## Real-Time Motion Planning and Safe Navigation in Dynamic Multi-Robot Environments (2006)

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Citations: | 4 - 3 self |

### BibTeX

@MISC{Bruce06real-timemotion,

author = {James Robert Bruce},

title = {Real-Time Motion Planning and Safe Navigation in Dynamic Multi-Robot Environments},

year = {2006}

}

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### Abstract

subcontract No. B4U528968 and prime contract No. W911W6-04-C-0058 with the US Army. The views and conclusions contained herein are those of the author, and do not necessarily reflect the position or policy of the sponsoring institutions, and no official endorsement should be inferred. Keywords: Robotics, Robot Navigation, Motion Planning, Path Planning, Multi-Robot

### Citations

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Citation Context ...ing collision checks to the graph search stage, making it more appropriate for dynamic environments. Another family of randomized planners are based on the Rapidly Exploring Random Tree (RRT) concept =-=[64, 65]-=-. This interleaves roadmap construction with search by growing a tree incrementally from the initial position. Configurations are sampled randomly from C-space, and the nearest node in the current roa... |

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Citation Context ...RT can be tuned to work for varying levels of domain dynamics faced in a particular application. Bidirectional Multi-Bridge ERRT introduces additional parameters to the Kuffner’s RRTConnect algorithm =-=[51]-=-. These new parameters allow a tradeoff between planner efficiency and plan length optimality. • Survey of Collision Detection for Motion Planning: Existing work on collision detection is evaluated fo... |

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Citation Context ...lowing: • The DSS Cooperative Multi-Robot Safety Algorithm: The novel multi-agent Dynamics Safety Search (DSS) algorithm is described. It is based on Fox et al.’s single-agent Dynamic Window approach =-=[38]-=-. DSS offers guaranteed safety for singleagent and coordinated multi-agent systems. The Dynamic Window approach cannot guarantee exact safety even in the single agent case. DSS is shown to have polyno... |

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Citation Context ...it is a reasonable question to ask whether it offers any advantage over traditional methods. Because ERRT is a continuous domain planner, it is most directly comparable to the Visibility Graph method =-=[69]-=- (see 6.1.3). Although ERRT is not limited to 2D, it can be compared with the Visibility Graph within this context. In addition, as the Visibility Graph is a minimum-length-optimal planner, we can com... |

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Citation Context ...nd secondary control loop, the robot is able to maintain a stable heading even during periods of no vision lasting several seconds. B.3 Robot Model Thus we can assume wheel centers at vectors wi, i ∈ =-=[0, 3]-=- relative to the center of the robot, each pointed perpendicular to the wi vector along unit vectors ni. Figure B.5: Model of a CMDragons holonomic robot with four omni-directional wheels (left), and ... |

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Citation Context ...dedicating the entire CPU to the task. Figure A.5: The CMDragons’02 Robots. More recent robots use use the same marker pattern. The environment in which most of this work has been done is the RoboCup =-=[55]-=- F180 ”Small Size” League, where robots up to 18cm in diameter play soccer on a 2.8m by 2.3m carpeted soccer field. The game is played with two teams with five robots each, and uses an orange golf bal... |

259 | Rapidly-exploring random trees: A new tool for path planning
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Citation Context ...ing collision checks to the graph search stage, making it more appropriate for dynamic environments. Another family of randomized planners are based on the Rapidly Exploring Random Tree (RRT) concept =-=[64, 65]-=-. This interleaves roadmap construction with search by growing a tree incrementally from the initial position. Configurations are sampled randomly from C-space, and the nearest node in the current roa... |

248 |
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Citation Context ...tion. 137138Chapter 6 Related Work 6.1 Motion Planning Motion planning is one of the most studied problems in mobile robotics. Latombe [62] gives a thorough overview of early approaches, while Reif =-=[76]-=- establishes the exponential complexity of the general path planning problem. This complexity has inspired many approximation methods, such as local minima free grid-based potentials [56], and common ... |

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Citation Context ...re generally be expressed as an evaluation function G : q → R. In this case the qgoal is set to be the maximum of G over C. • τ(s): A path is denoted as τ(s), and is a continuous function mapping s ∈ =-=[0, 1]-=- to a configuration in C. A path is constrained by τ(0) = qinit. • valid: A path τ(s) is said to be valid if ∀s.s ∈ [0, 1] ⇒ τ(s) ∈ Cfree, i.e., the path does not touch any obstacles. • solution: A pa... |

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Citation Context ... extending it using a random action. These algorithms can be thought of as modern descendents of the RPP algorithm. One of the first descendents was Hsu’s Expansive Configuration Space Planner (ECSP) =-=[48]-=-. ECSP initializes its search with the initial and goal configuration as roots of two search trees. It then executes and Expand operation on each tree, where a vertex v is chosen at random with probab... |

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Citation Context ...rent actions in a possibly loosely coupled way to support the overall team objective. A great body of existing work exists for task assignment and execution in multi-agent systems. Gerkey and Mataric =-=[43]-=- provide an overview and taxonomy of task assignment meth188ods for multi-robot systems. Uchibe [85] points out the direct conflicts that can arise between multiple executing behaviors, as well as co... |

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Citation Context ...amic 1 motion planning problem with added dynamics dimensions. The definition adopted here is by no means the only way of expressing the concept of safety, and alternate formulations exist (see [32], =-=[46]-=-,and [36,37,61]). However, the author is not aware of any alternate formulation that has become dominant, so we adopt our single formulation of cooperative safety for the remainder of this thesis. We ... |

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Citation Context ...e resulting roadmap is a tree. These are most useful for problems where path length optimality is not an issue. Another optimization trades slower queries to gain a faster learning phase. In Lazy PRM =-=[7,8]-=-, collision checks are not done while constructing the roadmap; instead of testing if an edge can be added it is added as a “potentially free” local path. During the query, the graph is searched to fi... |

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Citation Context ...inodynamic 1 motion planning problem with added dynamics dimensions. The definition adopted here is by no means the only way of expressing the concept of safety, and alternate formulations exist (see =-=[32]-=-, [46],and [36,37,61]). However, the author is not aware of any alternate formulation that has become dominant, so we adopt our single formulation of cooperative safety for the remainder of this thesi... |

152 | Randomized preprocessing of configuration space for fast path planning
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Citation Context ...sampling of the Cspace in order to construct a roadmap. The Probabilistic Roadmap (PRM) family of planners first samples configurations from C-space at random drawn from some distribution over Cspace =-=[53, 54]-=-. First, vertices are drawn at random from the distribution, and the initial and goal configurations are also added as vertices. Then, a local search algorithm attempts to connect nearby pairs of vert... |

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Citation Context ...t is tested on the QRIO humanoid robot. (Chapter 4) • The mathematical approach to iterative swept-sphere collision detection developed in this thesis, although simple, appears to be novel. Quinlan’s =-=[75]-=- related approach does not use the explicit iterative formulation. (Chapter 3) • Requirements for robust motion planning for robotics applications are introduced, and in particular robustness to locat... |

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126 | Motion Planning in Dynamic Environments Using Velocity Obstacles
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Citation Context ...tion planning problem with added dynamics dimensions. The definition adopted here is by no means the only way of expressing the concept of safety, and alternate formulations exist (see [32], [46],and =-=[36,37,61]-=-). However, the author is not aware of any alternate formulation that has become dominant, so we adopt our single formulation of cooperative safety for the remainder of this thesis. We have found our ... |

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Citation Context ... search space is the velocities of the robot’s actuated degrees of freedom. Fox et al [38] derived the case of a synchro-drive robots with a linear velocity and an angular velocity, while Brock et al =-=[12]-=- developed the case of holonomic robots with two linear velocities. Both methods use the concept of a “velocity space” where actions can be tested for safety. each point in 114the velocity space corr... |

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Citation Context ... changed the sampling method of PRM to focus on the boundaries of free space in their Gaussian PRM approach. Amato and Wu [1, 2] create another modified sampling approach called Obstacle PRM, and Hsu =-=[47]-=- created a bridge test to bias sampling to difficult 139narrow passages. Isto [49] looked at applying complex local planners to PRM, replacing the commonly used “straight-line” method for local plann... |

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Citation Context ... planners based on Kavraki et al.’s Probabilistic Roadmap (PRM) framework [53, 54]. RRT grows random trees in configuration space to solve single-query problems efficiently, and was extended by Bruce =-=[23]-=- to work efficiently in unpredictably changing domains by using continuous replanning with a bias from past plans. PRM separates planning into a learning and query phase. In the learning phase, a rand... |

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Citation Context ...es a splitting plane, the query volume is subdivided and each portion is checked recursively. If the query is itself represented as a spatial tree (such as a BSP), the checking can be quite efficient =-=[71]-=-. Figure 3.1: Examples of KD and BSP spatial partitioning trees One method not mentioned above is the interval tree, which is popular in computational geometry [30, 31]. It can be thought of as a spec... |

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Citation Context ...next variable to determine is patch shape. We chose circles, because they guarantee rotational invariance, and analytical corrections for the projective distortions of their image centroids are known =-=[44]-=-. In addition, they are compact, minimizing the length of the border with other regions, where thresholding is most difficult. In experiments, other regular shapes such as squares, hexagons, and octag... |

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Citation Context ...7. To extend the planner to 3D stepping actions, the occupancy grid world model was extended to include height values for each cell. This creates a heightmap, similar to that used in Chestnutt et al. =-=[25]-=-. The point obstacle check used for nodes in the roadmap was modified to check the flatness of the heightmap, using the standard deviation of the cells on which the robot would stand as a metric. The ... |

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Citation Context ...the checking can be quite efficient [71]. Figure 3.1: Examples of KD and BSP spatial partitioning trees One method not mentioned above is the interval tree, which is popular in computational geometry =-=[30, 31]-=-. It can be thought of as a special case of a KD-tree with a special construction algorithm. The elements of an interval tree are pairs of extents for a particular axis [xk, x ′ k ], along with a maxi... |

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Citation Context ... planner must generate both regular egomotion goals for the walking controller as well as appropriate calls to the climbing/descent module when transitions are reached. Due to the Open-R architecture =-=[40]-=-, planning can either run onboard the robot, or on an offboard computer via a wireless ethernet link. The robot has a slower relative navigation speed when compared to the small-size robots, and thus ... |

41 | Using interpolation to improve path planning: The Field D* algorithm
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Citation Context ...sition itself. D ∗ updates only the affected portion of the A ∗ search tree when changes are made to the environment, allowing more efficient update steps when compared to A ∗ . The popular Field D ∗ =-=[35]-=- algorithm relaxes the assumption of paths at fixed angles between cells, resulting in shorter paths on average compared to D ∗ , while sharing its replanning efficiency properties with D ∗ . In contr... |

33 | Efficient nearest-neighbor searching for motion planning
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Citation Context ...tion Extended RRT (ERRT) Some optimizations over the basic described in existing work are bidirectional search to speed planning, and encoding the tree’s points in an efficient spatial data structure =-=[4]-=-. In this work, a KD-tree was used to speed nearest neighbor lookup, but bidirectional search was not used because it decreases the generality of the goal state specification (it must then be a specif... |

30 | The gaussian sampling strategy for probabilistic roadmap planners
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Citation Context ...replacement probability of a node is based on its proximity to obstacles, decreasing as it gets further from obstacles. After many iterations, this converges to a distribution similar to Gaussian PRM =-=[9]-=-, which samples more configurations near the boundary of free space. However Dynamic PRM can achieve that density without the necessity for running more costly rejection sampling techniques for free c... |

30 | Fast and accurate vision-based pattern detection and identification
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Citation Context ...On top of this system lies a high-level vision system for detecting the ball and robot patterns. Our robot pattern detector uses an efficient and accurate algorithm for multidot patterns described in =-=[20]-=-. Tracking is achieved using a probabilistic method based on Extended Kalman-Bucy filters to obtain filtered estimates of ball and robot positions. Additionally, the filters provide velocity estimates... |

29 | Motion planning in dynamic environments using the relative velocityparadigm
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Citation Context ...tion planning problem with added dynamics dimensions. The definition adopted here is by no means the only way of expressing the concept of safety, and alternate formulations exist (see [32], [46],and =-=[36,37,61]-=-). However, the author is not aware of any alternate formulation that has become dominant, so we adopt our single formulation of cooperative safety for the remainder of this thesis. We have found our ... |

28 | Multi-robot team response to a multi-robot opponent team
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Citation Context ...l size league. For the team control system, offboard sensing, computation, and communication are allowed. This has lead nearly every team to adopt a centralized approach for most of the robot control =-=[19,45,78]-=- Sensing in a typical system is provided by two or more overhead cameras mounted 4m above the field. The camera signals then feed into a central computer to process the image and locate the 10 robots ... |

28 | Constructing probabilistic roadmaps with powerful local planning and path optimization
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Citation Context ...st,target) 5 then nearest ← s; 6 return nearest; Table 4.1: The basic RRT planner stochastically expands its search tree to the goal or to a random state. 75chosen or the local planner which is used =-=[6, 49]-=-. The implementation is the earliest variant as described in Kavraki et al. [53, 54]. The query phase for PRM is shown in the function PRMQuery. It begins by adding the initial and goal states to the ... |

27 | Robust Real Time Color Tracking - Simon, Behnke, et al. - 2001 |

22 |
Fast Tree-Based Exploration of State Space for Robots with Dynamics
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Citation Context ...a heuristic to limit search on finite graphs. It also made use of the forward planning possible with ECSP to sample actions, thus allowing highly non-holonomic problems to be solved. The PDST-Explore =-=[59]-=- planner takes this further, planning exclusively in action space using forward simulation. Local density estimates are calculated in a coarse way using KD-trees, and nodes are chosen for expansion de... |

21 |
A small humanoid robot SDR-4X for entertainment applications
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Citation Context ... a kinematically constrained search tree is shown in Figure 2.6. 2.3 QRIO Humanoid Robot The Sony QRIO robot is a small humanoid robot with both complex actuation and significant sensory capabilities =-=[41]-=-. The robot, shown in Figure 2.7, is able to use a stereo pair located in the robot’s head to generate a 3D occupancy grid model of the environment. This data can be used to generate a 2D grid of heig... |

20 |
Towards Real-Time Global Motion Planning in a Dynamic Environment Using the NLVO
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Citation Context ...tion planning problem with added dynamics dimensions. The definition adopted here is by no means the only way of expressing the concept of safety, and alternate formulations exist (see [32], [46],and =-=[36,37,61]-=-). However, the author is not aware of any alternate formulation that has become dominant, so we adopt our single formulation of cooperative safety for the remainder of this thesis. We have found our ... |

19 | An incremental learning approach to motion planning with roadmap management
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- 2002
(Show Context)
Citation Context ...an be achieved. 144Figure 6.2: Example Growth of RRT 6.1.6 RRT Variants Two variants of RRT exist which attempt to tackle the replanning problem. The first, called Reconfigurable Random Forest (RRF) =-=[66]-=-, extends RRT-Connect by allowing a forest of random trees instead of just the two rooted at the initial and goal configurations. For an initial plan, RRT-Connect is executed as normal, but for replan... |

18 | Motion planning in the presence of drift, underactuation and discrete system changes
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- 2005
(Show Context)
Citation Context ...to uniform coverage of control space, and thus is probabilistically complete even for non-holonomic problems. It has been applied successfully to non-holonomic problems with drift and under-actuation =-=[60]-=-. However, it does not currently have a variant tailored for replanning. 1506.2 Safety Methods 6.2.1 Dynamic Window Though not a path planner in the same sense as the other algorithms, the dynamic wi... |

16 | behavior architecture for autonomous mobile robots based on potential fields
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(Show Context)
Citation Context ...ilar to SPAR but with purely continuous functions defined on a grid. Continuous functions guarantee all locations have a well defined value so that A* [72] search can be directly applied. Laue et al. =-=[63]-=- describe a workspace potential field system with a tree-based continuous planner to calculate a path to the location of maximum potential. Task allocation in our system is described in Browning et al... |

14 | Fast color fiducial detection and dynamic workspace extension in video see-through self-tracking augmented reality
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Citation Context ... Augmented Reality. For these environments, patterns are tracked in order to localize head mounted displays and locate objects in the physical environment that are mapped into the virtual environment =-=[26, 27]-=-. Detection must be fast and accurate to minimize observable lag and jitter in the visualization. Due to work in these two environments, fast, accurate, multiple pattern detection has become better un... |

13 |
The weighted nearest neighbor rule for class dependent sample sizes
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Citation Context ...n associated classification. To classify a new pixel, a list of the K nearest exemplars are found, then the pixel is classified according to the largest proportion of classifications of the neighbors =-=[15]-=-. Both linear thresholding and nearest neighbor classification provide good results in terms of classification accuracy, but do not provide real-time performance using off-the-shelf hardware. Another ... |

13 |
Safe multi-robot navigation within dynamic constraints
- Bruce, Veloso
- 2006
(Show Context)
Citation Context ...y almost all behaviors is the navigation module, which uses the RRT-based ERRT randomized path planner [23, 51, 65] combined with a dynamics-aware safety method to ensure safe navigation when desired =-=[24]-=-. It is an extension of the Dynamic Window method [12, 38]. The robot motion control uses trapezoidal velocity profiles (bang-bang acceleration) as described in [16, 22]. B.2 Robot Hardware Figure B.3... |