Abstract:
The problem of controlling the rolling of a spherical robot with a pendulum actuator pursuing
a moving target by the pursuit method, but with a minimal control, is considered. The mathe-
matical model assumes the presence of a number of holonomic and nonholonomic constraints, as
well as the presence of two servo-constraints containing a control function. The control function
is defined in accordance with the features of the simulated scenario. Servo-constraints set the
motion program. To implement the motion program, the pendulum actuator generates a control
torque which is obtained from the joint solution of the equations of motion and derivatives of
servo-constraints. The first and second components of the control torque vector are determined
in a unique way, and the third component is determined from the condition of minimizing the
square of the control torque. The system of equations of motion after reduction for a given
control function is reduced to a nonautonomous system of six equations. A rigorous proof of
the boundedness of the distance function between a spherical robot and a target moving at
a bounded velocity is given. The cases where objects move in a straight line and along a curved
trajectory are considered. Based on numerical integration, solutions are obtained, graphs of the
desired mechanical parameters are plotted, and the trajectory of the target and the trajectory
of the spherical robot are constructed.
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