A THREE DIMENSIONAL MOVEMENT MODEL FOR PEDESTRIAN NAVIGATION

Kurzfassung

A movement model that realistically imitates real pedestrian movement can be used for numerous applications such as transport infrastructure design, evacuation planning, architecture, human like robot movement or indoor/outdoor navigation. Within the scope of this paper, the purpose of such models is to quantitatively represent the stochastic nature of pedestrian movement in order to generate a pedestrian movement model for sequential Bayesian filtering techniques, such as particle-filtering. Within the work that has led to this paper we have been particularly interested in finding suitable movement models for further use in a sequential Bayesian estimation algorithm for navigation purposes in 2D and 3D. A movement model in the sense of a first order Markov process can, therefore, be used to represent and predict the current set of human motion and behavioral parameters as a function of previous parameters and other affecting states. The prediction stage of sequential Bayesian estimation depends entirely on the movement model to determine the probability density function of the pedestrian’s location and motion at each time step. A movement model that accurately models the pedestrian’s motion strongly determines the performance of the sequential Bayesian estimation algorithm, and ensures that measurement data used for positioning is correctly weighted with the movement model prediction. Furthermore, the model has to be efficiently implemented to that it can be employed in realizations such as Particle Filters. We note that the model does not need to predict the motion of a single pedestrian accurately in any singular experiment; it needs to correctly model the expected motion in a probabilistic sense. In this paper, a three dimensional movement model at the microscopic level that is suitable for pedestrian navigation will be illustrated. A combination of three dimensional movement models will be used to model the pedestrian movement. The constituents are a three dimensional Stochastic Behavioral Movement Model and a three dimensional Targeted Movement Model. Some specific constraints are applied on the pedestrian movement while moving on stairs to have a realistic stairs movement. A three dimensional Stochastic Behavioral Movement Model Human movement is parameterized by physical parameters such as speed, direction and as a result the position. Building layouts are obviously amongst the main parameters that affect the movement of the pedestrian. For instance, the pedestrian cannot penetrate a wall under any normal circumstances. In order to add the third dimension, the model was extended to be able to predict the height of the pedestrian at each time step. A linear speed function is used for modeling the height. This speed is designed to be a function of time, steepness of the stairs and activeness of the pedestrian. Accordingly, the distance moved in the Z-direction could be predicted in addition to the distances in X and Y. The direction of vertical movement could also be modeled, but in order to have a more realistic movement in the stairs area, the direction is predicted using the Targeted Movement Model. Outside the stairs area, the height is assumed to be constant. A three dimensional Target Driven Movement Model To overcome the problem of tending to stay too long in rooms or displaying motion that is not goal orientated, the diffusion movement model is applied. This model is derived from the gas diffusion in space studied in thermodynamics and is a standard solution for path finding of robots: The idea is to have a source continuously effusing gas that disperses in free space and which gets absorbed by walls and other obstacles. A path towards this source is computed by following the steepest gradient, starting at the current position. To model the stochastic nature of a human’s motion, the destination points are chosen randomly, and a Markov process models the fact that the destination may change more or less frequently. In order to add the third dimension, the set of destinations are spread over all the floors. The stairs area is projected into a 2D area that can be included in the respective floor plan of each floor. Accordingly, the diffusion matrix calculation could be started at any of the floors. The diffusion matrix at the stairs area of the destination floor is calculated for the stairs going up and down and then copied to the stairs areas of the respective neighboring floors. The diffusion matrix is then calculated from the stairs area to the rest of the respective floor. The stairs diffusion matrix of the next upper or lower stairs is calculated using the values of the current floor and so on. Paths to the destinations are found in the same 2D manner but continuing to the upper or lower floors until the destination is reached. Combined Model If the pedestrian is outside the stairs area a top-level Markov process is used to determine whether to use the stochastic behavioral or the diffusion model; therefore, the model switches between motion that is more goal oriented or stochastic. The destination point for the diffusion model is kept until the destination is reached or until the top-level Markov process determines that the stochastic behavioral movement model is again used. When applying the diffusion model the path is computed in two steps: the direction is chosen to follow the gradient of the gas diffusion towards the target while the speed of the pedestrian is predicted with the stochastic behavioral movement model. If the pedestrian enters the stairs area then the three dimensional Stochastic Movement Model will be used to predict distance moved in the Z-direction. This distance is passed to the Targeted Movement Model to calculate distances moved in X, and Y and additionally the directions. A realistic pedestrian movement in the stairs is more target driven and that is why we are more biased toward the Targeted Movement Model while being in the stairs area.