A general framework for computing robust controllable sets ofconstrained nonlinear uncertain discrete-time systems as well ascontrolling such complex systems based on the computed robustcontrollable sets is introduced in this paper. The addressedone-step control approach turns out to be a robust model predictivecontrol scheme with feasible unit control horizon and contractiveconstraint. The solver of 1-dimensional quantified set inversion inmodal interval analysis is extended to 2-dimensional cases forcomputing robust controllable sets off-line with a clear semanticinterpretation, where both universal and existential quantifiers areconcerned simultaneously. An interval-based solver of constrainedminimax optimization is also proposed to compute one-step controlinputs online in a reliable way, which guarantee to drive the systemstate contractively along the computed robust controllable sets to aselected terminal robust control invariant set.

A new global isotropy index (GII) is proposed to quantify the configuration independent isotropy of a robot's Jacobian or mass matrix. A new discrete global optimization algorithm is also proposed to optimize either the GII or some local measure without placing any conditions on the objective function. The algorithm is used to establish design guidelines and a globally optimal architecture for a planar haptic interface from both a kinematic and dynamic perspective and to choose the optimum geometry for a 6-DOF Stewart Platform. The algorithm demonstrates consistent effort reductons of up to six orders of magnitude over global searching with low sensitivity to initial conditions.