Stochastic Extended LQR for Optimization-Based Motion Planning Under Uncertainty

We introduce a novel optimization-based motion planner, Stochastic Extended LQR (SELQR), which computes a trajectory and associated linear control policy with the objective of minimizing the expected value of a user-defined cost function. SELQR applies to robotic systems that have stochastic non-linear dynamics with motion uncertainty modeled by Gaussian distributions that can be state- and control-dependent. In each iteration, SELQR uses a combination of forward and backward value iteration to estimate the cost-to-come and the cost-to-go for each state along a trajectory. SELQR then locally optimizes each state along the trajectory at each iteration to minimize the expected total cost, which results in smoothed states that are used for dynamics linearization and cost function quadratization. SELQR progressively improves the approximation of the expected total cost, resulting in higher quality plans. For applications with imperfect sensing, we extend SELQR to plan in the robot's belief space. We show that our iterative approach achieves fast and reliable convergence to high-quality plans in multiple simulated scenarios involving a car-like robot, a quadrotor, and a medical steerable needle performing a liver biopsy procedure

EG-RRT: Environment-guided random trees for kinodynamic motion planning with uncertainty and obstacles

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.Postprint (author’s final draft

Multi-armed bandit models for 2D grasp planning with uncertainty

Abstract — For applications such as warehouse order fulfill-ment, robot grasps must be robust to uncertainty arising from sensing, mechanics, and control. One way to achieve robustness is to evaluate the performance of candidate grasps by sampling perturbations in shape, pose, and gripper approach and to com-pute the probability of force closure for each candidate to iden-tify a grasp with the highest expected quality. Since evaluating the quality of each grasp is computationally demanding, prior work has turned to cloud computing. To improve computational efficiency and to extend this work, we consider how Multi-Armed Bandit (MAB) models for optimizing decisions can be applied in this context. We formulate robust grasp planning as a MAB problem and evaluate convergence times towards an optimal grasp candidate using 100 object shapes from the Brown Vision 2D Lab Dataset with 1000 grasp candidates per object. We consider the case where shape uncertainty is represented as a Gaussian process implicit surface (GPIS) with Gaussian uncertainty in pose, gripper approach angle, and coefficient of friction. We find that Thompson Sampling and the Gittins index MAB methods converged to within 3 % of the optimal grasp up to 10x faster than uniform allocation and 5x faster than iterative pruning. I

Meso-scale planning for multi-agent navigation

Abstract-We introduce a new concept; meso-scale planning in real-time multi-agent navigation. Whereas many traditional approaches to multi-agent navigation typically consist of twolevels -a macro-scale level providing agents with a global direction of motion around (large) static obstacles, and a microscale level in which agents seek to avoid collision with other agents -our approach adds a meso-scale level to give agents realistic behavior in scenarios where groups of other agents (e.g. families or crowds in a virtual world) form coherent entities. Rather than moving straight through such groups, our approach lets agents move around them. Our formulation considers each agent as an individual that may perceive sets of other agents as a group, and plans its motion accordingly. We base our approach on the velocity obstacle concept, and we show using simulation results that our method dramatically improves the quality of the trajectories computed for the agents

Citations (this article cites 5 articles hosted on the SAGE Journals Online and HighWire Press platforms):

The probabilistic roadmap (PRM) planner is a popular method for robot motion planning problems with many degrees of freedom. However, it has been shown that the method performs less well in situations where the robot has to pass through a narrow passage in the scene. This is mainly due to the uniformity of the sampling used in the planner; it places many samples in large open regions and too few in tight passages. Cell decomposition methods do not have this disadvantage, but are only applicable in low-dimensional configuration spaces. In this paper, a hybrid technique is presented that combines the strengths of both methods. It is based on a robot independent cell decomposition of the free workspace guiding the probabilistic sampling more toward the interesting regions in the configuration space. The regions of interest (narrow passages) are identified in the cell decomposition using a method we call watershed labeling. It i

www.cs.uu.nl Roadmap-based Motion Planning in Dynamic Environments

In this paper a new method is presented for motion planning in dynamic environments, that is, finding a trajectory for a robot in a scene consisting of both static and dynamic, moving obstacles. We propose a practical algorithm based on a roadmap that is created for the static part of the scene. On this roadmap an approximate time-optimal trajectory from a start to a goal configuration is computed, such that the robot does not collide with any moving obstacle. The trajectory is found by performing a search for a shortest path on an implicit grid in state-time space. The approach is applicable to any robot type in configuration spaces with any dimension, and the motions of the dynamic obstacles are unconstrained, as long as they are known beforehand. The approach has been implemented for a free-flying robot in a three-dimensional workspace and experiments show that the method achieves interactive performance in complex environments.

www.cs.uu.nl The Visibility–Voronoi Complex and Its Applications ∗

We introduce a new type of diagram called the VV (c)-diagram (the Visibility–Voronoi diagram for clearance c), which is a hybrid between the visibility graph and the Voronoi diagram of polygons in the plane. It evolves from the visibility graph to the Voronoi diagram as the parameter c grows from 0 to ∞. This diagram can be used for planning natural-looking paths for a robot translating amidst polygonal obstacles in the plane. A natural-looking path is short, smooth, and keeps — where possible — an amount of clearance c from the obstacles. The VV (c)-diagram contains such paths. We also propose an algorithm that is capable of preprocessing a scene of configuration-space polygonal obstacles and constructs a data structure called the VV-complex. The VV-complex can be used to efficiently plan motion paths for any start and goal configuration and any clearance value c, without having to explicitly construct the VV (c)-diagram for that c-value. The preprocessing time is O(n 2 log n), where n is the total number of obstacle vertices, and the data structure can be queried directly for any c-value by merely performing a Dijkstra search. We have implemented a Cgal-based software package for computing the VV (c)-diagram in an exact manner for a given clearance value, and used it to plan natural-looking paths in various applications.