An RRT-Based Algorithm for Testing and Validating Multi-Robot Controllers

Kim, Jong-Woo; Esposito, Joel M.; Kumar, Vijay

doi:10.15607/rss.2005.i.033

Cited by 32 publications

(76 citation statements)

References 16 publications

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“…Using a suitable metric for distance and a sampling scheme, simulations are used to find an error trajectory of the system. These approaches have been successful in the case of linear systems, and a few hybrid systems [10], [14], [29], [33], [35]. Hybrid systems pose interesting problems to sequential search because directional information available from the dynamics in each mode need not be useful in the presence of mode switches.…”

Section: ) Direct Multiple Shootingmentioning

confidence: 99%

A trajectory splicing approach to concretizing counterexamples for hybrid systems

Zutshi

Sankaranarayanan

Deshmukh³

et al. 2013

52nd IEEE Conference on Decision and Control

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Abstract-This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory.We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations.

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Section: ) Direct Multiple Shootingmentioning

confidence: 99%

A trajectory splicing approach to concretizing counterexamples for hybrid systems

Zutshi

Sankaranarayanan

Deshmukh³

et al. 2013

52nd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

show abstract

“…These values are updated while building the tree and used to select nodes during exploration. The RRT extension proposed in [8] is similar, in which the algorithm keeps the history of expansion attempts on nodes, considering failed attempts as both collisions, as well as repetition of previous expansions. Furthermore, in place of the Euclidean distance metric, this algorithm calculates the cost-to-go from each node in the tree toward the sample using a linear approximation of the dynamics for each node.…”

Section: Rrt Modificationsmentioning

confidence: 99%

Reachability-guided sampling for planning under differential constraints

Shkolnik

Walter

Tedrake

2009

2009 IEEE International Conference on Robotics and Automation

120

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Abstract-Rapidly-exploring Random Trees (RRTs) are 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. INTRODUCTIONThe problem of robotic motion planning, whether for a wheeled robot, an aerial vehicle, or a quadruped, has motivated the development of powerful tools for planning in high dimensional spaces. Of these techniques, randomized sample-based planning strategies have proven particularly effective in quickly solving for a series of actions that drive the system to a desired state. Perhaps the most widely used single-query sample-based planners are those based upon Rapidly-exploring Randomized Trees (RRTs). RRTs have been used to solve a broad range of planning problems that include motion for manipulators and kinematic chains [1], [2].It is well-known that these algorithms can quickly become inefficient when planning on systems with complicated kinodynamic constraints [3], and there has been considerable work in attempting to modify the basic RRT algorithm for these situations [3], [4]. The essential symptom of this inefficiency is that nodes at the boundaries of these constraints tend to be sampled and expanded repeatedly, with little progress towards the ultimate goal.In this paper, we present a modified adaptive sampling strategy for the RRT algorithm which takes into account local reachability, as defined by differential constraints, while building the tree. The algorithm is based on the observation that sampling points at random and checking collisions is relatively cheap, but adding extra nodes to the tree (through the Extend algorithm) is relatively more expensive -both in its instantaneous cost and in the added cost of having a larger tree. Therefore, we attempt to build sparse trees through kinodynamic obstacles, with a simple heuristic that quickly throws away random samples that otherwise would not have the effect of extending the tree into previously unexplored regions of state space. This effectively changes the sampling distribution, so that points are selected uniformly from a

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“…When the counter reaches a given limit number l, the node is considered to be exhausted and it is no longer selected. A similar strategy discussed in [16] uses an expansion failure counter to devise a weighted metric for the nearest node selection.…”

Section: Avoiding Exhausted Nodesmentioning

confidence: 99%

Molecular Disassembly With Rrt-Like Algorithms

Cortés

Jaillet

Siméon

2007

Proceedings 2007 IEEE International Conference on Robotics and Automation

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Abstract-This paper addresses the problem of computing pathways for a ligand to exit from the active site of a protein. Such problem can be formulated as a mechanical disassembly problem for two articulated objects. Its solution requires searching paths in a constrained high-dimensional configurationspace. Indeed, the ligand passageway inside the protein is often extremely cluttered so that current path planning techniques are unable to solve the disassembly problem in reasonable computing time. The techniques presented in this paper are based on the RRT algorithm. First we discuss some simple and general modifications of the basic algorithm that significantly improve its performance. Then we describe a new variant of the planner that treats ligand and protein degrees of freedom separately. This new algorithm outperforms the basic RRT, particularly for very constrained problems, and is able to handle models with hundreds of degrees of freedom. We analyze the effects of each RRT variant via several examples of different complexity. Although discussions and results of this paper focus on molecular models, the ideas behind the algorithms are general and can be applied to path planners for disassembling articulated mechanical parts.

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An RRT-Based Algorithm for Testing and Validating Multi-Robot Controllers

Cited by 32 publications

References 16 publications

A trajectory splicing approach to concretizing counterexamples for hybrid systems

A trajectory splicing approach to concretizing counterexamples for hybrid systems

Reachability-guided sampling for planning under differential constraints

Molecular Disassembly With Rrt-Like Algorithms

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