Objective-based stochastic framework for manipulation planning

We consider the problem of determining robot manipulation plans when sensing and control uncertainties are specified as conditional probability densities. Traditional approaches are usually based on worst-case error analysis in a methodology known as preimage backchaining. We have developed a general framework for determining sensor-based robot plans by blending ideas from stochastic optimal control and dynamic game theory with traditional preimage backchaining concepts. We argue that the consideration of a precise loss (or performance) functional is crucial to determining and evaluating manipulation plans in a probabilistic setting. We consequently introduce a stochastic, performance preimage that generalizes previous preimage notions. We also present some optimal strategies for planar manipulation tasks that were computer by a dynamic programming-based algorithm.