Optimal motion planning of hopping robot based on pseudospectral method during flight phase

The energy optimal motion planning of a hopping robot with three links is investigated in the flight phase. Firstly, the conservation equation of angular momentum of the hopping robot in the flight phase is established which is a nonholonomic constraint. Then the energy consumption of the robot in the flight phase is selected as the optimization goal. Given the initial and terminal positions, the Gaussian pseudospectrum method is used to solve the optimal control problem. The simulation results show that the initial angular momentum has a great influence on the performance of the hopping robot. With thezero initial angular momentum, although the flight time can be selected arbitrarily, the greater the flight time, the smaller the energy consumption, the force required by the robot is greater. Thus, it is necessary to select an appropriate value.