Sampling-based planners have solved difficult problems in many applications of motion planning in recent years. In particular, techniques based on the Rapidly-exploring Random Trees (RRTs) have generated highly successful singlequery planners. Even though RRTs work well on many problems, they have weaknesses which cause them to explore slowly when the sampling domain is not well adapted to the problem. In this paper we characterize these issues and propose a general framework for minimizing their effect. We develop and implement a simple new planner which shows significant improvement over existing RRT-based planners. In the worst cases, the performance appears to be only slightly worse in comparison to the original RRT, and for many problems it performs orders of magnitude better.

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.

Abstract — Motion planning research has been successful in developing planning algorithms which are effective for solving problems with complicated geometric and kinematic constraints. Various applications in robotics and in other fields demand additional physical realism. Some progress has been made for non-holonomic systems. However systems with significant drift, underactuation and discrete system changes remain challenging for existing planning techniques particularly as the dimensionality of the state space increases. In this paper, we demonstrate a motion planning technique for the solution of problems with these challenging characteristics. Our approach uses sampling-based motion planning and subdivision methods. The problem that we solve is a game that was chosen to exemplify characteristics of dynamical systems that are difficult for planning. To our knowledge, this is first application of algorithmic motion planning to a problem of this type and complexity. I.

Abstract—We present an efficient approach to generating paths for humanoids and other robotic manipulators that uses the Task Space Region (TSR) framework to specify manipulation tasks. TSRs can define acceptable goal poses of an end-effector or constraints on the end-effector’s pose during the path, or both. First presented as a method for goal-specification [1], TSRs are a straightforward representation of sets of end-effector poses which can be sampled and which entail a clear distance metric. This makes TSRs ideal for sampling-based motion planning. However, a finite set of TSRs is sometimes insufficient to capture the pose constraints of a given task. To describe more complex constraints, we present TSR Chains, which are defined by linking a series of TSRs. Though the sampling for TSR Chains follows clearly from that of TSRs, the distance metric for TSR Chains is radically different. We also present a new version of our Constrained Bidirectional RRT (CBiRRT2) planner, which is capable of planning with TSR chains as well as other constraints. We demonstrate our approach on the HRP3 robot by performing a variety of whole-body manipulation tasks. I.

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We present a manipulation planning framework that allows robots to plan in the presence of constraints on end-effector pose, as well as other common constraints. The framework has three main components: constraint representation, constraintsatisfaction strategies, and a general planning algorithm. These components come together to create an efficient and probabilistically complete manipulation planning algorithm called the Constrained BiDirectional RRT (CBiRRT2). The underpinning of our framework for pose constraints is our Task Space Regions (TSRs) representation. TSRs are intuitive to specify, can be efficiently sampled, and the distance to a TSR can be evaluated very quickly, making them ideal for sampling-based planning. Most importantly, TSRs are a general representation of pose constraints that can fully describe many practical tasks. For more complex tasks, such as those needed to manipulate articulated objects, TSRs can be chained together to create more complex end-effector pose constraints. TSRs can also be intersected, a property that we use to represent pose uncertainty. We provide a detailed description of our framework, prove probabilistic completeness for our planning approach, and describe several real-world example problems that illustrate the efficiency and versatility of the TSR framework. 1 1

Abstract: The motion planning problems encountered in manipulation and legged locomotion have a distinctive multi-modal structure, where the space of feasible configurations consists of overlapping submanifolds of non-uniform dimensionality. These spaces do not possess expansiveness, a property that characterizes whether planning queries can be solved with traditional sample-based planners. We present a new sample-based multi-modal planning algorithm and analyze its completeness properties. In particular, it converges quickly when each mode is expansive relative to the submanifold in which it is embedded. We also present a variant that has the same convergence properties, but works better for problems with a large number of modes. These algorithms are demonstrated in a legged locomotion planner. 1

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.

One of the fundamental tasks robots have to perform is planning their motions while avoiding collisions with obstacles in the environment. This is the central topic of the thesis. We restrict ourselves to motion planning for two- and three-dimensional rigid bodies and articulated robots moving in static and known virtual environments. This thesis has been divided into two parts. The first part deals with comparing and analyzing sampling-based motion planning techniques, in particular variants of the Probabilistic Roadmap Method (PRM). The PRM consists of two phases: a construction and a query phase. In the construction phase, a roadmap (graph) is built, approximating the motions that can be made in the environment. First, a free random sample is created. Such a sample describes a particular placement of the moving object (robot) in the workspace. Then, a simple local planner is employed to connect the sample to some neighbors. Samples and connections are added to the graph until the roadmap is dense enough. In the query phase, the start and goal samples are connected to the graph. The path is obtained by a Dijkstra's shortest path algorithm. Many variants of the PRM have been developed over the past decade. Using both time-based as well as reachability-based analysis, we compare some of the most prominent techniques. The results are surprising in the sense that techniques often perform differently than claimed by the designers. In addition, contrary to general belief, the main challenge is not getting the free space covered but getting the nodes connected, especially when the problems get more complicated, e.g. when a narrow passage is present. By using this knowledge, we can tackle the narrow passage problem by incorporating a more powerful local planner, a refined neighbor selection strategy and a hybrid sampling strategy. The analysis also shows why the PRM successfully deals with many motion planning problems. The second part deals with quality aspects of paths and roadmaps. A good path is relatively short, keeps some distance (clearance) from the obstacles, and is smooth. We will provide algorithms that increase path clearance. A big advantage of these algorithms is that high-clearance paths can now be efficiently created without using complex data structures and algorithms. We also elaborate on algorithms that successfully decrease path length. Then, we introduce the Reachability Roadmap Method which creates small roadmaps for two- and three-dimensional problems. Such a small roadmap has many advantages over a roadmap that is created by the PRM. In particular, the method assures low query times, low memory consumption, and the roadmap can be optimized easily. The algorithm also ensures that a path is always found (if one exists) at a given resolution. We unify the techniques to create high-quality roadmaps for interactive virtual environments. That is, we use the Reachability Roadmap Method to create an initial roadmap. We add useful cycles to provide alternative routes and short paths, and we add clearance to the roadmap to obtain high-clearance paths in real-time.