Task Constraints Specification Via Optimized Hyperellipsoids

This paper proposes a method to numerically construe task constraints 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 volume substitute ellipsoids are compared against the bounded domains themselves and against a competing maximum volume substitute box. The aforementioned numerical method is presented and is gauged against the known analytical solutions.