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Ellipsoid-based manipulability measures are often used to characterize theforce/velocity task-space capabilities of robots. While computationally simple,this approach largely approximate and underestimate the true capabilities.Force/velocity polytopes appear to be a more appropriate representation tocharacterize robot's task-space capabilities. However, due to the computationalcomplexity of the associated vertex search problem, the polytope approach ismostly restricted to offline use, e.g. as a tool aiding robot mechanicaldesign, robot placement in work-space and offline trajectory planning. In thispaper, a novel on-line polytope vertex search algorithm is proposed. Itexploits the parallelotop geometry of actuator constraints. The proposedalgorithm significantly reduces the complexity and computation time of thevertex search problem in comparison to commonly used algorithms. In order tohighlight the on-line capability of the proposed algorithm and its potentialfor robot control, a challenging experiment with two collaborating Franka EmikaPanda robots, carrying a load of 12 kilograms, is proposed. In this experiment,the load distribution is adapted on-line, as a function of the configurationdependant task-space force capability of each robot, in order to avoid, as muchas possible, the saturation of their capacity.

On-line force capability evaluation based on efficient polytope vertex search