this paper presents optimal control method to path planning of mobile robots with flexible joints. dynamic equations are derived and additional kinematic constraints are used to solve the extra dofs arose from base mobility. then with modeling the elasticity at each joint as a linear torsinal spring, the set of equations are formed. the hamiltonian function is formed and the necessary condition...

In this paper, we study the nonlinear boundary value problem consisting of the equation y′′ + w(t) f (y) = 0 on [a,b] and two multi-point boundary conditions. We establish the existence of various nodal solutions of this problem by matching the solutions of two boundary value problems, each of which involves one separated boundary condition and one multi-point boundary condition, at some point ...