robots with more degrees of freedom and better bending characteristics [12]. Elastic objects are often used as the body support for continuous robots, and have good bending characteristics and barrier capabilities. It can show different corresponding configurations for differentenvironments and form a smooth curve. It has superior bending characteristics and strong obstacle avoidance ability. It also has strong motion flexibility, which is suitable for the narrowness with obstacles [13; 14; 15]. Most continuous snake robots achieve passive environmental adaptability through the flexibility of materials or structures [16; 17], to achieve the desired position in a complex environment. Nonetheless, this type of robot has low positioning accuracy under load and is hard to achieve accurate control in a small space [18]. The super-redundant hierarchical driven continuous robot can effectively solve the above problems. At present, there is little research on the structure design and motion planning of this type of robot [19; 20; 21]. In [20], a cable-driven hyper-redundant manipulator with 17 degrees of freedom is presented for narrow and complex environments. Based on the mechanical structure, the MDA + RRT algorithms is proposed for path planning considering the maximum deflection angle of joint. Although this method can be applied to the planning of small spaces, it cannot control the position of the fuselage of each cell of the continuum, and does not consider whether the envelope of the fuselage will collide with the environment. Obstacle avoidance motion is the motion planning of super-redundant manipulators. For the traditional intelligent algorithm's obstacle avoidance effect is not strong, scholars [22; 23; 24; 25; 26] proposed a path following motion method called follow end trajectory. The characteristic of following the end trajectory is that the links and joints of the super-redundant robotic arm move along the path curve in the restricted area, the entire robotic arm is as close to the path curve as possible in the movement to achieve the smallest possible stroke in space regional goals. According to analysis, most of the currently designed hyper-redundant manipulators have a series structure, which has low rigidity and poor bearing capacity. In addition, the joint cannot be guaranteed to be on the path curve with low accuracy. At the same time, the solution is complicated and the efficiency is low. Therefore, a hyper-redundant robotic arm trajectory-planning algorithm is provided in this paper. The robotic arm is composed of 8 UCR parallel joints connected in series. The UCR parallel joints have three degrees of freedom that rotate around the \(X\), \(Y\)-axis and move around the \(Z\)-axis. Parallel mechanism, which consists of a fixed platform, three branch chains, and a moving platform.