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 classical pose estimation problem, and is based on explicit linear matrix inequality (LMI) representations for the convex hulls of SE(2) and SE(3). Given these representations, the relaxed pose estimation problem can be framed as a robust least squares problem with the optimization variable constrained to these convex sets. Although this formulation is a relaxation of the original problem, numerical experiments indicates that it is indeed exact - i.e. its solution is a member of SE(2) or SE(3) - in many interesting settings. We additionally show that this method is guaranteed to be exact for a large class of pose estimation problems.

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 several existing results in navigation functions. It is shown that the HJB and that existing navigation functions in the literature sit on ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. In particular, it is shown that under certain criteria the optimal navigation function is related to Laplace's equation, previously used in the literature, through an exponential transform. Further, analytical solutions to the HJB are available in simplified domains, yielding guidance towards optimality for approximation schemes. Examples are used to illustrate the role that noise, and optimality can potentially play in navigation system design.

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 control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. Each individual reachability problem is solved via the Hamilton-Jacobi-Bellman (HJB) partial differential equation of stochastic optimal control theory. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the partial differential equation allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to conservatively satisfy a complex temporal logic specification.

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. The natural uncertainty and difficulties in observation in such tasks is modeled as a Partially Observable Markov Decision Process (POMDP). Recent advances in point-based methods as well as a novel state space representation specific to the grasping problem are leveraged to overcome state space growth issues. Simulation results are presented for the combined localization, manipulation, and grasping of a small nut on a table.

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, combinations of the individually determined solutions. This paper formulates the combined problem of grasp contact selection, grasp force optimization, and manipulator arm/hand trajectory planning as a problem in optimal control. That is, the locally optimal trajectory for the manipulator, hand mechanism, and contact locations are determined during the pre-grasping, grasping, and subsequent object transport phase. Additionally, a barrier function approach allows for non-feasible grasps to be optimized, enlarging the region of convergence for the algorithm. A simulation of a simple planar object manipulation task is used to illustrate and validate the approach.

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 can be mitigated using a decentralized adaptive control technique based on hybrid control. Results are verified in an experiment using three agents.