An optimal trajectory planning method has been proposed for the walking locomotion of a biped mechanical system with thighs, shanks and small feet, which is modelled as a 3 DOF link system consisting of an inverted pe...An optimal trajectory planning method has been proposed for the walking locomotion of a biped mechanical system with thighs, shanks and small feet, which is modelled as a 3 DOF link system consisting of an inverted pendulum and a 2 DOF swing leg. The locomotion of swing and supporting legs is solved by the optimal trajectory planning based on function approximation. The optimal trajectory planning based on function approximation. The optimal walking locomotion solution with minimum square of input torque exhibits a natural walking gait with one step period of 0.64 s similar to the human walking gait by using the link parameters of an adult’s leg. It is concluded from the computation results that the method proposed in this paper has been proved to be an effective tool for solving the optimal walking locomotion and joint control torque problems for a 3 DOF biped mechanism; when the ankle joint of the supporting leg is a passive joint, a nearly, optimal walking solution can be obtained at t 1=0.49 s and t 2=10 s, and however, when the knee is a passive joint, it is impossible to obtain a solution which satisfies the constraint condition; for the link parameters used in this paper, the length of an optimal stride is 0.3 m.展开更多
In this paper we construct a new operator Hn,r（N,B） （f; z） by means of the partial sums S（N,S） （f; z） of Neumann-Bessel series. The operator converges uniformly to any fixed continuous function f（z） on the u...In this paper we construct a new operator Hn,r（N,B） （f; z） by means of the partial sums S（N,S） （f; z） of Neumann-Bessel series. The operator converges uniformly to any fixed continuous function f（z） on the unit circle ｜ z ｜= 1 and has the best approximation order for f（z） on ｜ z ｜= 1.展开更多
文摘An optimal trajectory planning method has been proposed for the walking locomotion of a biped mechanical system with thighs, shanks and small feet, which is modelled as a 3 DOF link system consisting of an inverted pendulum and a 2 DOF swing leg. The locomotion of swing and supporting legs is solved by the optimal trajectory planning based on function approximation. The optimal trajectory planning based on function approximation. The optimal walking locomotion solution with minimum square of input torque exhibits a natural walking gait with one step period of 0.64 s similar to the human walking gait by using the link parameters of an adult’s leg. It is concluded from the computation results that the method proposed in this paper has been proved to be an effective tool for solving the optimal walking locomotion and joint control torque problems for a 3 DOF biped mechanism; when the ankle joint of the supporting leg is a passive joint, a nearly, optimal walking solution can be obtained at t 1=0.49 s and t 2=10 s, and however, when the knee is a passive joint, it is impossible to obtain a solution which satisfies the constraint condition; for the link parameters used in this paper, the length of an optimal stride is 0.3 m.
文摘In this paper we construct a new operator Hn,r（N,B） （f; z） by means of the partial sums S（N,S） （f; z） of Neumann-Bessel series. The operator converges uniformly to any fixed continuous function f（z） on the unit circle ｜ z ｜= 1 and has the best approximation order for f（z） on ｜ z ｜= 1.
