Final-state control of a two-link cat robot

In this study, we deal with the twisting motion of a falling cat robot by means of two torque inputs around her waist. The cat robot consists of two rigid columns and has two internal actuators at the joint to generate torque inputs around normal coordinates. This system is a nonholonomic system whose angular momentum is conserved. We formulate the state equation that has torque inputs to the joint by using the nonholonomic constraint and the Lagrange-d'Alembert principle. Then, we transform the system into a linear parameter varying system. In order to improve error learning of a final-state control method, we provide the initial inputs in order to determine the appropriate rotation direction in the early stage of the twisting motion. Next, we introduce the method of the artificial potential function to the final-state control in order to make the maximum bending angle small. The feedforward torque inputs can be obtained by the final-state control in order to bring the system from the initial state to the final state in the desired time. In simulations, we also demonstrate that the two-link cat robot can land on her feet by using the 2-d.o.f. control system even when her waist damping coefficient varies.