Stephen J. Guy

Reciprocal n-Body Collision Avoidance

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.

ClearPath: highly parallel collision avoidance for multi-agent simulation

We present a new local collision avoidance algorithm between multiple agents for real-time simulations. Our approach extends the notion of velocity obstacles from robotics and formulates the conditions for collision free navigation as a quadratic optimization problem. We use a discrete optimization method to efficiently compute the motion of each agent. This resulting algorithm can be parallelized by exploiting data-parallelism and thread-level parallelism. The overall approach, ClearPath, is general and can robustly handle dense scenarios with tens or hundreds of thousands of heterogeneous agents in a few milli-seconds. As compared to prior collision avoidance algorithms, we observe more than an order of magnitude performance improvement.

PLEdestrians: a least-effort approach to crowd simulation

We present a new algorithm for simulating large-scale crowds at interactive rates based on the Principle of Least Effort. Our approach uses an optimization method to compute a biomechanically energy-efficient, collision-free trajectory that minimizes the amount of effort for each heterogeneous agent in a large crowd. Moreover, the algorithm can automatically generate many emergent phenomena such as lane formation, crowd compression, edge and wake effects ant others. We compare the results from our simulations to data collected from prior studies in pedestrian and crowd dynamics, and provide visual comparisons with real-world video. In practice, our approach can interactively simulate large crowds with thousands of agents on a desktop PC and naturally generates a diverse set of emergent behaviors.

The Hybrid Reciprocal Velocity Obstacle

We present the hybrid reciprocal velocity obstacle for collision-free and oscillation-free navigation of multiple mobile robots or virtual agents. Each robot senses its surroundings and acts independently without central coordination or communication with other robots. Our approach uses both the current position and the velocity of other robots to compute their future trajectories in order to avoid collisions. Moreover, our approach is reciprocal and avoids oscillations by explicitly taking into account that the other robots sense their surroundings as well and change their trajectories accordingly. We apply hybrid reciprocal velocity obstacles to iRobot Create mobile robots and demonstrate direct, collision-free, and oscillation-free navigation.

Simulating heterogeneous crowd behaviors using personality trait theory

We present a new technique to generate heterogeneous crowd behaviors using personality trait theory. Our formulation is based on adopting results of a user study to derive a mapping from crowd simulation parameters to the perceived behaviors of agents in computer-generated crowd simulations. We also derive a linear mapping between simulation parameters and personality descriptors corresponding to the well-established Eysenck Three-factor personality model. Furthermore, we propose a novel two-dimensional factorization of perceived personality in crowds based on a statistical analysis of the user study results. Finally, we demonstrate that our mappings and factorizations can be used to generate heterogeneous crowd behaviors in different settings.

Reciprocal collision avoidance with acceleration-velocity obstacles

We present an approach for collision avoidance for mobile robots that takes into account acceleration constraints. We discuss both the case of navigating a single robot among moving obstacles, and the case of multiple robots reciprocally avoiding collisions with each other while navigating a common workspace. Inspired by the concept of velocity obstacles [3], we introduce the acceleration-velocity obstacle (AVO) to let a robot avoid collisions with moving obstacles while obeying acceleration constraints. AVO characterizes the set of new velocities the robot can safely reach and adopt using proportional control of the acceleration. We extend this concept to reciprocal collision avoidance for multi-robot settings, by letting each robot take half of the responsibility of avoiding pairwise collisions. Our formulation guarantees collision-free navigation even as the robots act independently and simultaneously, without coordination. Our approach is designed for holonomic robots, but can also be applied to kinematically constrained non-holonomic robots such as cars. We have implemented our approach, and we show simulation results in challenging environments with large numbers of robots and obstacles.

Universal Power Law Governing Pedestrian Interactions

Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power-law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory in nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds, and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena.

A statistical similarity measure for aggregate crowd dynamics

We present an information-theoretic method to measure the similarity between a given set of observed, real-world data and visual simulation technique for aggregate crowd motions of a complex system consisting of many individual agents. This metric uses a two-step process to quantify a simulators ability to reproduce the collective behaviors of the whole system, as observed in the recorded real-world data. First, Bayesian inference is used to estimate the simulation states which best correspond to the observed data, then a maximum likelihood estimator is used to approximate the prediction errors. This process is iterated using the EM-algorithm to produce a robust, statistical estimate of the magnitude of the prediction error as measured by its entropy (smaller is better). This metric serves as a simulator-to-data similarity measurement. We evaluated the metric in terms of robustness to sensor noise, consistency across different datasets and simulation methods, and correlation to perceptual metrics.

Parameter estimation and comparative evaluation of crowd simulations

We present a novel framework to evaluate multi‐agent crowd simulation algorithms based on real‐world observations of crowd movements. A key aspect of our approach is to enable fair comparisons by automatically estimating the parameters that enable the simulation algorithms to best fit the given data. We formulate parameter estimation as an optimization problem, and propose a general framework to solve the combinatorial optimization problem for all parameterized crowd simulation algorithms. Our framework supports a variety of metrics to compare reference data and simulation outputs. The reference data may correspond to recorded trajectories, macroscopic parameters, or artist‐driven sketches. We demonstrate the benefits of our framework for example‐based simulation, modeling of cultural variations, artist‐driven crowd animation, and relative comparison of some widely‐used multi‐agent simulation algorithms.

Independent navigation of multiple mobile robots with hybrid reciprocal velocity obstacles

We present an approach for smooth and collision-free navigation of multiple mobile robots amongst each other. Each robot senses its surroundings and acts independently without central coordination or communication with other robots. Our approach uses both the current position and the velocity of other robots to predict their future trajectory in order to avoid collisions. Moreover, our approach is reciprocal and avoids oscillations by explicitly taking into account that the other robots also sense their surroundings and change their trajectories accordingly. We build on prior work related to velocity obstacles and reciprocal velocity obstacles and introduce the concept of hybrid reciprocal velocity obstacles for collision avoidance that takes into account the kinematics of the robots and uncertainty in sensor data. We apply our approach to a set of iRobot Create robots using centralized sensing and show natural, direct, and collision-free navigation in several challenging scenarios.