A Bayesian framework for optimal motion planning with uncertainty

Modeling robot motion planning with uncertainty in a Bayesian framework leads to a computationally intractable stochastic control problem. We seek hypotheses that can justify a separate implementation of control, localization and planning. In the end, we reduce the stochastic control problem to path- planning in the extended space of poses x covariances; the transitions between states are modeled through the use of the Fisher information matrix. In this framework, we consider two problems: minimizing the execution time, and minimizing the final covariance, with an upper bound on the execution time. Two correct and complete algorithms are presented. The first is the direct extension of classical graph-search algorithms in the extended space. The second one is a back-projection algorithm: uncertainty constraints are propagated backward from the goal towards the start state

Probabilistic approach to physical object disentangling

Physically disentangling entangled objects from each other is a problem encountered in waste segregation or in any task that requires disassembly of structures. Often there are no object models, and, especially with cluttered irregularly shaped objects, the robot can not create a model of the scene due to occlusion. One of our key insights is that based on previous sensory input we are only interested in moving an object out of the disentanglement around obstacles. That is, we only need to know where the robot can successfully move in order to plan the disentangling. Due to the uncertainty we integrate information about blocked movements into a probability map. The map defines the probability of the robot successfully moving to a specific configuration. Using as cost the failure probability of a sequence of movements we can then plan and execute disentangling iteratively. Since our approach circumvents only previously encountered obstacles, new movements will yield information about unknown obstacles that block movement until the robot has learned to circumvent all obstacles and disentangling succeeds. In the experiments, we use a special probabilistic version of the Rapidly exploring Random Tree (RRT) algorithm for planning and demonstrate successful disentanglement of objects both in 2-D and 3-D simulation, and, on a KUKA LBR 7-DOF robot. Moreover, our approach outperforms baseline methods