Improved Person-Tracking Motion Model using Goal-Oriented Trajectories, Papers of Computer Science

Download Improved Person-Tracking Motion Model using Goal-Oriented Trajectories and more Papers Computer Science in PDF only on Docsity! Better Motion Prediction for People-tracking Allison Bruce Robotics Institute Carnegie Mellon University Pittsburgh, PA 15213 Email: abruce@ri.cmu.edu Geoffrey Gordon Center for Automated Learning and Discovery Carnegie Mellon University Email: ggordon@cs.cmu.edu Abstract— An important building block for intelligent mobile robots is the ability to track people moving around in the environ- ment. Algorithms for person-tracking often incorporate motion models, which can improve tracking accuracy by predicting how people will move. More accurate motion models produce better tracking because they allow us to average together multiple predictions of the person’s location rather than depending entirely on the most recent observation. Many implemented systems, however, use simple conservative motion models such as Brownian motion (in which the person’s direction of motion is independent on each time step). We present an improved motion model based on the intuition that people tend to follow efficient trajectories through their environments rather than random paths. Our motion model learns common destinations within the environment by clustering training examples of actual trajectories, then uses a path planner to predict how a person would move along routes from his or her present location to these destinations. We have integrated this motion model into a particle-filter-based person-tracker, and we demonstrate experimentally that our new motion model performs significantly better than simpler models, especially in situations in which there are extended periods of occlusion during tracking. I. INTRODUCTION Accurately tracking moving people is of critical importance to robots. Knowing a person’s current position or being able to anticipate a person’s future position is useful for navigation in populated areas. Many tracking methods perform well when it is possible to observe the person being tracked at each time step. However, in realistic environments, people’s trajectories are often partially occluded. Long periods of occlusion can lead to a person becoming lost by the tracker and falsely identified as a different person when they return to view. We assert that in many situations, this problem can be avoided by using an improved motion model which gives the tracker a better idea of where to look for the person when they return to view. When people move through familiar environments, they do not wander according to brownian motion or always continue to move in the direction that they are currently moving. Yet many trackers naively make these assumptions in their motion models. Typically, people in public buildings walk between a finite number of points of interest (e.g., doors, corridors), often following set paths that are determined by a combination of practicality and unwritten social rules. Their motion is goal- oriented, and if we use that information in our motion model, we are more likely to successfully track a person despite periods of occlusion. Information about the location of goals can be obtained by clustering a set of recorded trajectories. We take advantage of the goal-directed nature of this motion and use the goals as a concise representation of the trajectories. Motion updates are obtained planning a path from a person’s location to the set of goals. The method we propose consists of two steps. In the training phase, given a set of previously collected trajectories, the goal locations are fit using an algorithm that approximately maximizes their likelihood. In the tracking phase, a planner plans paths from the person’s last observed position to these goals, and the resulting paths are used in the motion model of our tracker. We will explain the details of this approach, suggest when the assumptions on which it relies may and may not hold, and present results which show improved tracking performance for an experiment in which a physical robot tracks real people using a particle filter. II. RELATED WORK Most work using Bayes filters for people tracking assumes a Brownian motion model [1], or a first order motion model such as would be used with a Kalman filter [2]. Both of these simple models have limitations. The Brownian model is extremely conservative and does not attempt to model the dynamics of human motion. Because all of the motion is represented as dispersion, the hypotheses become equally spread out over a broad area when there are no observations. This is often a poor estimate of the actual distribution over a person’s possible position because people do not move randomly. Additionally, the expected distance travelled by a particle under the Brownian motion model increases as
, where
is the number of timesteps. This means that the longer a moving person is unobserved, the less likely the displacement predicted by Brownian motion is to be accurate. A first order model of a person’s dynamics is less conservative, and therefore often more accurate. But it assumes that a person will continue to move in the direction that they were last observed moving in. People often turn corners and avoid obstacles. There is no way to represent those kinds of actions with a first order model. More sophisticated models of human motion for tracking have been proposed. A piecewise-linear gaussian mixture has been used as the motion model for a person-tracking task using Wavelan signal strength as the sensor [3]. The model uses a gaussian to represent the probability of each possible action in a cell (go forward, go backward, go left, go right, stop) of a coarse grid over the map of the environment. While this approach works for Wavelan-based tracking because the high error in localization necessitates a coarse discretization of the space, it would be difficult to collect enough data to learn an accurate model at the fine discretization needed to be useful for tracking with a more accurate sensor. Also, this motion model treats future actions as only dependent on the current location, rather than viewing both as part of a path that is moving a person towards a chosen destination many steps in the future. Another learned motion model is described by Liao et al [4]. They track people using a particle filter with a motion model that is constrained to move only along the voronoi graph of the environment. The parameters of this motion model are trained using the EM algorithm. The voronoi constraint works well in this case because their goal is to recover high-level motion behavior (e.g., which rooms a person has visited) using sparse and noisy sensors rather than to recover a person’s location with a much metric accuracy. One thing that differentiates both this approach and the one described above from ours is that the movements represented in these motion models are fixed and constrained to a coarse set of possible directions. By using high level goals and a path planner in the motion model, the major axes of motion are dependent on a person’s current location. This allows a greater range of possible motion directions, which makes the motion model more likely to make accurate proposals from a variety of locations. Learning a model of common paths through through a space was first proposed for service robots by (Bennewitz, 2002). The model used for paths in that paper was a closely- spaced sequence of waypoints with Gaussian errors. This model was used to classify which group of trajectories a tracked trajectory belonged to, but it was not used to improve the performance of the underlying tracker. Additionally, the sequence-of-waypoints model is less expressive than the model we propose here: taking into account the goal-directed nature of human motion means that each cluster needs far fewer parameters while predicting motion accurately over a wider area. While there is a considerable amount of work on appearance-based people-tracking, we will not discuss it be- cause the issues involved are significantly different from the range-sensor based tracking that is used for our application. III. TRACKING USING BAYES FILTERS A. Bayes Filters The use of Bayes filters (Kalman filters, particle filters, etc.) for tracking is common. These approaches combine prior information about the state history with observations to come to a new estimate of the state. The Markov assumption allows the current state to represent the entire history, reducing computational cost. 
   
    
  
    The normalizing constant,  , is given by  "! 
# $  % & 
# '  
    and is dependent on the likelihood function, 
#     . The normalization constant is a good measure of accuracy for a bayes filter because it is proportional to the probability of the next observation given the last state. The two modeling choices that determine the characteristics of the filter are the choice of the measurement model, 
#     , and the motion model, 
     . While some filters control the complexity of the posterior distribution by making simplifying assumptions about the form of the motion and observation models, particle filters instead approximately represent arbitrarily complex posterior distributions with sets of state samples, or particles [5]. Particle filters are especially useful for our application because they can be used to represent distributions that cannot be expressed in closed form. B. Tracking The primary contribution of our approach is the proposal of a complex motion model that is trained on prior examples of people’s movements in an area. Our approach is based on the assumption that people’s movements through a space can be represented at a high level as progress towards one of a finite set of goal locations. Paths from a person’s current location to these goals (such as can be obtained by a planner) give use information about that person’s possible future position. Each sample, or particle, in our filter represents a hypothesis about the person’s current state. The state is made up of the person’s location and which goal they are moving towards. We assume that a particle’s goal is static and cannot change as long as that hypothesis exists. The likelihood that a person will approach a particular goal location can be easily estimated from the data during the training phase. This prior distribution over possible goals is represented by the percentage of particles that have each goal in their state when the filter is initialized. The motion update propagates a hypothesis along the path returned by the planner to its goal. First, the line segment of the plan that is closest to the location of the hypothesis,(*)+-,/.+-021 , is determined, and the direction of that line segment is found. The hypothesis is then displaced in that direction by a distance randomly sampled from a gaussian,  , and then a small amount of gaussian noise is added to that location,
354
6 . In our implementation, 789 was 64 times greater than78: . 0 20 40 60 80 100 120 0 100 200 300 400 500 600 Fig. 3. The particle filter normalization constants at each timestep of a trajectory. The part of the graph in the middle with zero weight is the period of time when the person was occluded by the wall. 1 2 0 10 20 30 40 50 60 70 80 90 95% confidence interval Plan−based Brownian Difference Fig. 4. The particle filter normalization constants. The first group of bars is the average over all timesteps when the person was observed, except the first 2 time steps after the person was reacquired. The second group is the average over the 2 time steps after reacquisition. Higher normalization constants correspond to smaller tracking error. show how the plan-based motion model focuses the particles in the more likely parts of the space. In the pictures of the plan-based filter, the shade of a particle indicates which goal its motion is determined by. On average, our motion model performed better overall than the Brownian motion model. The advantage of our approach is most pronounced for the first two timesteps when a person is observed again after the period of occlusion. This is because the motion models have had many timesteps to project the particles forward in time without being “corrected” by the perception update. It can be seen in Figure 1 that our motion model focuses the particles in the locations where the person is most likely to actually be while they are occluded, unlike the Brownian motion model, which just disperses its particles evenly over the space. We measured the performance by analyzing the differences between the normalization constants, described in Section III- A, for each filter at each timestep. The normalization constant was Figure VI shows the normalization constants of each filter plotted over the duration of a single example trajectory. These weights are a measure of the performance of the filter: they are estimates of the probability of the most recent observation given the previous state, so filters that do better at predicting actual observations will produce larger weights. The results of the experiment are summarized in Figure 4. The first group of bars shows the average normalization constant for the plan-based and Brownian motion model and the average difference between the normalization constants of the two filters. The averages were computed over each timestep that a person was observed, except for the first two timesteps when he or she was reacquired after the period of occlusion. The second group of bars shows the same averages for only the first two timesteps when a person had been reaccquired. A matched t-test was performed on the averages for each group. The differences in the means of both groups were determined to be significant, at
    for the first group and     for the second group. A 95% confidence interval on the difference of the means is shown on the graph. These results show that the plan-based motion model performs significantly better than the brownian motion model, both overall and immediately after reacquisition. The results suggest that the benefit in performance is larger right after reacquisition, but this comparison is not statistically significant. VII. CONCLUSION In this paper, we proposed a motion model for people tracking that is inspired by the goal-oriented nature of people’s movement. This motion model involves a learning component that allows it to use information about people’s common trajectories in a specific environment to learn goal locations. The goal locations are optimized so that paths produced by a planner agree well with the training trajectories. Paths planned from the location of a person being tracked to these goals are used by the motion update to project the hypotheses forward in time. We compared the performance of our motion model to a simple Brownian motion model within the framework of a particle filter based people tracker. Experimental results verified that our motion model performed better, creating a more realistic distribution over positions. ACKNOWLEDGEMENT Thanks to Matt Rosencrantz for his help with deciphering the internal workings of CARMEN. REFERENCES [1] S. T. M. Montemerlo and W. Whittaker, “Conditional particle filters for simultaneous mobile robot localization and people-tracking,” in IEEE International Conference on Robotics and Automation (ICRA), 2002. [Online]. Available: citeseer.nj.nec.com/thrun02conditional.html [2] E. Meier and F. Ade, “Using the condensation algorithm to implement tracking for mobile robots,” in Third European Workshop on Advanced Mobile Robots, Eurobot99, 1999, pp. 73–80. [Online]. Available: citeseer.nj.nec.com/meier99using.html [3] B. G. F. M.Berna, B.Lisien and S.Thrun, “A learning algorithm for localizing people based on wireless signal strength that uses labeled and unlabeled data,” in International Joint Conference on Artificial Intelligence, 2003. [4] J. H. H. K. L. Liao, D. Fox and D. Schulz, “Voronoi tracking: Location estimation using sparse and noisy sensor data,” in Proceedings of the Conference on Intelligent Robots and Systems (IROS), 2003. [5] S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for on-line non-linear/non-gaussian bayesian tracking,” vol. 50, no. 2, pp. 174–188, 2002. [Online]. Available: citeseer.nj.nec.com/maskell01tutorial.html [6] M. Bennewitz, W. Burgard, and S. Thrun, “Learning motion patterns of persons for mobile service robots,” in IEEE Conference on Robotics and Automation, 2002. [Online]. Available: citeseer.nj.nec.com/bennewitz02learning.html [7] N. Roy and S. Thrun, “Motion planning through policy search,” in Proceedings of the Conference on Intelligent Robots and Systems (IROS), Lausanne, Switzerland, 2002.