J. Forbes, T. Huang, K. Kanazawa and S. Russell.  "The BATmobile: Towards a
Bayesian Automated Taxi," IJCAI-95, pages 1878-1885.

1 The BAT Project
- under Intelligent Vehicle and Highway Systems (IVHS) project
  - improve traffic congestion and accidents
- IVHS funds California's Partners for Advanced Transit and Highways (PATH)
  - groups of closely-spaced vehicles improves highway capacity
  - PATH funds BAT, although BAT focuses on individual vehicle autonomy
- BAT encompasses most of AI
  - low-level problems maturing
    - visual vehicle monitoring
    - visual lane following
  - knowledge representation, uncertainty, planning, uncertainty, learning,
    vision, speech and natural language processing, ...
  - partially accessible, nondeterministic, nonepisodic, dynamic, continuous
- input is a 3D rendering of a traffic situation
  - noisy, possibly failing, sensors
- output is high-level actions like braking, accelerating, lane changing
- maximum error rate 1 in 100,000,000 secs = 3.17 years
- model driving problem as Partially Observable Markov Decision Process (POMDP)
  - optimal decision a function of current belief state only
  - current belief state can incorporate previous percepts

2 Maintaining the Current Belief State
- state
  - BAT's and neighboring vehicles' position, velocity and intentions
  - road and weather conditions
  - only partially observable
  - noisy, possibly failing, sensors

2.1 Dynamic Probabilistic Networks (DPNs)
- probabilistic networks (see Chap 15 R&N)
  - also called Belief Networks
  - directed, acyclic graph
  - nodes are random variables with CPT based on parents
  - edges denote causal dependence
  - succinctly represents exponential joint probability distribution
- dynamic PNs (see figure 2)
  - partially observable Markov process
    - P(S_t+1 | S_t, S_t-1, ...) = P(S_t+1 | S_t)
    - next state does not depend on previous states
    - but, past percepts influence the current state
  - state evolution and sensor models
  
2.2 Efficient Updating
- update DPN by removing past time slices
- Temporary Invariant Networks (see figure 3)
  - temporally variant networks require the addition of new arcs
  - invariants have a node deletion ordering avoiding new arcs
- Stochastic Simulation in DPNs
  - generate samples of variable assignments biased by observed evidence
    - logic sampling uses no evidence bias
    - liklihood weighting biases based on CPTs
  - use samples to determine desired probabilities
  - still generates many samples far from evidence
    - don't allow unobserved parents to evidence variables
    - use liklihood weightings to choose only likely samples

2.3 Network Structure (see figure 5)
- each vehicle represented by separate DPN
- note nodes linking in other vehicles
- alternatively putting all vehicles in one network too expensive

2.4 Sensor Models and Sensor Failures (see figure 6)
- high variance in or no values indicates degradation or failure (SensorStatus)
- linking SensorStatus_i nodes allows poor status to persist

3 Decision Making in the BAT
- POMDP decision problem is hard
- BAT uses approximate solutions (see 3.1, 3.2 and 3.3 below)

3.1 Dynamic Decision Networks (see figure 7)
- add to DPNs nodes for actions and utilities
- since partially observable, must maximize over unobserved evidence as
  well as actions
- inefficiency constrains this approach to offline processing of training
  examples to generate an efficient state/action policy

3.2 Decision Tree Policy Representation
- hand-constructed decision trees (e.g., see figure 8)
- tests are actually sets of probability thresholds on variables

3.3 POMDP Policy Learning
- reinforcement learning to learn action-value function Q(a,i)
  - expected utility of taking an action in a state
- mapping of time-varying CPTs and evidence to action-value

4 Scenarios and Results
- traffic scenarios drive a time-step simulator
- simulator computes trajectories for all vehicles
- vehicle percepts communicated through sensors (possibly noisy)
  - not via 3D images as indicated in Section 1
- only one BAT in traffic
  - one 300 node, highly connected network is slow enough
- BAT's goal is to maintain a target speed and target lane
- five situations
  - passing a slower car (figure 9)
  - reacting to unsafe drivers (figure 10)
  - avoiding a stalled car (figure 11)
  - aborting a lane change (figure 12)
  - merging into traffic (figure 13)

5 Summary and Future Work
- benefits
  - DPNs solve noise and partial observability of driving problem
  - one DPN per vehicle works
  - handles sensor degradation and failure
  - real-time updating using temporally invariant networks and stochastic
    simulation
  - decision-tree-based policies work
- future
  - learning DPNs from time-series data
  - vision system -> learning models from videotape of human drivers
  - continuous variables in the DPN
  - appropriate utility functions
  - validation
    - real-world response from videotape


Automated Taxi?
- grand challenge
- taxis in "Total Recall"
- possible?
- guaranteed control versus rational autonomy