A new NCP-function for the box constrained variational inequality VI([a, b], F) is proposed and its properties are investigated. Using this NCP-function the box constrained variational inequality is reformulated as a ...A new NCP-function for the box constrained variational inequality VI([a, b], F) is proposed and its properties are investigated. Using this NCP-function the box constrained variational inequality is reformulated as a system of semismooth equa- tions whose merit function is differentiable every where. For the P0-function F, any stationary point of the merit function solves the VI([a, b], F). The related Newton-type method is proposed. For continuously differentiable and monotone function F, the generalized Newton equation involved in the method is always a uniquely solvable system of linear equations and affords a direction of sufficient decrease for the merit function. Under the condition of BD-regular solution, the algorithm is globally convergent and has a superlinear or possibly quadratic rate of convergence. The numerical results suggest that the algorithm is robust and efficient.展开更多
By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities (BVIs) was constructed. The function is simple and has some good differential pr...By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities (BVIs) was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it.Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.展开更多
A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landi...A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landing phase is added between the swing phase and the stance phase, where the desired contact force is set as a small positive constant. Secondly, the joint torque optimization of the stance legs is formulated as a quadratic programming(QP) problem subject to equality and inequality/bound constraints. And a primal-dual dynamical system solver based on linear variational inequalities(LVI) is applied to solve this QP problem. Furthermore, based on the optimization results, a hybrid motion/force robust controller is designed to realize the tracking of the contact force, while the constraints of the stance feet landing angles are fulfilled simultaneously. Finally, the experiments are performed to validate the proposed methods.展开更多
文摘A new NCP-function for the box constrained variational inequality VI([a, b], F) is proposed and its properties are investigated. Using this NCP-function the box constrained variational inequality is reformulated as a system of semismooth equa- tions whose merit function is differentiable every where. For the P0-function F, any stationary point of the merit function solves the VI([a, b], F). The related Newton-type method is proposed. For continuously differentiable and monotone function F, the generalized Newton equation involved in the method is always a uniquely solvable system of linear equations and affords a direction of sufficient decrease for the merit function. Under the condition of BD-regular solution, the algorithm is globally convergent and has a superlinear or possibly quadratic rate of convergence. The numerical results suggest that the algorithm is robust and efficient.
基金Project supported by the Teaching and Research Award Program for the Outstanding YoungTeachers in Higher Education Institutes of Munistry of Education, P.R.China
文摘By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities (BVIs) was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it.Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.
基金Project(61473304)supported by the National Natural Science Foundation of ChinaProject(2015AA042202)supported by Hi-tech Research and Development Program of China
文摘A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landing phase is added between the swing phase and the stance phase, where the desired contact force is set as a small positive constant. Secondly, the joint torque optimization of the stance legs is formulated as a quadratic programming(QP) problem subject to equality and inequality/bound constraints. And a primal-dual dynamical system solver based on linear variational inequalities(LVI) is applied to solve this QP problem. Furthermore, based on the optimization results, a hybrid motion/force robust controller is designed to realize the tracking of the contact force, while the constraints of the stance feet landing angles are fulfilled simultaneously. Finally, the experiments are performed to validate the proposed methods.
