Research on trajectory planning of a robot inspired by free-falling cat based on numerical approximation

A robot may be at the risk of falling from a high place when it works in an unknown complex environment, so the attitude control ability of the robot in the air should be considered to reduce the damage caused by the wrong dropping posture. When a cat drops in the upside-down posture with zero angular momentum, it can always right itself and land on its feet safely. Inspired by this biological phenomenon, we studied the optimal falling trajectory for adjusting the attitude of the falling cat robot. Firstly, we formulated a mathematical model based on the twisted model of two identical axially symmetric rigid cylinders, owing to nonintegrable conservation laws, a problem for controlling the attitude of the falling cat robot could be transformed to the problem of the nonholonomic motion planning. Then, taking the energy cost of the joint of the system as the optimal control function to find a control torque input, which was approximated by the spline approximation, with the method one can solve the problem that the initial and terminal values of control torque input are not zero. We found the optimal solution of control function through particle swarm optimization. Finally, we carried out numerical simulation, and the result shows the spline approximation is a valid method for trajectory planning of the falling cat robot.