Abstract This paper presents a technique for planning and controlling bevel-tip steerable needles towards a target location in 3-D anatomy under the guidance of partial, noisy sensor feedback. Our approach minimizes the probability that the needle intersects obstacles such as bones and sensitive organs by (1) explicitly taking into account motion uncertainty and sensor types, and (2) allowing for efficient optimization of sensor placement. We allow for needle trajectories of arbitrary curvature through duty-cycled spinning of the needle, which is believed to make a needle path small-time locally “trackable ” [13]. This enables us to use LQG control to guide the needle along the path. For a given path and sensor placement, we show that a priori probability distributions of the needle state can be estimated in advance. Our approach then plans a set of candidate paths and sensor placements and selects the pair for which the estimated uncertainty is least likely to cause intersections with obstacles. We demonstrate the performance of our approach in a modeled prostate cancer treatment environment. 1

Abstract — Existing sampling-based robot motion planning methods are often inefficient at finding trajectories for kinodynamic systems, especially in the presence of narrow passages between obstacles and uncertainty in control and sensing. To address this, we propose EG-RRT, an Environment-Guided variant of RRT designed for kinodynamic robot systems that combines elements from several prior approaches and may incorporate a cost model based on the LQG-MP framework to estimate the probability of collision under uncertainty in control and sensing. We compare the performance of EG-RRT with several prior approaches on challenging sample problems. Results suggest that EG-RRT offers significant improvements in performance. I.

Abstract — Many tasks in robot-assisted surgery, food handling, manufacturing, and other applications require planning and controlling the motions of manipulators or other devices that must interact with highly deformable objects. We present a unified approach for motion planning under uncertainty in deformable environments that maximizes probability of success by accounting for uncertainty in deformation models, noisy sensing, and unpredictable actuation. Unlike prior planners that assume deterministic deformations or treat deformations as a type of small perturbation, our method explicitly considers the uncertainty in large, time-dependent deformations. Our method requires a simulator of deformable objects but places no significant restrictions on the simulator used. We use a samplingbased motion planner in conjunction with the simulator to generate a set of candidate plans based on expected deformations. Our method then uses the simulator and optimal control to numerically estimate time-dependent state distributions based on uncertain parameters (e.g. deformable material properties or actuation errors). We then select the plan with the highest estimated probability of successfully avoiding obstacles and reaching the goal region. Using FEM-based simulation of deformable tissues, we demonstrate the ability of our method to generate high quality plans in two medical-inspired scenarios: (1) guiding bevel-tip steerable needles through slices of deformable tissue around obstacles for minimally invasive biopsies and drug-delivery, and (2) manipulating planar tissues to align interior points at desired coordinates for precision treatment. I.

Abstract We present an approach to motion planning under motion and sensing uncertainty, formally described as a continuous partially-observable Markov decision process (POMDP). Our approach is designed for non-linear dynamics and observation models, and follows the general POMDP solution framework in which we represent beliefs by Gaussian distributions, approximate the belief dynamics using an extended Kalman filter (EKF), and represent the value function by a quadratic function that is valid in the vicinity of a nominal trajectory through belief space. Using a variant of differential dynamic programming, our approach iterates with second-order convergence towards a linear control policy over the belief space that is locally-optimal with respect to a user-defined cost function. Unlike previous work, our approach does not assume maximum-likelihood observations, does not assume fixed estimator or control gains, takes into account obstacles in the environment, and does not require discretization of the belief space. The running time of the algorithm is polynomial in the dimension of the state space. We demonstrate the potential of our approach in several continuous partially-observable planning domains with obstacles for robots with non-linear dynamics and observation models. 1

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Abstract — Being able to navigate accurately is one of the basic capabilities a mobile robot needs to effectively execute a variety of tasks, including collision avoidance, docking, manipulation, and path following. One popular approach to achieve the desired accuracy is to use artificial landmarks for a sufficiently accurate localization. In this paper, we consider the problem of optimally placing landmarks for robots navigating repeatedly along a given set of trajectories. Our method aims at minimizing the number of landmarks for which a bound on the maximum deviation of the robot from its desired trajectory can be guaranteed with high confidence. The proposed approach incrementally places landmarks utilizing linearized versions of the system dynamics of the robot, thus allowing for an efficient computation of the deviation guarantee. To verify this guarantee for the real and possibly non-linear system dynamics of the robot, our method then performs a Monte Carlo simulation. We evaluate our algorithm in extensive experiments carried out both in simulation and with a real robot. The experiments demonstrate that our method requires substantially fewer landmarks than other approaches to achieve the desired accuracy.

In this paper, we describe an integrated strategy for planning, perception, state-estimation and action in complex mobile manipulation domains. The strategy is based on planning in the belief space of probability distribution over states. Our planning approach is based on hierarchical goal regression (pre-image back-chaining). We develop a vocabulary of fluents that describe sets of belief states, which are goals and subgoals in the planning process. We show that a relatively small set of symbolic operators lead to task-oriented perception in support of the manipulation goals. An implementation of this method is demonstrated in simulation and on a real PR2 robot, showing robust, flexible solution of mobile manipulation problems with multiple objects and substantial uncertainty. 1