## 4 Geometrical Synthesis with Flower Pollination Algorithm  
The kinematic chain structure was chosen during structural synthesis based on the below defined requirements and presumptions. * Drives should be installed on the platform directly (to reduce mass of the elements attached to the structure). * The mechanism should allow to follow the desired trajectory with a single drive only. * The total number of freedom degrees of a single mechanism equals 4 (Figure 5). For synthesis purposes, this can be reduced to 3 as the driving motor introduces the \(f_{2}\) independently to the suspension mechanism. It can also be noted that turning can be obtained with a simple gear attached at a fixing point of the BLDC motor. Taking these assumptions into consideration, only two degrees of freedom have to be reproduced with a suspension kinematic chain. * Both translational and rotational joints can be used. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Device** & **Raspberry Pi Pico** & **STM32F103R** & **ESP32** \\ \hline Power consumption & \(<\)1 W & \(<\)1 W & 5 W \\ Core & Raspberry RP2040 ARM Cortex M0+ & ARM Cortex M & Dual-Core Tensilica LX6 \\ Clock rate & 133 MHz & 72 MHz & 240 MHz \\ User memory size & 2 MB & 64 kB & 4 MB \\ RAM & 264 kB & 20 kB & 520 kB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The specifications of the programmable devices used in the project, compiled based on refs. [44, 45, 46]. Figure 4: The position control structure applied for the chassis. A four-bar ABCD linkage mechanism was selected as the base of the construction (Figure 6). The simple structure was chosen because of two fixing points placed directly on the platform chassis. Both of the mentioned points were also the propulsive elements--the rotational joint (in point A) was responsible for level, and the translational joint (between points C and D--second fixing point) was designed to performs several steps of the robot. After selection of the fixing points, the heavy drives were attached to the chassis. Therefore, the inertia of the mechanism was reduced. The AB rocker (_a crank_) was considered as a constant length element, while the CD bar (_a follower_) was designed with an adjustable length. Such ability, as well as high torque and easy control, were provided through a linear actuator. If the required position is obtained, the drive can be switched off, which leads to low power consumption. The in-wheel BLDC motor was combined with an \(e\) element (in point W), connected to a four-bar mechanism (in point B) and oriented with BC linkage (_a coupler_). The geometry was defined; however, the exact lengths of the elements were required to assure appropriate operation. The following conditions were assumed for the construction:  
* A linear trajectory, perpendicular to ground level;
* Movement along the desired trajectory proportional to the controlled angle (in joint A). The above issue is related to the geometrical synthesis task. Different approaches may be used to solve the problem. In the presented work, the flower pollination algorithm (FPA) was used to find the optimal configuration of the kinematic chain lengths. The method was firstly described by [PERSON] [47]. It was inspired with observations of pollination phenomena. Two ways of pollination can be taken into consideration with the presence of a single or more species. The self-pollination or geitonogamy process describes  
Figure 5: Required degrees of freedom. Figure 6: Four-bar linkage suspension structure of analyzed robot. the situation in which pollen of a single specimen is moved between its flowers. Such a process is considered as local, where the distance between two flowers of the same plant is marginal. A unique case, called autogamy, is even more local and is where pollen is moved between the anther and the stigma of an individual flower. The method observed in nature requires external pollinators such as insects or birds. The pollen of a single plant adheres to legs, antennae, feathers, etc.