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

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

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

On the observability of resonant structures in planetesimal disks due to planetary migration

We present a thorough study of the impact of a migrating planet on a planetesimal disk, by exploring a broad range of masses and eccentricities for the planet. We discuss the sensitivity of the structures generated in debris disks to the basic planet parameters. We perform many N-body numerical simulations, using the symplectic integrator SWIFT, taking into account the gravitational influence of the star and the planet on massless test particles. A constant migration rate is assumed for the planet. The effect of planetary migration on the trapping of particles in mean motion resonances is found to be very sensitive to the initial eccentricity of the planet and of the planetesimals. A planetary eccentricity as low as 0.05 is enough to smear out all the resonant structures, except for the most massive planets. The planetesimals also initially have to be on orbits with a mean eccentricity of less than than 0.1 in order to keep the resonant clumps visible. This numerical work extends previous analytical studies and provides a collection of disk images that may help in interpreting the observations of structures in debris disks. Overall, it shows that stringent conditions must be fulfilled to obtain observable resonant structures in debris disks. Theoretical models of the origin of planetary migration will therefore have to explain how planetary systems remain in a suitable configuration to reproduce the observed structures.Comment: 16 pages, 13 figures. Accepted for publication in A&

Investigating the flyby scenario for the HD 141569 system

HD 141569, a triple star system, has been intensively observed and studied for its massive debris disk. It was rather regarded as a gravitationally bound triple system but recent measurements of the HD 141569A radial velocity seem to invalidate this hypothesis. The flyby scenario has therefore to be investigated to test its compatibility with the observations. We present a study of the flyby scenario for the HD141569 system, by considering 3 variants: a sole flyby, a flyby associated with one planet and a flyby with two planets. We use analytical calculations and perform N-body numerical simulations of the flyby encounter. The binary orbit is found to be almost fixed by the observational constraint on a edge-on plane with respect to the observers. If the binary has had an influence on the disk structure, it should have a passing time at the periapsis between 5000 and 8000 years ago and a distance at periapsis between 600 and 900 AU. The best scenario for reproducing the disk morphology is a flyby with only 1 planet. For a 2 Mj (resp. 8 Mj) planet, its eccentricity must be around 0.2 (resp. below 0.1). In the two cases, its apoapsis is about 130 AU. Although the global disk shape is reasonably well reproduced, some features cannot be explain by the present model and the likehood of the flyby event remains an issue. Dynamically speaking, HD 141569 is still a puzzling system

Quantum Statistical Calculations and Symplectic Corrector Algorithms

The quantum partition function at finite temperature requires computing the trace of the imaginary time propagator. For numerical and Monte Carlo calculations, the propagator is usually split into its kinetic and potential parts. A higher order splitting will result in a higher order convergent algorithm. At imaginary time, the kinetic energy propagator is usually the diffusion Greens function. Since diffusion cannot be simulated backward in time, the splitting must maintain the positivity of all intermediate time steps. However, since the trace is invariant under similarity transformations of the propagator, one can use this freedom to "correct" the split propagator to higher order. This use of similarity transforms classically give rises to symplectic corrector algorithms. The split propagator is the symplectic kernel and the similarity transformation is the corrector. This work proves a generalization of the Sheng-Suzuki theorem: no positive time step propagators with only kinetic and potential operators can be corrected beyond second order. Second order forward propagators can have fourth order traces only with the inclusion of an additional commutator. We give detailed derivations of four forward correctable second order propagators and their minimal correctors.Comment: 9 pages, no figure, corrected typos, mostly missing right bracket