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— The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems with more than moderate state space size due to the curse of dimensionality. This work combines recent results in the(More)
This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential equation. This approach allows for optimality criteria to be incorporated into the navigation function, and generalizes(More)
Cooperative manipulation with multiple, independent agents can be complicated by changing dynamics as the agents come in and out of contact with the object they are manipulating. This effect, combined with uncertainty in the environment, leads to nontrivial issues in terms of guaranteeing convergence and task completion. Here we illustrate how these effects(More)
This paper develops a technique for an autonomous robot endowed with a manipulator arm, a multi-fingered gripper, and a variety of sensors to manipulate a known, but poorly observable object. We present a novel grasp planning method which not only incorporates the potential collision between object and manipulator, but takes advantage of this interaction.(More)
This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of SE(2) and SE(3). The approach can use dense point cloud data from stereo vision or an RGB-D sensor (such as the Microsoft Kinect), as well as visual appearance data as input. The method is a convex relaxation of the(More)
We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a(More)
Many manipulation planning problems involve several related sub-problems, such as the selection of grasping points on an object, choice of hand posture, and determination of the arm's configuration and evolving trajectory. Traditionally, these planning sub-problems have been handled separately, potentially leading to sub-optimal, or even infeasible,(More)