Abstract
By a News Reporter-Staff News Editor at Robotics & Machine Learning Daily News Daily News-Investigators discuss new findings in Robotics. According to news reporting from Rio de Janeiro, Brazil, by NewsRx jou rnalists, research stated, "In this paper, we study mechanical optimal control p roblems on a given Riemannian manifold (Q, g) in which the cost is defined by a general cometric g. This investigation is motivated by our studies in robotics, in which we observed that the mathematically natural choice of cometric g = g* - the dual of g - does not always capture the true cost of the motion." Financial support for this research came from National Science Foundation The news correspondents obtained a quote from the research from Federal Universi ty Rio de Janeiro, "We then, first, discuss how to encode the system's torque-ba sed actuators configuration into a cometric g. Second, we provide and prove our main theorem, which characterizes the optimal solutions of the problem associate d to general triples (Q, g, g) in terms of a 4th order differential equation. We also identify a tensor appearing in this equation as the geometric source of ‘b iasing' of the solutions away from ordinary Riemannian splines and geodesics for (Q, g)."
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