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Research on trajectory planning of a robot inspired by free-falling cat based on modified quasi-Newton algorithm

The attitude control ability of the robot in the air is needed when we design a robot that can jump, run, climb and land. With such a robot, we can reduce the damage caused by the wrong dropping posture. As we all know, when a free-falling cat drops from upside-down with no initial angular momentum, she can always right herself and land on her feet safely. Inspired by the free-falling cat, we studied the application of a modified quasi-Newton algorithm to obtain the optimal trajectory of a falling cat robot. To get the optimal trajectory, firstly, we formulated the mathematical equation based on the model of two identical axial symmetric cylinders, as it is impossible to integrate the velocity constraint into position constraint about time, we transformed the control of a falling cat robot to nonholonomic motion planning problem. Then, using Ritz approximation theory, we discussed a modified quasi-Newton algorithm for trajectory planning of a falling cat robot. Finally, we verified our algorithm through simulation. The results show that the algorithm is an effective one for a falling cat robot problem.