Behavior Identification and Prediction for a Probabilistic Risk Framework
Jasprit Singh Gill, Pierluigi Pisu, Venkat N. Krovi, Matthias J. Schmid
BBEHAVIOR IDENTIFICATION AND PREDICTION FOR A PROBABILISTIC RISKFRAMEWORK
Jasprit Singh Gill, Pierluigi Pisu, Venkat N. Krovi, Matthias J. Schmid ∗ Department of Automotive EngineeringClemson University International Center of Automotive ResearchGreenville, South Carolina, [email protected], [email protected], [email protected], [email protected]
ABSTRACT
Operation in a real world traffic requires autonomous ve-hicles to be able to plan their motion in complex environments(multiple moving participants). Planning through such environ-ment requires the right search space to be provided for the tra-jectory or maneuver planners so that the safest motion for theego vehicle can be identified. Given the current states of the en-vironment and its participants, analyzing the risks based on thepredicted trajectories of all the traffic participants provides thenecessary search space for the planning of motion. This paperprovides a fresh taxonomy of safety / risks that an autonomousvehicle should be able to handle while navigating through traf-fic. It provides a reference system architecture that needs to beimplemented as well as describes a novel way of identifying andpredicting the behaviors of the traffic participants using classicMulti Model Adaptive Estimation (MMAE). Preliminary simula-tion results of the implemented model are included.
INTRODUCTION
Deployment of highly autonomous vehicles on the road re-quires them to be able to plan their motion in complex envi-ronment(environments with multiple maneuvering participants).Planning problem in any environment can basically be consid-ered as an optimization problem with following steps: (i) identi-fying the possible states (i.e. search space) that the vehicle canattain while staying within safety constraints; (ii) performing anoptimized search through this search space using an objectivefunction (cost function) that represents the identified constraintsof the motion; and (iii) provide a reference to the motion execu-tion modules of the vehicle. Depending on the different factors ∗ corresponding author considered while generating a search space, the different levelsof planning are involved in navigation.1. Path planning: A path is a collection of poses that a vehi-cle has followed in the past or might be following in a fi-nite future [1]. It usually consists of states like longitudinalposition, lateral position and orientation in case of 2D nav-igation in a road environment but without any informationof time. Path planning is determining the future path of thevehicle given its present states, available map and missionlevel goals. States of the other participants of the traffic en-vironment are usually not considered in this.2. Trajectory planning: Trajectory is a collection of position,orientation, velocity and/or higher derivative states of a ve-hicle marked with time stamps. A path can be extracted froma trajectory, but trajectory cannot be recreated from path dueto lack of time information [1]. Trajectory planning deter-mines the future trajectory of the vehicle given its presentstates, map, goal and may also involve states of the partici-pants of the environment.3. Maneuver planning: A maneuver is a collection of motionsequences that a vehicle executes in order to achieve a locallevel mission objective, e.g. lane change, lane merging, leftturn, right turn. As seen in the literature [2, 3, 4, 5], the termsmaneuver and behavior will be used interchangeably in thisdocument. Maneuvers can typically be described by trajec-tories since they involve specifying stopping times, veloc-ities and possibly accelerations at different spatiotemporalpoints in the future. Maneuver planning can either be plan-ning to identify a maneuver or it can encompass trajectoryplanning.Navigation through a complex traffic environment requiresplanning to be performed at the trajectory level or maneuver1 a r X i v : . [ c s . R O ] M a y evel. Given the current states of the environment and its par-ticipants, analyzing the risks provides the necessary search spacefor such planners. Risk analysis can be decomposed into follow-ing 3 steps [5,6,4]: (i) identify states of all the traffic participants;(ii) predict their future states in a time step t+s in the future; and(iii) check the possibility of a risky event (e.g. collision) at eachtime step.To assess the risks in the correct domain space for effectiveplanning, we need to understand the needs of real-world drivingscenarios. Collisions with other entities (pedestrian, bicyclists,other vehicles, stationary objects, etc.) are the primary risks thatneed to be avoided. However, the risks can also include violat-ing a road traffic rule, road ethics, or even inconvenient drivingconditions that can lead to an injury to the occupants or the ve-hicle functionality in the short or long term. For instance, thedrivers actively avoid behaviors that can lead to a probable col-lision. Hence, identifying the behaviors and predicting the tra-jectories of all the traffic participants becomes a key in analyzingthe risks.This paper seeks to approach the challenges of navigationthrough complex traffic environments by collectively looking atthe needs of the operating domain as well as the state-of-the-art of the technology from a broader perspective followed by anarrowed down identification of solutions. The contribution ofthis paper are as follows:1. It provides a fresh taxonomy of safety / risks that an au-tonomous vehicle needs to address while navigating throughtraffic.2. It presents a reference system architecture suited for imple-mentation in an autonomous vehicle in order to navigatethrough traffic successfully. Then, it discusses an existingprobabilistic framework in the literature and demonstrateshow it can be mapped to the architecture.3. It describes a novel way of identifying and predicting the be-haviors of the traffic participants using classic Multi ModelAdaptive Estimation (MMAE) and demonstrating how it canbe integrated into the discussed probabilistic framework. Fi-nally, some preliminary simulation results of implementedmodel are described.The paper is organized as follows. The next section de-scribes the classification of risk assessment based on the needs ofthe traffic environment. This is followed by the reference systemarchitecture and the proposed model for behavior identification.Due to the breadth of the topics covered in this paper, the relatedwork has been discussed in the respective sections. RISK ASSESSMENT CLASSIFICATION
At the broadest level, the risk assessment can be classified aseither near term (short horizon) or long horizon as described in
FIGURE 1 . RISK ASSESSMENT CLASSIFICATION figure 1. When the foreseen evaluation of the risk is in the tem-poral vicinity of human response time, its in the near term else itcan be considered long horizon. This classification is importantdue to one key factor in determining the risk mitigation strategy(i.e. motion planning) - whether the traffic rules should be fol-lowed or not. For near term risk prevention, the primary priorityof the planners needs to be risk avoidance with or without rulefollowing. For long horizon risk prevention, the planners need toobey the traffic rules. As a result mitigation strategies for boththe categories of risks require different policy models to be fol-lowed. In both the cases, identifying whether a traffic participantperforms an expected behavior as per the traffic rules or an unex-pected behavior, can further help identify a risky situation. Oneof the recent works in identifying such unexpected behaviors waspresented in [4].
Near term risk assessment
For the near-term risk assessment, in the literature, the in-teractions between the traffic participants are ignored. Physicsbased models (like constant velocity, constant acceleration, con-stant turning rate acceleration, constant curvature, etc. [7]) areused for predicting the trajectories in the future as if the partici-pants are moving independent of each other. The argument thatthe interactions between the vehicles can be ignored holds trueonly for the time horizon of a human response time, which isabout 1-2 seconds.If an unexpected behavior is observed such that the othertraffic participant (due to a rule breaking or a failure) is at fault,the risk analysis needs to determine if the collision is inevitableor avoidable. Metrics such as time-to-collision, time-to-react,distance-to-collision, etc. can be utilized for this. The examplesituations in this category are: a participant cutting across whilethe ego car drives straight, or an on-coming vehicle crossing thedivider and coming into the lane. If the collision is inevitable,then the risk analysis module needs to be able to provide the as-sessment of impact so that a behavior that minimizes the dam-age can be planned while the system is preparing for a colli-ion. Most of the emergency advanced driver assistance systems(ADAS) fall in this category. For the case in which the collisionis avoidable, the risk analysis module should be able to providethe assessment of the situation so that an evasive behavior (brak-ing only, steering only or a combination of braking and steering)with least possible consequences can be planned. Whether thecollision is avoidable or inevitable, the planning in this case isdone with a lower priority attributed to the rule following andhigher priority attributed to the maneuver that leads to the leastpossible consequence.If an unexpected behavior is observed for an ego vehicle,which is likely due to a failure in some vehicle module, then thefault diagnosis and fault mitigation routines need to take over astypical models may fail in this case. This research area is out ofscope of the presented work.In case where all the participants are behaving as theyshould, and no rule is broken, the main objective of the risk as-sessment module is to help short term rule adherence for the egovehicle and analyze the trajectories that may lead to dangeroussituations. Driver assistance systems such as lane keeping, adap-tive lane following (adaptive cruise control), etc fall under thiscategory.
Related work
Most of the ADAS systems address risksin this category. Lane merge assist systems that are on the hori-zon also address such risks, however a lane merge maneuver isn’talways a short term maneuver. Collision-based risk predictionhas been an active topic for researchers for quite some time nowwith a large body of literature available. The popular approachin such cases is to ignore the driver inputs, make assumptionsabout constant velocity, acceleration, steering angle or steeringrate, predict the trajectories of the traffic participants based onthis, and then check for an event like time-to-collision, distance-to-collision [5], time to closest approach, etc. to determine possi-ble conflicts. Some of the notable works that implement compu-tationally effective methods to determine possible conflicts arediscussed here. Campos et. al. [6] provide the 3 step proce-dure for the threat assessment for collision avoidance at inter-sections. The three step procedure is: (i) use unscented trans-form to predict the trajectories using constant turn rate accelera-tion (CTRA) model; (ii) define some geometric areas (collisionzones approximated as rectangles) on the vehicles for calculat-ing the time-to-collision (TTC) and distance-to-collision (DTC)and then use bivariate normal distribution integral approxima-tion (Drezner, 1978 [8]) to find the probability of collision. (iii)employ reachability analysis for assessment of threat. This pub-lication also gives the values of covariance parameters from ex-periments, which are typically challenging to determine. Batz etal [9] use unscented transform for predicting trajectories. Here,covariance ellipses are utilized in calculating the area represent-ing the position of the vehicles, adding uncertainty of orientation and then applying Minkowski’s sum operator to it for every ve-hicle. Then for every vehicle pair, the approach calculates theminimum distance in the short time in the future, if this distancefalls below certain threshold it flags a dangerous situation. How-ever, these methods are usable only for short term prediction asmost of them ignore driver intent, which is the key uncertaintyfor long horizon risk assessment.
Long horizon risk assessment
When the risks being analyzed are spatially or temporallyfar enough to take risk averse actions to gracefully handle thesituation, it comes under this category. The assessment in thiscase is more for a possible risk rather than an event, althoughthis is as important as the latter. The models in this case can as-sume the traffic participants to be either interaction-aware or non-interactive, however for complete risk assessment former needsto be considered. Irrespective of whether an unexpected behaviorwas observed or not, the rule adherence in the planning needs tobe ensured in this case.If an unexpected behavior on part of another participant isobserved, the risk assessment module analyzes different behav-iors to help plan a risk-averse maneuver that gracefully handlesthe situation. The risk assessment in this case can either bebased on the possible maneuvers that the ego vehicle can pos-sibly make. Or it can simply be on the input space of the vehicleafter compounding all the risk assessment from different possi-ble maneuvers [10]. Example in this case would be a vehiclebroken down in the middle of the road. Or an intersection sce-nario where the ego vehicle comes across another vehicle fromthe perpendicular road stopped in the middle of an intersectionwhile the signal is green. The graceful behavior in such caseswould be for the ego car to either brake to a complete stop orchanging the lanes to drive around the vehicle.If no unexpected behaviors are observed for the traffic par-ticipants, then the risk assessment in this case will be safety anal-ysis and efficiency analysis of driving maneuvers such that onesthat can lead to a possible near-term risk can be avoided. Ex-amples of such situations can be when a car is parked on theshoulder. Typical behavior in this case of the vehicles drivingin the adjoining lane is either to slow down or change the lanes.Another example would be in a multiple lane intersection withmerge ins, where other vehicles are merging in, behaviors of thevehicle in the adjoining lane can be changing the lane so as toavoid any possible conflicts.For the long term risks, the steps that need to be followed forrisk assessment are: 1. Model and predict the possible expectedbehaviors of the traffic participants. 2. Analyze the possible riskof every possible behavior of the ego vehicle, against the possi-ble predicted behaviors of the traffic participants. 3. Once thetraffic participant executes the behavior, the module should beable to identify the behavior. 4. If an unexpected maneuver wasxecuted, the module should be able to differentiate it from theexpected ones.
Related work
The frameworks and the works address-ing the challenges in this area are relatively recent. Gindele et.al. [2] presented one of the first frameworks that considers vehi-cle interaction as well as the driver behavior for prediction. Thisframework will be discussed in detail in the section Probabilis-tic Framework. Lefevre et al. [4] presented an extension of thisframework for reasoning for collision risk at a semantic level bydifferentiating expected behaviors of the drivers from the unex-pected behaviors. The framework was demonstrated by applyingto the road intersections with interactions. Among the most re-cent works, Damerow [10] presents a situation-based risk eval-uation and behavior planning framework for highly automateddriving. Analysis of risks is performed using prototypical pre-dicted trajectories of the traffic participants and the result of theanalysis is a proposed risk map that basically a search space forthe behavior planner. The framework is demonstrated for paral-lel driving and intersection traffic scenes. Prototypical trajecto-ries based approaches however implicitly assume the availabilityof the high definition digital maps for effective operation. Fur-ther, the framework is decoupled from the environment percep-tion module and doesn’t reuse the information about uncertaintyalready available from it. However, the prediction sub-moduleof our reference architecture described in the next section, is in-spired from this framework.
SYSTEM ARCHITECTURE FOR HIGHLY AU-TONOMOUS DRIVING
Figure 2 provides the overall software architecture envi-sioned for a highly autonomous driving vehicle. The differentmodules in it are described below.Localization: This module uses proprioceptive and extero-ceptive sensors to determine the detailed pose (position and ori-entation) of the ego-vehicle, including the lane and offset fromthe center lane, in the operating environment. Typical proprio-ceptive sensors are inertia measurement unit (IMU) and wheelspeed sensor, whereas commonly used exteroceptive sensors arecamera, LiDAR and GPS.Perception (Environment perception): Uses exteroceptivesensors like cameras, lidar and radar to detect stationary anddynamic obstacles that are around ego vehicles and, classifiesthem and tracks them to estimate their kinematic states. It alsoseparates quasi-stationary features in the environment (obstacles)from permanent features that define the environment (like land-marks, lane information, traffic signs, for e.g.).Decision making module: The information about the ego-vehicle pose, the states of the other traffic participants and trafficconditions (signals, road geometry) determined from the local- ization and perception module are fed into the decision-makingmodule. This module can be further divided into situationalawareness (SA) and prediction sub-modules.Situational awareness sub-module: This module uses the in-formation from perception module to identify traffic scenarios.Traffic scenarios can be thought of as a high level semantic rep-resentation of the traffic environment, like signalized intersec-tion, non-signalized intersection, lane following, round about,etc. Each traffic scenario can be further divided into differentsituations depending on the larger objective of the ego vehicleand the current states of the other traffic participants. For e.g.,in an intersection where the ego vehicle intends to turn left, thesituation can vary depending on whether there is another partic-ipant present in an oncoming lane that is going straight. Thisidentification is important as it defines the traffic policies (likeright of the way) that apply to all the traffic participants in thesituation. The identification of an unexpected behavior by a traf-fic participant needs to happen in this module. After identifyingthe traffic scene, based on the current states of all the traffic par-ticipants, this sub-module is also responsible for identifying thecurrent situation of the scenario.Prediction sub-module: Based on the current situation, pre-diction module is responsible for determining the possible situ-ations into which the current situation can evolve, depending onthe possible behaviors all the traffic participants may perform.For each possible situation, the module then needs to make someassumptions about every traffic participant and then forward sim-ulate their trajectories for a predefined look ahead. These pre-dicted trajectories of all traffic participants can then used to ana-lyze the safety or risks involved, considering the traffic policiesin place, against every possible maneuver that the ego-vehiclecan take. The metric for this conflict can be based on lane oc-cupancy, possible future collision, time to collision, distance tocollision, etc. The outcome of a risk analysis is a search spacethat the planning modules then use to plan the trajectory of theego vehicle.Mission planning module: This module uses the missionlevel parameters like current position, goal position and digitalmap information to plan the most optimal route for the vehicle.The planned route doesn’t consider traffic or lane level informa-tion. Further it only consists of waypoint or path information andnot trajectory information. This module is responsible in deter-mining when the assigned mission has been accomplished.Behavior planning module: This module takes the route in-formation from the mission planning module, and the risk/safetyinformation from the decision-making module to identify thesafest behavior that the ego-vehicle should perform specifyingthe trajectory to realize the behavior. Based on this a refer-ence trajectory is generated and provided to the trajectory trackermodule.Trajectory tracker: Based on the reference trajectory it re-ceives from the behavior planner and the current state of the ve-
IGURE 2 . AUTONOMOUS VEHICLE ARCHITECTURE hicle, this module executes the behavior in a smoothest possibleway.As can be seen, for an effective navigation, the situationalawareness, prediction and behavior planner work together in thedecision making. The success of behavior planner in navigatingsafely through a dynamic environment is dependent on the capa-bility of the prediction module to identify the risks. The predic-tion module in turn depends on the situational awareness moduleto identify the right traffic policy applicable based on the situa-tion and then analyze the risk. As a result, unlike near term riskplanning, where these modules are decoupled from each other,for a comprehensive analysis of long-term risks, there is a signif-icant information flow and interaction between the three modulesrequiring a probabilistic framework that meets this requirement.
PROBABILISTIC FRAMEWORK
Currently, the most comprehensive framework available forprediction is provided by Gindele et. al. [2]. The frameworkintroduces the concept of context and establishes the relation-ships between context, situations and behaviors. This sectionwill briefly cover the filter equations and explain how it maps toour reference architecture. For more details the reader is referredto the work [2].The joint probability density function of the dynamicbayesian network our work adopts from is given by: P ( X , X − , C , S , B , B − , T , T − , Z ) = P ( X − ) P ( B − ) P ( T − ) P ( X | T − ) P ( C | X ) P ( S | C ) P ( B | B − , S ) P ( T | T − , B , C , X ) P ( Z | X ) (1) The resulting filter equation can be given by P ( X , C , B , T , U | z ) ∝ P ( z | X ) (cid:90) B − , T − P ( X , C , S , B , T | B − , T − ) P ( B − ; T − ) (2)where, for N traffic participants in the scene, X: is the vectorcontaining the states of all the traffic participants. X = ( X X X ... X N ) T C: Vector containing the context, which is a list of features suchas distances from the surrounding traffic participants, that helpdefine a situation C = ( C C C ... C N ) T S: Vector containing the situations of all the traffic participants S = ( S S S ... S N ) T B: Vector containing the possible behaviors of all the traffic par-ticipants for a particular situation. X = ( B B B ... B N ) T T: Vector containing the trajectories that realize the behaviors forall the traffic participants. T = ( T T T ... T N ) T Z: Measurement vector for every observed vehicle Z = ( Z Z Z ... Z N ) T If we compare this with the system architecture presented in fig-ure 2, the probability density function (pdf) of the prior ( X − )is provided collectively by the perception and the localizationmodules. The scene identification sub-module in the situationalawareness block, uses the available digital maps and / or the priorinformation to identify the traffic scene. The situation classifica-tion sub-module then utilizes this information, derives the con-text information using helper functions (for details about helperfunctions refer to [2, 11]) and uses them to provide the condi-tional pdf of the situation ( P ( S | C ) ). Based on the traffic policiesefined within it, the trajectory prediction sub-module of the pre-diction module, provides a conditional pdf of the possible behav-iors that all the traffic participants may perform ( P ( B | B − , S ) ). Itthen identifies the likely trajectories that the traffic participantsmight execute to realize the behaviors ( P ( T | T − , B ) ). The riskevaluation sub-module uses these predicted trajectories of thetraffic participants to predict possible risks as per the identifiedmetrics.The focus of this study is the behavior identification of thetraffic participants and their trajectory prediction. Gindele et alemployed multiple motion models for different behaviors of theparticipants, however they realized the framework using parti-cle filters. The difference in our approach lies in the utilizationof Multiple Model Adaptive Estimation (MMAE) [12] for mod-eling the behaviors. This has two benefits: first, a variant ofMMAE called interactive multiple model (IMM) filter [7, 12, 13]is already one of the prevailing techniques in the tracking imple-mentations of perception modules. Hence, our approach helpsintegrating into the existing frameworks of perception. Second,the approach is less computationally intensive than particle fil-ters. BEHAVIOR IDENTIFICATION MODEL WITH MULTIPLEMODEL FILTERS
The presence of both discrete as well as continuous statesin the autonomous vehicle framework described above makesit a hybrid system. MMAE-based approaches are the prevail-ing techniques in the hybrid state estimation. For a compre-hensive review of MMAE based approaches the reader is sug-gested to refer to [14, 12]. These works also provide a classifi-cation of the MMAE into 3 generations: a) classic MMAE, b)the Interacting Multi Model (IMM) approach; and c) the vari-able structure MMAE approach. Of the above, the IMM aproachis adopted the most as it has proven to be superior to the clas-sic MMAE [14] and due to their simplicity compared to variablestructure approaches. Both classic MMAE and IMM run a bankof kalman filters, each with a different motion or measurementmodels, and then provide a combined state estimate calculatedfrom the weighted state estimate of every filter. The IMM ap-proach however, has an additional step called interaction step inwhich the most recent estimates from all single-model filters aremixed according to their predicted probabilities and then set asinitial estimates for their next cycles. It is this interaction stepthat makes the execution of IMM filter banks dependent on eachother in between every cycle. As a result, the models in IMM canrun truly parallel to each other only within a prediction step, butnot across multiple prediction cycles. In classic MMAE, on theother hand, all single model filters in its bank run independent ofeach other, and hence can run truly parallel across all cycles. Thisenables utilization of the recent advances in the parallel comput-ing technology. One related recent study by Xie et al also uses a multi modelapproach for prediction. The authors employ an IMM to differ-entiate between long term and near term trajectory prediction forthe same maneuver. In contrast, our study differs in two ways:first, We use the classic MMAE for trajectory prediction. Sec-ond, each single-model filter corresponds to a different maneu-ver. With the recent advances in computing and sensor technolo-gies, and due to a different set of requirements for predictionapplications as compared to tracking applications, a careful re-evaluation of MMAE is necessary. For the scope of this work,the MMAE approach is exemplary for only one observed vehi-cle. Expanding to multiple vehicle will be addressed in futurework.The classic MMAE has three stages [12]:Model specific filtering: The equations for prediction andupdate for each single-model filter follow the extended kalmanfilter (EKF) [12]. The different model assumptions for each filterwill be discussed in the next section.Model probability update: This stage determines the likeli-hood of the measurements for every single-model filter estimate,and then determines the associated weights for each filter. For Mfilters, initial weight for every filter w ( j ) = / M for j = 1, 2, ...M. w ( j ) k = w ( j ) k − p ( ˜ z k | ˆ x − ( j ) k ) (3) p ( ˜ y | ˆ x − ( j ) k ) = (cid:104) det (cid:16) π E − ( j ) k (cid:17)(cid:105) / e (cid:110) − / e − ( j ) Tk ( E − ( j ) k ) − e − ( j ) k (cid:111) (4) w ( j ) k ← w ( j ) k ∑ Mj = w ( j ) k (5)Combination: The estimates and covariances from allsingle-model filters are combined with their correspondingweights to provide a combined estimate.ˆ x + k = M ∑ j = w ( j ) k ˆ x +( j ) k (6) P + k = M ∑ j = w ( j ) k (cid:20)(cid:16) ˆ x +( j ) k − ˆ x + k (cid:17) (cid:16) ˆ x +( j ) k − ˆ x + k (cid:17) T + P +( j ) k (cid:21) (7) Motion models and measurement model
In the presented study, MMAE is applied to model three ma-neuvers: straight motion, lane change to the left and lane changeto the right. Constant velocity model is used to for straight mo-tions. Left and right lane changes are modeled using sinusoidalfunctions. A bank of three filters runs in parallel: one linearalman filter for straight motions and two extended kalman fil-ters (EKF) for the lane changes. The states of the traffic partic-ipants are defined as X = ( x , v x , y , v y ) , where x and y define theposition of the vehicle in the road coordinate frame, v x and v y arelongitudinal and lateral velocities of the vehicle. Model equations for straight motion:
For thestraight motion, the discrete time state transition function for asingle step k + T s results as, x k + v x ( k + ) y k + v y ( k + ) = T s
T s x k v x ( k ) y k v y ( k ) (8) Model equations for lane change maneuvers:
Forthe right lane change with the lane width w L , length of the lanechange maneuver L and longitudinal distance of the vehicle fromthe start of the maneuver ∆ x , the sinusoidal motion can be ex-pressed as: y ( ∆ x ) = w L cos (cid:16) π L ∆ x (cid:17) (9)For simplicity, we assume that at initial condition the vehicle isat the start of the maneuver with a constant velocity. The discretetime equations of motion can then be approximated as: x k + = x k + v xk T s (10) v x ( k + ) = v xk (11) y k + = y k + v yk T s (12) v y ( k + ) = − w L π v x L sin (cid:16) π L x k + (cid:17) (13)The Jacobian matrix for the right lane change maneuver yields: Φ = T s T sa b (14)where a = − w L (cid:16) π L (cid:17) v xk cos (cid:16) π L x k (cid:17) (15) b = − w L π L cos (cid:16) π L x k (cid:17) (16) Similarly, the equations for the left lane change can be describedby a phase shifted equation for the right lane change: y ( ∆ x ) = w L cos (cid:16) π L ∆ x − π (cid:17) (17) Measurement model
Assuming a hybrid sensor fusionarchitecture [15], the measurement model was chosen to be lin-ear, and the positions of the vehicle were assumed to be observ-able. The equations can be described by: (cid:20) z x z y (cid:21) = (cid:20) (cid:21) x k v xk y k v yk (18) VEHICLE DYNAMICS MODEL
In the second stage of simulations, a single track vehicle dy-namics model described below was used to evaluate our behavioridentification model. This model approximates the vehicle loadsby considering only the front and rear axle loads and ignoringthe roll and pitch motions, resulting in two translational and onerotational degree of freedoms. The equations of motion are givenby ˙ v x − v y ˙ ψ = m (cid:0) F x , f cos ( δ ) + F x , r − F y , f sin ( δ ) (cid:1) = F X m (19)˙ v y + v x ˙ ψ = m (cid:0) F y , f cos ( δ ) + F y , r − F x , f sin ( δ ) (cid:1) = F Y m (20) I zz ¨ ψ = ( l f F y , f cos ( δ ) − l r F y , r + F x , f sin ( δ ) = M z (21)where m is the mass of the vehicle, v x and v y are the longitudi-nal and lateral velocity, ψ is the yaw angle and δ is the steeringangle of the vehicle. F x , i and F y , i , with i = f,r are the net longi-tudinal and lateral forces acting on the front and rear wheels ofthe vehicle. l f and l r are the distances of the front and rear axlesfrom the center of gravity of the vehicle, and I z is the vehicle in-ertia. For more details as well as the parameter values selectedfor the equation above, the reader is referred to Berntorp et al.( [16]). The measurements for the behavior model were synthet-ically generated by adding dela-correlated (white) noise to thetruth from the vehicle model. SIMULATIONS OF THE BEHAVIOR IDENTIFICATIONMODELTuning of the model
For the first stage of the simulations, the measurements forthe filters were generated synthetically as described below to tune
IGURE 3 . LEFT LANE MANEUVER IDENTIFIED BY MMAEAPPROACH; Y-AXIS IS WEIGHTS and X-AXIS IS TIME
FIGURE 4 . STRAIGHT MANEUVER IDENTIFIED BY MMAEAPPROACH; Y-AXIS IS WEIGHTS and X-AXIS IS TIME the filter. The process noise covariance matrix for all the filterswas initially set to Q = diag([0.001 0.001 0.001 0.001]). Themeasurement noise covariance matrix for all the filters was set toR = [0.0025 0; 0 0.0025], i.e. a standard deviation of about 0.05m (5 cm). The measurements for positions x and y were then syn-thetically generated by simulating the motion models describedabove with additive white noise. The initial conditions for bothsynthetic measurements as well as the filter banks were set to x= 0 m, y = 0 m, v x =
10 m/s and v y = ( P ) set to 10 − signifying high confidence in the initial value es- FIGURE 5 . DETECTION OF RIGHT LANE CHANGE MANEU-VER FOR Q=0.1 and R=0.0025; Y-AXIS IS WEIGHTS and X-AXISIS TIME
FIGURE 6 . VARIATION OF PROCESS NOISE AND MEASURE-MENT NOISE ON BEHAVIOR MODEL timates. The maneuver length for left and right behavior modelswas set to 150 m. At the mentioned initial velocity, it takes about15 secs for the maneuver to be complete.Figure 3 shows that for a left lane change performed, themaneuver was detected correctly in about 1.3 seconds of initia-tion. The straight run on the other hand was detected in about 2.2seconds (Figure 4). It needs to be noted however that these re-sults are when the initial estimates of the observed vehicle matchthe initial conditions of the filter banks, and the measurement aswell as the process noises are very low. Realistically however,the initial conditions of the filter may defer from the true initialconditions of the vehicle due to multiple reasons: sensor noise,point of view of the sensor, environment noise to name a few. Asa result the covariance matrix of the initial condition should beset to a relatively higher value, signifying a lower confidence inthe initial estimate.
IGURE 7 . DETECTION OF RIGHT LANE CHANGE MANEU-VER WHEN Q=0.005 and R=0.0025 WITH VEHICLE MODEL; Y-AXIS IS WEIGHTS and X-AXIS IS TIME
Now we focus on the process noise, which should give ushow much variation it can tolerate. The table in figure 6 liststhe different cases that were considered. In all these cases, theinitial conditions of the filters and the actual initial conditionswere identical x0 = y0 = v y = 0, v x = 10. P = 100. Theprocess and the measurement noise was modeled as an additivewhite noise with same filter Q and R statistics for the syntheticmeasurements. As can be seen, increasing the process noise in-creases the detection times of the maneuver. Before detecting ineach of these cases, the weights switch between the left and rightlane change (LC) model filters. After a certain point (case 3), thebehavior identification module is not able to identify a straightmaneuver and keeps switching between left and right maneuver.For a given process noise, increasing the measurement noise hadlittle effect on the detection times, although it did add fluctua-tions in the probabilistic weights that ripple down to the weightedestimates. Interestingly, there is an asymmetry in the detectiontimes for left LC and right LC. For right LC it switches a littlelonger before settling down (figure 5). The cause for this is yetto be investigated. Evaluation with the single track vehicle model
In the second stage of simulations, the MMAE based behav-ior model was evaluated with the single track vehicle model asdescribed above. The parameters chosen for the vehicle were re-ferred from [16]. The straight maneuver was simulated by main-taining the steering wheel angle to zero for the vehicle model.The left and right lane change maneuvers were simulated by giv-ing a sinusoidal input of period 10 seconds to the steering wheel.
FIGURE 8 . DETECTION OF RIGHT LANE CHANG MANEUVERWHEN Q=0.025 and R=0.0025 WITH VEHICLE MODEL; Y-AXIS ISWEIGHTS and X-AXIS IS TIME
FIGURE 9 . RESULTS OF VARYING THE PROCESS ANDMEASUREMENT NOISE WHEN EVALUATING WITH VEHICLEMODEL
The resulting maneuver length for the the lane changes was about60 meters. Measurements were generated from this simulatedvehicle model by adding brownian motion as described in the ta-ble in figure 9. For the filters in the MMAE behavior model, themaneuver length for the right and left LC models was fixed to 60meters. The detection times for all the maneuvers for differentprocess and noise covariances can be seen in the table in figure9. For cases 1 and 2 in this table, the model confuses the lanechange behaviors with the straight maneuvers for the first fewseconds before eventually identifying them correctly. This canbe seen in figure 7 for the case 1. The likely reason for this isthat even though the input to the steering wheel is sinusoidal, theath followed by the vehicle isnt sinusoidal strictly. As a result,the innovations of the lane change maneuver and the straight ma-neuver compete with each other initially, resulting in the switch-ing. However, this can be addressed by modeling this differenceas a process noise. Figure 8 shows the results of the right lanechange for case 6 which seems to be the most optimal one for Qto be the same for all states. Realistically, the process noise willbe associated primarily to the modeling errors in the velocitiesas they vary with different driver behaviors. Attributing moreprocess noise to velocities compared to positions helped achievebetter results in cases 8 and 9. Increasing the measurement noisehad a marginal effect on the detection times, although it did addfluctuations in the weights.
CONCLUSION
A taxonomy for different risks that an autonomous vehi-cle needs to address, while navigating through traffic, was pre-sented. A reference architecture and a probabilistic frameworkthat collectively enables addressing such risks were described.The challenge in analyzing risks in complex traffic environmentsexists primarily due to the uncertainty in the maneuvers driversmay execute. A novel approach for identifying and predictingthe driver maneuvers using classic multi model adaptive estima-tion was presented and demonstrated how it can be integratedinto the reference architecture. Further, preliminary results offilter tuning and its evaluation with a single track vehicle modelwere presented. Since there is a significant variability in the waydrivers execute the maneuvers, popular approach is to model it asprocess noise. Hence, the results include detailed description ofhow the process and measurement noises affect the performanceof the maneuver identification model. More comprehensive anal-ysis is expected to be available along with the final manuscript.
ACKNOWLEDGMENT
The authors would like to thank Srivatsan Srinivasan for im-plementing the vehicle dynamics model as MATLAB/Simulinksource files.
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