This paper addresses widely applicable methods for solving the kinematics problem of any class of serial-link robot manipulators. First, the position and orientation of the manipulator hand, the Jacobian matrix and their symbolic generation are clearly presented using recursive relations. Second, the inverse problem to such formulations is posed as an unconstrained non-linear optimization one, where numerical techniques for the overdetermined and underdetermined kinematic problems are considered separately to derive consistent arm solutions. On the basis of several proposals on step lengths involved to maintain good numerical stability, the results of computer simulation show that performance is sufficiently reliable.

Let μ and ν be two probability measures on the real line and let c be a lower semicontinuous function on the plane. The mass transfer problem consists in determining a measure ξ whose marginals coincide with μ and ν, and whose total cost ∫∫ c(x,y)dξ(x,y) is minimum. In this paper we present three algorithms to solve numerically this Monge-Kantorovitch problem when the commodity being shipped is one-dimensional and not necessarily confined to a bounded interval . We illustrate these numerical methods and determine the convergence rate.

In previous papers, we used a Markovian model to determine the optimal functioning rules of a distributed system in various settings. Searchingoptimal functioning rules amounts to solve an optimization problemunder constraints. The hierarchy of solutions arising from the above problem is called the “first order hierarchy”, and may possibly yield equivalent solutions. The present paper emphasizes a specific technique for deciding between two equivalent solutions, which establishes the“second order hierarchy”.