  This paper primarily focuses on the practical applications of optimal control
theory for perturbed sweeping processes within the realm of robotics dynamics.
By describing these models as controlled sweeping processes with pointwise
control and state constraints and by employing necessary optimality conditions
for such systems, we formulate optimal control problems suitable to these
models and develop numerical algorithms for their solving. Subsequently, we use
the Python Dynamic Optimization library GEKKO to simulate solutions to the
posed robotics problems in the case of any fixed number of robots under
different initial conditions.
