This paper deals with the analysis of lightweight, flexible robotic limbs. A typical limb is a series of polymeric tube elements. One end is fixed and the payload at the other end is manipulated by varying the internal pressure in each element. The theoretical derivations relating limb position and its payload incorporate the nonlinear elastic properties of the element material and large deflections. A computer program stores information about limb position and after each successive limb manipulation the program adaptively upgrades itself to improve positioning accuracy. Results are illustrated with a numerical example.