This paper proposes a method to numerically construe task con straints ellipsoids from bounded task domains. The nature of tasks and bounded task domains are discussed, and some geometric bounded domains are presented with their suitable hyperquadratic approximations. Analytical solutions yielding their maximum vol ume substitute ellipsoids are compared against the bounded do mains themselves and against a competing maximum volume sub stitute box. The aforementioned numerical method is presented and is gauged against the known analytical solutions.
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