7/30/2019 simulating cvrowd with balance dynamics.pdf

1/1

Simulating Crowds with Balance Dynamics

Ori P. RatnerComputer Science Department

University of Virginia

David C. BroganComputer Science Department

University of Virginia

CR Categories: I.3.7 [Computing Methodologies]: Computer

GraphicsThree-Dimensional Graphics and Realism; I.6.8 [Com-puting Methodologies]: Simulation and ModelingTypes of Sim-ulation

Keywords: Synthetic human crowds, pedestrian simulation, loco-motion dynamics and control, autonomous agents

1 IntroductionThe dynamics of walking dramatically inuences the behaviors of pedestrians, yet few details of human biomechanics and walkingcontrol are addressed in crowd animations developed for virtual en-vironments and scientic applications. People cannot stop or startinstantaneously and their movements reect an attention to bal-ance as well as other environment-driven goals. This work seeksto ll the void between full-scale, computationally expensive mod-

els of articulated human motion and simplied particle/cell modelsused in many multiagent simulations. Comparison of our pedes-trian model results with those published elsewhere reveals that thiswork preserves phenomena like self-organization, lane formation,and semi-circular crowding at exits [Helbing et al. 2002]. Further-more, our pedestrian model enables novel behaviors such as trip-ping, stumbling, and falling which permit animating more extremescenarios; for example, earthquakes, where translational forces sig-nicantly affect pedestrian and crowd dynamics.

2 Pedestrian Model and CrowdsThe two-level system that we have constructed to accomplish crowdbehaviors is composed of autonomous characters that must perceivethe environment and accomplish goals subject to the physical lim-itations of humans. The high-level crowd control algorithms spec-ify a goal velocity for every pedestrian such that crowd objectivesare accomplished. The crowd control algorithm we use is simi-lar to those implemented by Reynolds, Helbing, and others in thatthe pedestrians exhibit centering, neighbor avoidance, and velocitymatching. Our low-level pedestrian model computes a sequence of actions for each pedestrian that seeks to accomplish the goal veloc-ity issued by the crowd control algorithms. The pedestrian modelmust create character animations that move like a human when nav-igating through crowded environments and it must respond realisti-cally when external forces are applied.

Because maintaining balance, in particular, is a critical element of human walking and it is dynamic in nature, we base our pedestrianmodel on a physical simulation of a classic inverted pendulum (cart-pole). The type of inverted pendulum that we create for these crowdbehaviors reproduces pedestrian acceleration and deceleration pro-les, nominal velocities, and balance maintenance. Specically, werequire a cart-pole simulation that can move forward from a dead

e-mail: opr9t@virginia.edu and dbrogan@cs.virginia.edu

Figure 1: Pedestrians exiting a room during an earthquake. Redpedestrians have fallen and yellow are falling.

stop without rst moving backward and must have a large stableregion. Unlike the classic inverted pendulum that balances a poleabout a xed point by applying forces to a cart, our cart balancesa wide pole, or bottle. When the relative velocity between the cartand bottle is small, the bottle remains stably balanced atop the cartthrough innitely strong friction forces. The bottle will tip to theside, however, when the relative velocity is sufciently large. Aphysical simulation of an inverted pendulum is used to model thetipping of the bottle. Using two instances of the tipping bottle issufcient to represent a bottle that tips along any point around itscircular base. Turning dynamics are not explicitly modeled. Thebottle is balanced using a proportional-derivative servo controllerthat is tuned to replicate human-like velocity proles reported in theliterature [Helbing et al. 2002; Brogan and Johnson 2003]. Throughthe application of external forces to the cart, the cart-bottle simula-tion can model character collisions and environmental disturbances.

Our system exhibits behaviors similar to those reported in previ-ous systems where crowds split around an obstacle, exit a roomthrough a doorway, and pass through a narrowing hallway. To ex-tend these previous systems, our model is capable of predicting andanimating the effects of tripping pedestrians. After a few pedes-trians have fallen and others trip over them, new crowd dynamicsappear through the subsequent blockages they create. Addition-ally, our model is capable of representing the effect of ground (orbuilding) translations as experienced during earthquakes (gure 1).Pedestrians are observed moving in irregular paths in order to coun-teract the shifting ground, some able to maintain balance, whileothers fall and become obstacles for those around them. Sizes of the crowds simulated in our test scenarios range from 100 to 1000characters at near-realtime speeds. Simulation timesteps on the or-der of 33 ms give accurate results, with even larger values suitablefor non-scientic applications. This work is ongoing, as we con-tinue to investigate locomotion controllers for physically simulatedheterogeneous crowds in natural environments.

References

B ROGAN , D., AN D JOHNSON , N. 2003. Realistic human walkingpaths. Computer Animation and Social Agents , 94101.

H ELBING , D. , F ARKAS , I . J . , M OLNAR , P., AN D V ICSEK , T.2002. Simulation of pedestrian crowds in normal and evacua-tion situations. Pedestrian and Evacuation Dynamics , 2158.