Abstract-A desirable property of path planning for robotic manipulation is the ability to identify solutions in a sufficiently short amount of time to be usable. This is particularly challenging for the manipulation problem due to the need to plan over high-dimensional configuration spaces and to perform computationally expensive collision checking procedures. Consequently, existing planners take steps to achieve desired solution times at the cost of low quality solutions. This paper presents a planning algorithm that overcomes these difficulties by augmenting the asymptotically-optimal RRT * with a sparse sampling procedure. With the addition of a collision checking procedure that leverages memoization, this approach has the benefit that it quickly identifies low-cost feasible trajectories and takes advantage of subsequent computation time to refine the solution towards an optimal one. We evaluate the algorithm through a series of Monte Carlo simulations of seven, twelve, and fourteen degree of freedom manipulation planning problems in a realistic simulation environment. The results indicate that the proposed approach provides significant improvements in the quality of both the initial solution and the final path, while incurring almost no computational overhead compared to the RRT algorithm. We conclude with a demonstration of our algorithm for single-arm and dual-arm planning on Willow Garage's PR2 robot.

We consider a continuous-time, inhomogeneous Markov chain M taking values in {0, 1} n . Processes of this type arise in finance as models of correlated default timing in a portfolio of firms, in reliability as models of failure timing in a system of interdependent components, and in many other areas. We develop a logarithmically efficient importance sampling scheme for estimating the tail of the distribution of the total transition count of M at a fixed time horizon.