Sampling based planners have become increasingly efficient in solving the problems of classical motion planning and its applications. In particular, techniques based on the Rapidly-exploring Random Trees (RRTs) have generated highly successful single-query planners. Recently, a variant of this planner called dynamic-domain RRT was introduced in [28]. It relies on a new sampling scheme that improves the performance of the RRT approach on many motion planning problems. One of the drawbacks of this method is that it introduces a new parameter that requires careful tuning. In this paper

Motivation: Motion is inherent in molecular interactions. Molecular flexibility must be taken into account in order to develop accurate computational techniques for predicting interactions. Energy-based methods currently used in molecular modeling (i.e. molecular dynamics, Monte Carlo algorithms) are, in practice, only able to compute local motions while accounting for molecular flexibility. However, large-amplitude motions often occur in biological processes. We investigate the application of geometric path planning algorithms to compute such large motions in flexible molecular models. Our purpose is to exploit the efficacy of a geometric conformational search as a filtering stage before subsequent energy refinements.

Randomly expanding trees are very effective in exploring high-dimensional spaces. Consequently, they are a powerful algorithmic approach to sampling-based single-query motion planning. As the dimensionality of the configuration space increases, however, the performance of tree-based planners that use uniform expansion degrades. To address this challenge, we present a utility-guided algorithm for the online adaptation of the random tree expansion strategy. This algorithm guides expansion towards regions of maximum utility based on local characteristics of state space. To guide exploration, the algorithm adjust the parameters that control random tree expansion in response to state space information obtained during the planning process. We present experimental results to demonstrate that the resulting single-query planner is computationally more efficient and more robust than previous planners in challenging artificial and real-world environments.

We propose a novel test coverage measure for continuous and hybrid systems, which is defined using the star discrepancy notion. We also propose a test generation method guided by this coverage measure. This method was implemented in a prototype tool that can handle high dimensional systems (up to 100 dimensions).

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Abstract — This paper explores the use of evolutionary algorithms (EAs) to formulate additional biases for a probabilistic motion planner known as the Rapidly Exploring Random Tree (RRT) algorithm in environments with changing obstacle locations. An offline EA is utilized to produce a bias in an obstacle filled environment prior to rearranging the obstacles. It is demonstrated that the offline EA finds a bias reflecting the original environment and improves the RRT’s efficiency during re-planning in environments with a small number of rearrangements. The Rapidly Exploring Evolutionary Tree (RET) algorithm is introduced as a hybrid RRT algorithm employing an online EA. It is demonstrated that the RET can improve the RRT's performance during replanning in environments with many rearranged obstacles by exploiting characteristics of a balanced spatial kd-tree.

widely used to solve large planning problems where the scope prohibits the feasibility of deterministic solvers, but the efficiency of these algorithms can be severely compromised in the presence of certain kinodynamics constraints. Obstacle fields with tunnels, or tubes are notoriously difficult, as are systems with differential constraints, because the tree grows inefficiently at the boundaries. Here we present a new sampling strategy for the RRT algorithm, based on an estimated feasibility set, which affords a dramatic improvement in performance in these severely constrained systems. We demonstrate the algorithm with a detailed look at the expansion of an RRT in a swingup task, and on path planning for a nonholonomic car. I.

Kinodynamic planning algorithms like Rapidly-Exploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, non-convex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow efficiently in systems with dynamics or differential constraints. This is due in part to the fact that the conventional proximity metric, Euclidean distance, does not take into account system dynamics and constraints when identifying which node in the existing tree is capable of producing children closest to a given point in state space. Here we argue that the RRTs ’ coverage of state space is maximized by using a proximity psuedometric proportional to the length, in time, of the quickest possible trajectory

There are two main philosophies for addressing the motion planning problem, in Formulation 4.1 from Section 4.3.1. This chapter presents one of the philosophies, sampling-based motion planning, which is outlined in Figure 5.1. The main idea is to avoid the explicit construction of Cobs, as described in Section 4.3, and instead conduct a search that probes the C-space with a sampling scheme. This probing is enabled by a collision detection module, which the motion planning algorithm considers as a “black box. ” This enables the development of planning algorithms that are independent of the particular geometric models. The collision detection module handles concerns such as whether the models are semi-algebraic sets, 3D triangles, nonconvex polyhedra, and so on. This general philosophy has been very successful in recent years for solving problems from robotics, manufacturing, and biological applications that involve thousands and even millions of geometric primitives. Such problems would be practically impossible to solve using techniques that explicitly represent Cobs. Notions of completeness It is useful to define several notions of completeness

Abstract — We present a novel motion planning algorithm that efficiently generates physics-based samples in a kinematically and dynamically constrained space of a highly articulated chain. Similar to prior kinodynamic planning methods, the sampled nodes in our roadmaps are generated based on dynamic simulation. Moreover, we bias these samples by using constraint forces designed to avoid collisions while moving toward the goal configuration. We adaptively reduce the complexity of the state space by determining a subset of joints that contribute most towards the motion and only simulate these joints. Based on these configurations, we compute a valid path that satisfies non-penetration, kinematic, and dynamics constraints. Our approach can be easily combined with a variety of motion planning algorithms including probabilistic roadmaps (PRMs) and rapidly-exploring random trees (RRTs) and applied to articulated robots with hundreds of joints. We demonstrate the performance of our algorithm on several challenging benchmarks. I.