Real-Time Online Re-Planning for Grasping Under Clutter and Uncertainty

We consider the problem of grasping in clutter. While there have been motion planners developed to address this problem in recent years, these planners are mostly tailored for open-loop execution. Open-loop execution in this domain, however, is likely to fail, since it is not possible to model the dynamics of the multi-body multi-contact physical system with enough accuracy, neither is it reasonable to expect robots to know the exact physical properties of objects, such as frictional, inertial, and geometrical. Therefore, we propose an online re-planning approach for grasping through clutter. The main challenge is the long planning times this domain requires, which makes fast re-planning and fluent execution difficult to realize. In order to address this, we propose an easily parallelizable stochastic trajectory optimization based algorithm that generates a sequence of optimal controls. We show that by running this optimizer only for a small number of iterations, it is possible to perform real time re-planning cycles to achieve reactive manipulation under clutter and uncertainty.Comment: Published as a conference paper in IEEE Humanoids 201

Forward Symplectic Integrators and the Long Time Phase Error in Periodic Motions

We show that when time-reversible symplectic algorithms are used to solve periodic motions, the energy error after one period is generally two orders higher than that of the algorithm. By use of correctable algorithms, we show that the phase error can also be eliminated two orders higher than that of the integrator. The use of fourth order forward time step integrators can result in sixth order accuracy for the phase error and eighth accuracy in the periodic energy. We study the 1-D harmonic oscillator and the 2-D Kepler problem in great details, and compare the effectiveness of some recent fourth order algorithms.Comment: Submitted to Phys. Rev. E, 29 Page

Pseudo-High-Order Symplectic Integrators

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa

The role of chaotic resonances in the solar system

Our understanding of the Solar System has been revolutionized over the past decade by the finding that the orbits of the planets are inherently chaotic. In extreme cases, chaotic motions can change the relative positions of the planets around stars, and even eject a planet from a system. Moreover, the spin axis of a planet-Earth's spin axis regulates our seasons-may evolve chaotically, with adverse effects on the climates of otherwise biologically interesting planets. Some of the recently discovered extrasolar planetary systems contain multiple planets, and it is likely that some of these are chaotic as well.Comment: 28 pages, 9 figure