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Abstract-In this paper, we propose a new conceptthe "Reciprocal Velocity Obstacle"-for real-time multi-agent navigation. We consider the case in which each agent navigates independently without explicit communication with other agents. Our formulation is an extension of the Velocity Obstacle concept [3], which was introduced for navigation among (passively) moving obstacles. Our approach takes into account the reactive behavior of the other agents by implicitly assuming that the other agents make a similar collision-avoidance reasoning. We show that this method guarantees safe and oscillationfree motions for each of the agents. We apply our concept to navigation of hundreds of agents in densely populated environments containing both static and moving obstacles, and we show that real-time and scalable performance is achieved in such challenging scenarios.

This paper presents LQG-MP (linear-quadratic Gaussian motion planning), a new approach to robot motion planning that takes into account the sensors and the controller that will be used during execution of the robot's path. LQG-MP is based on the linear-quadratic controller with Gaussian models of uncertainty, and explicitly characterizes in advance (i.e., before execution) the a-priori probability distributions of the state of the robot along its path. These distributions can be used to assess the quality of the path, for instance by computing the probability of avoiding collisions. Many methods can be used to generate the needed ensemble of candidate paths from which the best path is selected; in this paper we report results using Rapidly-Exploring Random Trees (RRT). We study the performance of LQG-MP with simulation experiments in three scenarios: A) a kinodynamic car-like robot, B) multi-robot planning with differential-drive robots, and C) a 6-DOF serial manipulator. We also apply Kalman Smoothing to make paths C k -continuous while avoiding obstacles and apply LQG-MP to precomputed roadmaps using a variant of Dijkstra's algorithm to efficiently find near-optimal paths.

We present a new approach to motion planning under sensing and motion uncertainty by computing a locally optimal solution to a continuous partially observable Markov decision process (POMDP). Our approach represent beliefs (the distributions of the robot's state estimate) by Gaussian distributions and is applicable to robot systems with non-linear dynamics and observation models. The method follows the general POMDP solution framework in which we approximate the belief dynamics using an extended Kalman filter and represent the value function by a quadratic function that is valid in the vicinity of a nominal trajectory through belief space. Using a belief space variant of iterative LQG (iLQG), our approach iterates with secondorder 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 state and action spaces. The running time of the algorithm is polynomial (O[n 6 ]) in the dimension n of the state space. We demonstrate the potential of our approach in simulation for holonomic and nonholonomic robots maneuvering through environments with obstacles with noisy and partial sensing and with non-linear dynamics and observation models.

We present Kinodynamic RRT*, an incremental sampling-based approach for asymptotically optimal motion planning for robots with linear differential constraints. Our approach extends RRT*, which was introduced for holonomic robots [8], by using a fixed-final-state-free-final-time controller that exactly and optimally connects any pair of states, where the cost function is expressed as a trade-off between the duration of a trajectory and the expended control effort. Our approach generalizes earlier work on extending RRT* to kinodynamic systems, as it guarantees asymptotic optimality for any system with controllable linear dynamics, in state spaces of any dimension. Our approach can be applied to non-linear dynamics as well by using their first-order Taylor approximations. In addition, we show that for the rich subclass of systems with a nilpotent dynamics matrix, closed-form solutions for optimal trajectories can be derived, which keeps the computational overhead of our algorithm compared to traditional RRT* at a minimum. We demonstrate the potential of our approach by computing asymptotically optimal trajectories in three challenging motion planning scenarios: (i) a planar robot with a 4-D state space and double integrator dynamics, (ii) an aerial vehicle with a 10-D state space and linearized quadrotor dynamics, and (iii) a carlike robot with a 5-D state space and non-linear dynamics.

Abstract-We present the hybrid reciprocal velocity obstacle for collision-free and oscillation-free navigation of multiple mobile robots or virtual agents. Each robot senses its surroundings and acts independently without central coordination or communication with other robots. Our approach uses both the current position and the velocity of other robots to compute their future trajectories in order to avoid collisions. Moreover, our approach is reciprocal and avoids oscillations by explicitly taking into account that the other robots also sense their surroundings and change their trajectories accordingly. We apply hybrid reciprocal velocity obstacles to iRobot Create mobile robots and demonstrate direct, collision-free, and oscillation-free navigation.

We consider the problem of autonomous robotic laundry folding, and propose a solution to the perception and manipulation challenges inherent to the task. At the core of our approach is a quasi-static cloth model which allows us to neglect the complex dynamics of cloth under significant parts of the state space, allowing us to reason instead in terms of simple geometry. We present an algorithm which, given a 2D cloth polygon and a desired sequence of folds, outputs a motion plan for executing the corresponding manipulations, deemed g-folds, on a minimal number of robot grippers. We define parametrized fold sequences for four clothing categories: towels, pants, short-sleeved shirts, and long-sleeved shirts, each represented as polygons. We then devise a model-based optimization approach for visually inferring the class and pose of a spread-out or folded clothing article from a single image, such that the resulting polygon provides a parse suitable for these folding primitives. We test the manipulation and perception tasks individually, and combine them to implement an autonomous folding system on the Willow Garage PR2. This enables the PR2 to identify a clothing article spread out on a table, execute the computed folding sequence, and visually track its progress over successive folds.

We address the problem of real-time navigation in dynamic environments for car-like robots. We present an approach to identify controls that will lead to a collision with a moving obstacle at some point in the future. Our approach generalizes the concept of velocity obstacles, which have been used for navigation among dynamic obstacles, and takes into account the constraints of a car-like robot. We use this formulation to find controls that will allow collision free navigation in dynamic environments. Finally, we demonstrate the performance of our algorithm on a simulated car-like robot among moving obstacles.