Road User Collision Prediction Using Motion Patterns Applied to Surrogate Safety Analysis

Surrogate safety analysis is the process of diagnosing road safety indirectly from measures of ordinary (non-collision) road user behaviour, such as absolute speed and time-to-collision. While absolute speed has enjoyed much popularity in the literature, other measures such as time-to-collision are currently under developed. Before conflict measures such as time-to-collision can be adopted, several challenges need to be overcome, notably the problem of accurately modeling collision courses and collision probability from normal road user behaviour. This paper describes and explores the feasibility of implementing discretized motion pattern maps for the purpose of predicting potential collisions between road users and their measures based on an empirical naturalistic behaviour model calibrated from site-specific data for use in surrogate safety analysis. The methodology is applied to a pre-existing framework which extracts road user trajectory data from video data of a traffic scene, and then predicts and estimates potential collisions. To this end, this paper examines the motion pattern model discretization process, the probabilistic framework, the resulting indicators, and then compares the motion prediction methodology with that of the classical constant velocity motion prediction methodology. The methodology is explored using road user behaviour inside the weaving zone of a roundabout to illustrate the flawed use of constant velocity motion prediction. St-Aubin, Saunier, Miranda-Moreno 3 INTRODUCTION Traffic conflicts are classically understood to be traffic events in which two or more road users (motorists, cyclists, pedestrians, etc.) enter some collision course containing some meaningful potential for collision. The majority of these collision courses are benign as users are given the opportunity to correct their course. However, when course correction fails, the collision course prediction is realised and a collision ensues. Course correction failure might be attributed to any number of causes; the broadest of these categories include: a) environmental causes, b) vehicular mechanical failures; or c) user control failures, i.e. a failure to avoid an obstacle. Furthermore, some of these factors might overlap, for example: a situation in which a mechanical failure causes a road user to lose control and a second vehicle fails to react in time. As these factors are complex and difficult to record (despite several attempts, notably (1)), methods for surrogate safety analysis aim to substitute these factors empirically in order to detect and characterize the potential for collisions among ordinary traffic events. The core concept of a traffic conflict, and it can be argued any safety-related traffic event, is the collision course, i.e. a situation at some instant(s) where, if a road users fails to correct their current course, they are expected to collide in the future with either another road user or some other roadside obstacle. For example: a road user is distracted and fails to correct a collision course in time for a collision with a pedestrian to occur. The general hypothesis of the surrogate safety methodology is that surrogate safety measures can be designed with predictive power such that the expected number of collisions can be estimated from non-collision traffic observations. One of the best known surrogate safety measures is the temporal proximity to a collision, namely time-to-collision (TTC). TTC is especially useful in the context of road user behavior as it shares the same dimension as distraction time, reaction time, breaking time, etc. This however leaves the problem of properly predicting uncorrected motion and detecting collision courses. This aspect will be the focus of the remainder of this paper. The classical approach to this problem assumes that the natural motion of a vehicle which has no control input is one simply undergoing Newton’s first law, that is, one undergoing zero significant net force (no acceleration and no change in heading) (2). In such a scenario, a collision would occur if both road users failed to correct their course vector in the time, i.e. TTC, it takes to arrive at a collision point defined by motion prediction at a constant velocity. However, outside of certain ideal situations, such as road users traveling in straight, isolated highway sections (3) and simultaneous loss of control/failure to initiate evasive action by both road users, collision courses predicted using constant velocity make some limiting assumptions about naturalistic motion paths of road users. For example, in a curved road section, the distraction or the slow reaction time of a road user does not necessarily translate to a tangential exit path from the roadway. In fact, a distraction, for example, might even lead a road user to fail to exit an ongoing turning manoeuvre which otherwise might lead to some collision. Furthermore, even in the event that an operator is no longer in physical contact with the controls of a vehicle, road vehicles do not behave as frictionless particles. As such, a more naturalistic model is needed to meet the needs of motion prediction. However, because naturalistic motion paths are complicated and possibly unique to a given environment, an appropriate solution is needed to learn the site-specific motion patterns of road users. This is an active field of research in the field of robotics (see the review in (4)). Motion patterns are used to make automated choices adapted to a specific environment through learning, especially for spatial tasks such as path finding and classification from image data. This paper explores the application of motion patterns by first attempting a basic learning process on a sample of 12-hours of traffic data (a full week day of typical, moderately heavy traffic flow) and then applying the motion pattern to collision prediction and computation of the surrogate safety measure timeto-collision. The results are then compared with the naïve method of motion prediction at constant velocity. St-Aubin, Saunier, Miranda-Moreno 4 BACKGROUND Previous vehicle trajectory prediction used simplifying assumptions about naturalistic road user behaviour to model deterministic behaviour (prediction at constant velocity) or made use of objective-based prototypes. As mentioned before, constant velocity is a staple of the surrogate safety methodology for estimating time-to-collision, and traces its roots all the way back to the earliest implementation of the traffic conflict technique which measured traffic conflict events via trained observers (2) (5). Prototypes are frequently used to describe objective-based spatial tasks, often scene entrance and exit tasks. Examples of prototypes applied to traffic scenery include Baiget et al. who measured origin and destination points of outdoor pedestrians in a traffic scene (6) and Saunier et al. who used motion patterns to form prototypes for turning decisions inside of traffic intersections (7). Mohamed and Saunier recently implemented more sophisticated methods stemming from the field of robotics and vision including normal adaptation which accounts for naturalistic variability between velocity vectors and evasive action, as well as variations on the collision detection algorithm (4), itself inspired from Broadhurst et al.’s modeling of control inputs (8). Motion patterns have been relatively well developed in the field of Robotics as they describe naturalistic trajectory patterns from normal behaviour, including user trajectories. Motion patterns are frequently described in a number of ways, including prototypes, discrete maps, and probabilistic models such as hidden Markov models (HMM). A very popular approach to learning these motion patterns is by using the Expectation-Maximisation (EM) algorithm (9). Motion patterns are frequently implemented in traffic scenes, though typically in contexts outside of road safety, or frequently concerning image processing (trajectory extraction). For example, Gryn et al. use motion patterns and direction maps to construct turning ratios in a scene from traffic video data (10). Bennewitz et al. use motion patterns from laser-based detection to model motion of pedestrians inside of a building (11). Morris and Trivedi have extensively reviewed motion patterns and trajectory path models and discussed the capability of trajectory prediction as well as collision prediction from learned behaviour (12). Paths are defined as one or a multiple of three type: i) centroid, ii) envelope, or iii) sub path models.