# Initial Estimation of Kinematic Structure of a Robotic Manipulator as an Input for Its Synthesis
## 1 Introduction  
Nowadays, manufacturing industry, the most common type of robotic manipulator has six serial axes (degrees of freedom--DoFs) that are arranged in a so-called universal kinematic structure, e.g., the robots of ABB, KUKA, Fanuc, Yaskawa, and many others. In a very simplified way, the typical process for the deployment of a robot is to analyse the manufacturing process and workplace area first, followed by the choosing of a universal robotic manipulator and simulating the process. If the manipulator can reach the desired poses and fulfil the given task, further deployment can be considered. However, using this universal kinematic structure is not always necessary, when a manipulator with fewer axes is suitable to perform the given task, or even possible, if the universal manipulator can face unavoidable collisions in an already existing environment. Additionally, they might not fulfil the desired advanced operation conditions, such as manipulability [1] and kinematic reliability [2]. Therefore, researchers are focused on the topic of the synthesis of the kinematic structure of manipulators, which means finding such a kinematic structure that is optimal for a given task. This approach of deployment of highly customised manipulators may lead to benefits like lowered energy consumption, accelerated manufacturing process cycles, or deploying manipulators in highly dense-built workplaces. An example of such a general structure is presented by [PERSON] et al., who delivered the so-called curved manipulator (CuMa) [3] with possible modifications of its structure during the operational process [4]. This is achieved by changing the temperature in the links so they become flexible. A different approach to a deformable manipulator was taken by [PERSON] et al. [5], where the links are composed of a few components and it is possible to change the orientation between them. [PERSON] et al. [6] uses air pressure to change thekinematic structure of the presented malleable robot. The custom design of manipulators is desired not only in the manufacturing industry, but for example, in healthcare for helping with human upper limb rehabilitation [7] and shoulder joint rehabilitation [8]. There are two approaches to the synthesis of the kinematic structure of a manipulator. Analytically, it was solved by [PERSON] et al. [9] in the synthesis of three-revolute spacial chain for five poses. However, once a path becomes more complex and requires more degrees of freedom (more manipulator axes), the numerical approach is applied utilising optimisation algorithms. Among them, evolutionary robotics with genetic algorithms (GA) are probably the most common. [PERSON] et al. [10] used an adaptive multi-chromosome evolutionary algorithm to build a modular manipulator. Furthermore, GA can be used to build a manipulator from adaptive modules to perform a desired task [11]. [PERSON] et al. [12] compared straight, rounded, and curved mechanism links synthesised using GA. [PERSON] et al. created so-called pseudo-joints (links which can be modified) and proposed a GA that tries to find the kinematic structure with the best manipulability [13]. It was later verified in an experiment with a real manipulator [14]. The synthesis of a parallel manipulator is addressed in [15]. As an example of non-industrial application, the work by [PERSON] et al. [16] deals with the optimisation of an eight-DoFs upper-limb exoskeleton. In addition to GAs, the global optimum of an objective function can be searched with Simulated Annealing algorithm [17] or by a heuristic-guided tree search algorithm [18]. Another numerical method for finding the optimal manipulator for a given task is to search for a local minimum of an objective function. To solve this, a nonlinear programming (NLP) can be used, as it was implemented by [PERSON] et al. [19] for the design of a modular manipulator. In the paper, an optimal kinematic structure was proposed based on the minimisation of the joint torques.