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Book ChapterDOI

Reciprocal n-Body Collision Avoidance

TL;DR: This paper presents a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace, and derives sufficient conditions for collision-free motion by reducing the problem to solving a low-dimensional linear program.
Abstract: In this paper, we present a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace In our formulation, each robot acts fully independently, and does not communicate with other robots Based on the definition of velocity obstacles [5], we derive sufficient conditions for collision-free motion by reducing the problem to solving a low-dimensional linear program We test our approach on several dense and complex simulation scenarios involving thousands of robots and compute collision-free actions for all of them in only a few milliseconds To the best of our knowledge, this method is the first that can guarantee local collision-free motion for a large number of robots in a cluttered workspace

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Citations
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Proceedings ArticleDOI
03 Dec 2010
TL;DR: IGP is developed, a nonparametric statistical model based on dependent output Gaussian processes that can estimate crowd interaction from data that naturally captures the non-Markov nature of agent trajectories, as well as their goal-driven navigation.
Abstract: In this paper, we study the safe navigation of a mobile robot through crowds of dynamic agents with uncertain trajectories. Existing algorithms suffer from the “freezing robot” problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing the predictive uncertainty for individual agents by employing more informed models or heuristically limiting the predictive covariance to prevent this overcautious behavior. In this work, we demonstrate that both the individual prediction and the predictive uncertainty have little to do with the frozen robot problem. Our key insight is that dynamic agents solve the frozen robot problem by engaging in “joint collision avoidance”: They cooperatively make room to create feasible trajectories. We develop IGP, a nonparametric statistical model based on dependent output Gaussian processes that can estimate crowd interaction from data. Our model naturally captures the non-Markov nature of agent trajectories, as well as their goal-driven navigation. We then show how planning in this model can be efficiently implemented using particle based inference. Lastly, we evaluate our model on a dataset of pedestrians entering and leaving a building, first comparing the model with actual pedestrians, and find that the algorithm either outperforms human pedestrians or performs very similarly to the pedestrians. We also present an experiment where a covariance reduction method results in highly overcautious behavior, while our model performs desirably.

547 citations


Cites background or result from "Reciprocal n-Body Collision Avoidan..."

  • ...We additionally remark that the illustration in Figure 2(b), the crowd experiments catalogued in the research of [8], [9], [7], the multi-robot coordination theorems of [26], [25], and the tracking experiments of [18], [19], [16], all corroborate the argument that autonomous dynamic agents utilize joint collision avoidance behaviors for successful crowd navigation....

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  • ...([26], [25]), show that robots programmed to jointly avoid each other are guaranteed to be collision free and show improved efficiency at joint navigation tasks....

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Proceedings ArticleDOI
01 Sep 2017
TL;DR: Using deep reinforcement learning, this work develops a time-efficient navigation policy that respects common social norms and is shown to enable fully autonomous navigation of a robotic vehicle moving at human walking speed in an environment with many pedestrians.
Abstract: For robotic vehicles to navigate safely and efficiently in pedestrian-rich environments, it is important to model subtle human behaviors and navigation rules (e.g., passing on the right). However, while instinctive to humans, socially compliant navigation is still difficult to quantify due to the stochasticity in people's behaviors. Existing works are mostly focused on using feature-matching techniques to describe and imitate human paths, but often do not generalize well since the feature values can vary from person to person, and even run to run. This work notes that while it is challenging to directly specify the details of what to do (precise mechanisms of human navigation), it is straightforward to specify what not to do (violations of social norms). Specifically, using deep reinforcement learning, this work develops a time-efficient navigation policy that respects common social norms. The proposed method is shown to enable fully autonomous navigation of a robotic vehicle moving at human walking speed in an environment with many pedestrians.

515 citations


Cites methods from "Reciprocal n-Body Collision Avoidan..."

  • ...[left-handed / right-handed] agents [Avg / 75th / 90th pctl] [10th pctl / avg] passing crossing overtaking 2 ORCA [6] 0.46 / 0.49 / 0.82 0.108 / 0.131 45 / 55 51 / 49 50 / 50 CADRL [14] 0.25 / 0.30 / 0.47 0.153 / 0.189 37 / 63 38 / 62 43 / 57 SA-CADRL(none) 0.27 / 0.28 / 0.54 0.169 / 0.189 10 / 90 32 / 68 63 / 37 SA-CADRL(lh) 0.30 / 0.36 / 0.67 0.163 / 0.192 98 / 2 85 / 15 86 / 14 SA-CADRL(rh) 0.31 / 0.38 / 0.69 0.168 / 0.199 2 / 98 15 / 85 17 / 83 4 ORCA [6] 0.86 / 1.14 / 1.80 0.106 / 0.125 46 / 54 50 / 50 48 / 52 CADRL(minimax) [14] 0.41 / 0.54 / 0.76 0.096 / 0.173 31 / 69 41 / 59 46 / 54 SA-CADRL(none) 0.44 / 0.63 / 0.85 0.162 / 0.183 33 / 67 33 / 67 62 / 38 SA-CADRL(lh) 0.49 / 0.69 / 1.00 0.155 / 0.178 83 / 17 67 / 33 73 / 27 SA-CADRL(rh) 0.46 / 1.63 / 1.02 0.155 / 0.180 12 / 88 29 / 71 30 / 70 (a) passing on the right (b) overtaking on the left Fig....

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  • ...On the two-agent test-set, all RL-based methods produced more time-efficient paths than ORCA3....

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  • ...The four-agent SA-CADRL (none) policy, in comparison, exhibited a stronger preference than ORCA and CADRL in each of the passing, crossing, and overtaking scenarios (third row in Table I)....

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  • ...Similarly, the bottom rows of Table I show that in the fouragent test set, all RL-based methods outperformed ORCA, and SA-CADRL (lh/rh) exhibited behaviors that respect the social norms....

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  • ...Evidently, the optimal reciprocal collision avoidance (ORCA) [6] algorithm – a reactive, rule-based method that computes a velocity vector based on an agent’s joint geometry with its neighbors – attains nearly 50-50 left/right-handedness on these test sets (first row of Table I)....

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Journal ArticleDOI
TL;DR: It is argued that the reduction in size leads to agility and the ability to operate in tight formations and experimental arguments in support of this claim are provided.
Abstract: We describe a prototype 75 g micro quadrotor with onboard attitude estimation and control that operates autonomously with an external localization system The motivation for designing quadrotors at this scale comes from two observations First, the agility of the robot increases with a reduction in size, a fact that is supported by experimental results in this paper Second, smaller robots are able to operate in tight formations in constrained, indoor environments We describe the hardware and software used to operate the vehicle as well our dynamic model We also discuss the aerodynamics of vertical flight and the contribution of ground effect to the vehicle performance Finally, we discuss architecture and algorithms to coordinate a team of these quadrotors, and provide experimental results for a team of 20 micro quadrotors

429 citations

Journal ArticleDOI
TL;DR: An extensive set of experiments suggests that the technique outperforms state-of-the-art methods to model the behavior of pedestrians, which also makes it applicable to fields such as behavioral science or computer graphics.
Abstract: Mobile robots are increasingly populating our human environments. To interact with humans in a socially compliant way, these robots need to understand and comply with mutually accepted rules. In this paper, we present a novel approach to model the cooperative navigation behavior of humans. We model their behavior in terms of a mixture distribution that captures both the discrete navigation decisions, such as going left or going right, as well as the natural variance of human trajectories. Our approach learns the model parameters of this distribution that match, in expectation, the observed behavior in terms of user-defined features. To compute the feature expectations over the resulting high-dimensional continuous distributions, we use Hamiltonian Markov chain Monte Carlo sampling. Furthermore, we rely on a Voronoi graph of the environment to efficiently explore the space of trajectories from the robot's current position to its target position. Using the proposed model, our method is able to imitate the behavior of pedestrians or, alternatively, to replicate a specific behavior that was taught by tele-operation in the target environment of the robot. We implemented our approach on a real mobile robot and demonstrated that it is able to successfully navigate in an office environment in the presence of humans. An extensive set of experiments suggests that our technique outperforms state-of-the-art methods to model the behavior of pedestrians, which also makes it applicable to fields such as behavioral science or computer graphics.

420 citations


Cites background or methods from "Reciprocal n-Body Collision Avoidan..."

  • ...To achieve more human-like behavior, Guy et al. (2010) extended RVO by introducing response and observation time to other agents....

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  • ...Such methods include the dynamic window approach by Fox et al. (1997), the velocity obstacles by Fiorini and Shillert (1998) as well as its extension to multiple obstacles, the reciprocal velocity obstacles (RVO) (van den Berg et al., 2009)....

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  • ...To optimize the parameters of the social forces method and RVO, we minimized the norm of the discrepancy between the feature values as induced by the methods and the empirical feature values using stochastic gradient descend....

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  • ...We compared our approach to the approach of Kuderer et al. (2012), the social forces algorithm by Helbing and Molnar (1995), and the RVO introduced by van den Berg et al. (2009)....

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  • ...Similarly, van den Berg et al. (2009) presented an approach to reciprocal collision avoidance that allows a set of mobile robots to navigate without collisions....

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Journal ArticleDOI
01 Mar 2015-Robotica
TL;DR: Methods applicable to stationary obstacles, moving obstacles and multiple vehicles scenarios are reviewed, and particular attention is given to reactive methods based on local sensory data, with a special focus on recently proposed navigation laws based on model predictive and sliding mode control.
Abstract: We review a range of techniques related to navigation of unmanned vehicles through unknown environments with obstacles, especially those that rigorously ensure collision avoidance (given certain assumptions about the system). This topic continues to be an active area of research, and we highlight some directions in which available approaches may be improved. The paper discusses models of the sensors and vehicle kinematics, assumptions about the environment, and performance criteria. Methods applicable to stationary obstacles, moving obstacles and multiple vehicles scenarios are all reviewed. In preference to global approaches based on full knowledge of the environment, particular attention is given to reactive methods based on local sensory data, with a special focus on recently proposed navigation laws based on model predictive and sliding mode control.

390 citations

References
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Proceedings ArticleDOI
01 Aug 1987
TL;DR: In this article, an approach based on simulation as an alternative to scripting the paths of each bird individually is explored, with the simulated birds being the particles and the aggregate motion of the simulated flock is created by a distributed behavioral model much like that at work in a natural flock; the birds choose their own course.
Abstract: The aggregate motion of a flock of birds, a herd of land animals, or a school of fish is a beautiful and familiar part of the natural world. But this type of complex motion is rarely seen in computer animation. This paper explores an approach based on simulation as an alternative to scripting the paths of each bird individually. The simulated flock is an elaboration of a particle systems, with the simulated birds being the particles. The aggregate motion of the simulated flock is created by a distributed behavioral model much like that at work in a natural flock; the birds choose their own course. Each simulated bird is implemented as an independent actor that navigates according to its local perception of the dynamic environment, the laws of simulated physics that rule its motion, and a set of behaviors programmed into it by the "animator." The aggregate motion of the simulated flock is the result of the dense interaction of the relatively simple behaviors of the individual simulated birds.

7,365 citations

Journal ArticleDOI
TL;DR: This paper reformulated the manipulator con trol problem as direct control of manipulator motion in operational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and geometric transformation.
Abstract: This paper presents a unique real-time obstacle avoidance approach for manipulators and mobile robots based on the artificial potential field concept. Collision avoidance, tradi tionally considered a high level planning problem, can be effectively distributed between different levels of control, al lowing real-time robot operations in a complex environment. This method has been extended to moving obstacles by using a time-varying artificial patential field. We have applied this obstacle avoidance scheme to robot arm mechanisms and have used a new approach to the general problem of real-time manipulator control. We reformulated the manipulator con trol problem as direct control of manipulator motion in oper ational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and kine matic transformation. Outside the obstacles' regions of influ ence, we caused the end effector to move in a straight line with an...

6,515 citations

MonographDOI
01 Jan 2006
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

6,340 citations


"Reciprocal n-Body Collision Avoidan..." refers background in this paper

  • ...1 Note that the problem of (local) collision-avoidance differs from motion planning, where the global environment of the robot is considered to be known and a complete path towards a goal configuration is planned at once [18], and collision detection, which simply determines if two geometric objects intersect or not (see e....

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Book
01 Jan 1997
TL;DR: In this article, an introduction to computational geometry focusing on algorithms is presented, which is related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems.
Abstract: This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

4,805 citations

Book
01 Jan 2006

4,417 citations