Control of wheeled platforms straight motions taking into account jerk restrictions under speeding-up from the state of rest
Abstract
The generalized mathematical model of wheeled platforms straight motions on the ideal horizontal plane under speeding-up from the state of rest mode is proposed, and the controls satisfying the restrictions of motion jerks are find. The pure mechanical and electromechanical wheeled platforms are considered, as well as the computer simulations of the researched processes are made. The jerks restrictions are reduced to limiting the value of the wheeled platform acceleration time derivative. The proposed approaches are based on the holonomic systems mechanics and on the electromechanical analogies allowing to consider the different kinds of the wheeled platforms taking into account the electric on-board systems like the drive electric motors and the control systems by using the Lagrange equations of second kind. The examples of the proposed approaches using to define the controls satisfying the jerks restrictions under speeding-up from the state of rest are considered for the pure mechanical and electromechanical wheeled platforms. It is obtained the inequality allowing to chose the instantly supplied driving mechanical couple which will provide the admissible jerks of the motion of the wheeled platform under speeding-up from the state of rest. It is shown that the rolling friction and the viscous damping are the principal causes of the wheeled platforms jerks under speeding-up from the state of rest. It is obtained the inequality defining the voltage instantly supplied on the drive electric motors which will provide the admissible jerks of the motion of the electromechanical wheeled platform during speeding-up from the state of rest, and it is shown that the proposed general approaches are suitable for considering the different kinds of wheeled platforms. The computer simulations of the processes of speeding-up from the state of rest for the electromechanical wheeled platform are considered to show results correctness and to illustrate satisfying the restrictions of the motion jerks. The obtained results of the computer simulations are in the full agreement with the well-known fundamental property inherent for the wheeled platforms. The results for the jerks show that the maximum value of the jerk is really at the initial time as was suggested before, and it is shown that the jerks values at the initial time obtained by using the computer simulations are in full agreement with the theoretically defined correspondent exact values. The big jerks of the considered electromechanical wheeled platform are due to the voltage instantly supplying on the drive electric motors at the initial time, and it is understandable that limiting of such instantly supplied voltage value cannot provide any wished small jerks. The smooth time depending for the voltages supplying on the drive electric motors are required to provide any wished small jerks of the electromechanical wheeled platforms.
