COMPUTER SIMULATIONS OF CONTROLLABILITY PROCESSES FOR ROBOTIC WHEELED PLATFORMS TAKING INTO ACCOUNT RESTRICTIONS OF JERK MOTIONS - Alyokhina, Svitlana; Nevliudov, Igor; Romashov, Yurii (INNOVATIVE TECHNOLOGIES AND SCIENTIFIC SOLUTIONS FOR INDUSTRIES, 2022)
The computer simulations are considered as the required tool to design the suitable autonomous control systems optimal in different senses and especially in providing the restrictions of the jerk motions for the robotic wheeled platforms. The subject matter of this research is the development of the theory and methods for computer simulations of the controllability processes of the robotic wheeled platforms. The goal of this research is to consider the jerks of the wheeled platforms, and the jerks are reduced to the limitation of the acceleration time derivative of the mass center of the wheeled platform, so that this derivative is considered as the quantitative estimation of the jerks. The incorrectness in the Hadamard’s sense for direct defining the jerks by differentiations of the phase coordinates in the case of computer simulations using the numerical methods is discussed. Tasks of this research are in developing the generalized approaches for mathematical modelling and computer simulations and in theoretical receiving of the properties inherent for the wheeled platforms and suitable for verification the computer simulations results, as well as in making the calculations to have the quantitative results about the controllability processes for the particular case of the electromechanical four-wheeled platform under the straight motion with the mode of speeding-up from the state of the rest. Methods of this research are based on the Lagrange’s equations of second kind, as well as on the electromechanical analogies, and on final representing the mathematical models in the form of the system of the first ordered ordinary differential equations with the initial conditions for further numerical solving. The computer simulations are accomplished by using the Scilab free open source software. Results of this research are in the proposed suitable way for computing the jerks by the phase coordinates without its differentiations allow excluding the incorrectness in the Hadamard’s sense, as well as in representing the controllability processes for the electromechanical wheeled platform, including the results for the velocities, the accelerations and the jerks which are necessary to illustrate the controllability processes for the robotic wheeled platforms. By comparison with the theoretically established inherent properties of the wheeled platforms it is shown the correctness of the results of the computer simulations. Conclusions about this research are that the developed approaches for computer simulations of the controllability processes for the robotic wheeled platforms allow considering influence of the control on the different characteristics including the velocity, the acceleration, as well as the jerk motions which are required for designing the controls optimal in different senses.