Citation Context

...e system dynamics. Subsequently, during so-called smoothing, they seek to find a controller and system-specific trajectory that satisfies the dynamics and roughly follows the path computed previously =-=[11]-=-. As such, the actual path planning component is purely kinematic, with the system dynamics essentially being ignored during the planning stage. This has several negative consequences. Firstly, such s...

Citation Context

...to obstacles. For highly dynamical systems, which often possess drift, potential fields can lead to oscillations unless the heuristic function is very carefully designed. Probabilistic roadmaps (e.g. =-=[9]-=-) construct a graph by generating random configurations q in C-space that do not collide with obstacles and then using a local planner to connect pairs of nearby configurations. This connection step, ...

Citation Context

...e close to xgoal. This, however, incurs significant performance penalty when compared to the bidirectional method. 5 Results We first briefly describe the dynamic model and experimental setup used in =-=[12]-=-, followed by a summary of results LaValle & Kuffner report for their example systems of increasing complexity. Some results from further research on trajectory design using RRTs are also presented. D...

Citation Context

...being restricted to rather low DOF and/or simplistic systems. 2.2 Randomized planning techniques A technique that has been successful for holonomic path planning are randomized potential fields (e.g. =-=[1]-=-). As seen in class, they define a potential field on the configuration space using a heuristic function rewarding distance to the goal and penalizing closeness to obstacles, ’steering’ the robot towa...

Citation Context

..., all the while satisfying both global constraints and local differential constraints. General kinodynamic planning, given the high-dimensional state space, has been proven to be at least PSPACE-hard =-=[15]-=-, with exact, time-optimal trajectory planning in state space being NP-hard [7]. Randomized techniques have enjoyed considerable success in ameliorating computational complexity and enabling simple, e...

Citation Context

...omized planning techniques, which the work by LaValle & Kuffner seeks to fuse. 1sq init Figure 1: A potential field guiding the robot from the initial state qinit to the goal state qgoal. Figure from =-=[14]-=-. 2.1 Kinodynamic planning Sahar & Hollerbach [16] presented one of the earliest kinodynamic planning algorithms to find minimum-time trajectories in state space, employing dynamic programming to redu...

Citation Context

...s of closed kinematic chains of robotic manipulators connected by solid objects. Carpin & Pagello [4] parallelize the RRT algorithm for planning problems involving more than one robot. Bruce & Veloso =-=[2]-=- extend the RRT algorithm using caching to apply it in real time to a team of coordinating robots. 6sFigure 5: RRTs for the translation & rotation planning tasks in 2D (left) and 3D (right). Figure 6:...

Citation Context

...aints. General kinodynamic planning, given the high-dimensional state space, has been proven to be at least PSPACE-hard [15], with exact, time-optimal trajectory planning in state space being NP-hard =-=[7]-=-. Randomized techniques have enjoyed considerable success in ameliorating computational complexity and enabling simple, efficient yet incomplete planning solutions to be devised for basic holonomic pa...

Citation Context

... degree based on the optimal metric (which always exists but is at least as hard to compute as the solution to the planning problem itself) and the use of approximate nearest neighbor techniques (see =-=[13]-=- for an overview done by Andrew Moore’s group) as possible ways to deal with these concerns. However, their original implementation uses a straightforward Euclidean metric and linear nearest neighbor ...

Citation Context

...n bounds. The first provably good approximation algorithm (running in polynomial time) to such point mass problems was presented by [7]. The same authors have suggested further generalizations, as in =-=[8]-=-. All these approaches share the problem of being restricted to rather low DOF and/or simplistic systems. 2.2 Randomized planning techniques A technique that has been successful for holonomic path pla...

Citation Context

...RTs of up to 2500 nodes. For this trivial task, it is clear that a kinodynamic planner carries more overhead than benefit and is easily outperformed by a purely kinematic planner. Kuffner reports (in =-=[10]-=-) planning times of < 0.2 seconds for a similar task on inferior hardware. For a similar body translating in 3D with six force-only translational controls |X | = 6 in a generalized maze in 3D (free fl...

Citation Context

... trajectories in state space, employing dynamic programming to reduce the search complexity. It has been attempted to solve the trajectory finding problem algebraically, most notably by Canny et. al. =-=[3]-=-, although such approaches have so far only been successful for point masses with low dimensional velocity and acceleration bounds. The first provably good approximation algorithm (running in polynomi...

Citation Context

...lle & Kuffner seeks to fuse. 1sq init Figure 1: A potential field guiding the robot from the initial state qinit to the goal state qgoal. Figure from [14]. 2.1 Kinodynamic planning Sahar & Hollerbach =-=[16]-=- presented one of the earliest kinodynamic planning algorithms to find minimum-time trajectories in state space, employing dynamic programming to reduce the search complexity. It has been attempted to...

Citation Context

...ned a following. Cortes [6] applies an RRT algorithm augmented with sampling techniques to plan motions of closed kinematic chains of robotic manipulators connected by solid objects. Carpin & Pagello =-=[4]-=- parallelize the RRT algorithm for planning problems involving more than one robot. Bruce & Veloso [2] extend the RRT algorithm using caching to apply it in real time to a team of coordinating robots....

Citation Context

...aranteed to find a solution trajectory (if one exists) as the number of vertices examined tends to infinity. Also, it can be proven that in the limiting case, an RRT will sample state space uniformly =-=[12, 5]-=-. 5.1 Dynamic model All example systems are modeled as rigid bodies with a given mass, inertia tensor and quantities: p (position of center of mass), q (unit quaternion representing rotation), v (line...

Citation Context

...orward bidirectional planning mechanism yields promising initial results for systems with significant dynamics. Since the first mention of the RRT algorithm, it has quickly gained a following. Cortes =-=[6]-=- applies an RRT algorithm augmented with sampling techniques to plan motions of closed kinematic chains of robotic manipulators connected by solid objects. Carpin & Pagello [4] parallelize the RRT alg...