A survey on motion prediction and risk assessment for intelligent vehicles

Abstract

• Major challenge:

  • detect & react dangerous situations

• Content:

  • a survey of methods for motion prediction and risk assessment

• Conclusion:

  1. tradeoff between model completeness & real-time constraints
  2. choice of a risk assessment method $\underleftarrow{\ \ \ influences\ \ \ }$ the selected motion model

Intro

This paper surveys mathematical models and their relation with risk assessment.

Mathematical models

1. Physics-based:

   • simplest, only depends on the laws of physics

2. Maneuver-based:

   • consider the future motion of a vehicle $\underleftarrow{\ \ depends\ on\ \ }$ the maneuver (driver intends to perform)

3. Interaction-aware:

   • inter-dependencies between vehicles’ maneuvers

Classifiction of risk

1. physical collsions between entities.

2. vehicles behaving differently from what is expected of them given the context (e.g. according to traffic rules).

Physics-based motion models

• Represent vehicles as dynamic entities governed by the laws of physics

• Future motion is predicted using dynamic and kinematic models linking some parameters

  • control inputs: steering, acceleration...
  • car properties: weight...
  • external conditions: friction coefficient of the road surface

• Limited to short-term (< 1s) motion prediction, unable to anticipate any change in the motion of the car caused by the execution of a particular maneuver

2 Evolution models

• Dynamic models
  • Based on Lagrange’s equations, condisder different forces that affect the motion of a vehicle
  • Complex, used in control-oriented applications
• Kinematic models
  • Based on the parameters of the movement (e.g. position, velocity, acceleration), without considering the forces that affect the motion (e.g. friction force)
  • Simple yet popular, used for trajectory prediction

Trajectory prediction

Evolution models$\underrightarrow{\quad are\ used\ for\quad}$ trajectory prediction

• Single trajectory simulation

  • apply an evolution model to the current perfect known state
  • computational efficiency & for real time application
  • not reliable for long term (>1s ) prediction

• Gaussian noise simulation

  • Uncertainty of the current state be modeled by a normal distribution (K.F Kalman Filter)
  • Modeling uncertainties using a unimodal normal distribution is insufficient to represent the different possible maneuvers (Solution: Switching Kalman Filters, SKF)

• Monte Carlo simulation

  • In general case(unknown analytical expression for the distribution on the predicted states )
  • Randomly sample from the input variables of the evolution model $\underrightarrow{\ to \ }$ generate potential future trajectories

Maneuver-based motion models

• Maneuver $\approx$ behavior
• covers approaches based on maneuver intention estimation( more relevant and reliable in the long term)

Prototype trajectories

• the trajectories of vehicles can be grouped into a finite set of clusters $\approx$ a typical motion pattern
• Motion patterns (prototype trajectoriees ) are learned from data during a training phase

Representation method

• motion patterns can be identified in advance -> trajectory in the training dataset is already assigned to a cluster
• representing a motion pattern:
  • compute a unique prototype trajectory for each motion pattern
  • have several prototypes for each trajectory class

Trajectory prediction

• Define metrics to measure the distance of a partial trajectory to a motion pattern
  • Gaussian Processes: the distance is computed as the probability of the partial trajectory
  • finite set of prototype trajectories: its similarity with the prototype trajectories:
    • average Euclidian distance
    • modified Hausdorff
    • the Longest Common Subse- quence (LCS)
• Limitations:
  • strictly deterministic representation of time
  • hard to adaptation to different road layouts (road intersections)

Maneuver intention estimation & execution

Focuses on maneuver intention estimation at road intersections

• Context and heuristics: discriminative learning algorithms
  • Multi-Layer Perceptrons (MLP) Logistic regression
  • Relevance Vector Machines (RVM)
  • Support Vector Machines (SVM)
• break down each maneuver into a chain of consecutive events and to represent this sequence of events using a Hidden Markov Model (HMM)

Limitations: the assumption that vehicles move independently does not hold.

Interaction-aware motion models

Represent vehicles as maneuvering entities which interact with each other.

Models based on trajectory prototypes

• No intervehicle influences during the learning phase (intractable number of motion patterns)
• Consider mutual influences during the matching phase

Models based on Dynamic Bayesian Networks (DBN)

• Pairwise dependencies between multiple moving entities $\underrightarrow{\quad\ be\ modeled \ with\quad }$ Coupled HMMs (Hidden Markov model ) or (CHMMs)

  • complexity is not manageable -> simplify the model is to make CHMMs asymmetric by assuming that the surrounding traffic affects the vehicle of interest.

• Limitations: expensive in compution & not compatible with realtime risk assessment

Risk assessment

Risk based on colliding future trajectories (2)

1. Predict the potential future trajectories for all the moving entities in the scene.
2. Detect collisions between each possible pair of trajectories, and derive a risk estimate based on the overall chance of collision.

Binary collision prediction

• the collision risk can be binary (0 or 1)
• solving the linear differential equations of the motion model -> analytical solution for the state of the vehicles at a specific time

Probabilistic collision prediction

• compute collision risk in a probabilistic manner

Other risk indicators

• velocity
• the amount of overlap between the shapes representing the vehicles
• he probability of simultaneous occupancy of the conflict area by both vehicles
• Time-To-Collision (TTC) & Time-To-React (TTR):

Risk based on unexpected behavior

extends the concept of risk beyond collisions, by taking into account the emotional strain caused by drivers performing unexpected maneuvers

Detecting unusual events

• define a set of normal rules
• use real data to learn the typical behavior of road users

Detecting conflicting maneuvers

• estimating the maneuver intentions of the drivers

• learn models for specific dangerous events in addition to the models for the nominal behavior( classification problem)