# Finding Optimal Manipulator Arm Shapes to Avoid Collisions in a Static Environment
## 1 Introduction
### Overview of Related Work  
The following overview focuses on articles related to the topic of this paper--manipulator arm collision avoidance and manipulators with general shapes of arms. The most relevant articles with use cases that were as close to our research as possible were selected. Collision avoidance for industrial robotic manipulators is typically associated with the selection of a proper trajectory. This can be done either manually during robot programming (teaching), which requires a lot of time and experience, or, quite effectively, by autonomous path planning in the configuration space [1; 2; 3; 4; 5; 6]. Path planning can also be used in dynamically changing environments [7], where it can be beneficial to utilize some innovative methods, such as vision-based planning using neural networks [8]. As far as manipulators with a general shape of the links are concerned, there has been some related research, mostly focusing on theoretical and some practical issues of such manipulators--for example, real-time collision-free trajectory planning for manipulators with arbitrary shapes in point-to-point tasks [9], where the authors proposed a novel obstacle avoidance algorithm using a signed distance function to deal with collisions on the whole body of the manipulator. Changing the shape and kinematic structure of a robot has been used to allow adaptation of the same robot for different tasks, effectively replacing the need for additional degrees of freedom with the possibility to manually change the kinematic structure as needed. This principle is applied to a low-cost home service robot with four degrees of freedom composed of rigid joints and two deformable links [10; 11; 12]. The deformable manipulator can create a relatively dexterous and extended workspace with fewer joints by bending its deformable links. A kinematic chain that allows mechanical modifications to match the desired Denavit-Hartenberg parameter set in a wide range is introduced in [13]. Another common topic of research is continuum robots; for example, the authors in [14] try to deal with the problem that, despite extensive research in kinematic and dynamic modeling, the inaccuracies and shape deformation of the robot due to unknown loads and collisions with the anatomy make shape sensing important for intraoperative navigation. To address this issue, vision-based solutions have been explored to find the actual shape of the robot. A similar issue regarding finding the actual shape of a surgical robot during a medical procedure using a small number of X-ray projection images has been addressed in [15; 16]. General key issues involved in the design and implementation of continuum robots and the potential of these types of robots for enhanced productivity in novel applications are discussed in [17]. The challenges related to the control of continuum robots (stability and performance) emerging from the structural flexibility of such robots are addressed in [18] by presenting a robust tracking control approach using interval arithmetic and in [19] by a robust control for continuum robots that are modeled by Cosserat Rod theory. So-called soft robots are, to some extent, also related to this research. The design and modeling of joints for inflatable robotic arms for long-range inspection are investigated in [20]. The authors in [21] propose a novel soft inflatable arm for telepresence robots using a common and low-cost inflatable material with a low weight. The focus of this research is on joint compressed models, joint kinematic models, and kinematic models for the whole inflatable robot arm. As far as the possible mechanical construction of an arm with a changeable general shape is concerned, some research projects have focused on finding a method of making an object that can transform from a flexible into a rigid state and vice versa at will. [PERSON] et al.