Source-linked AI summary
PORCA: Modeling and Planning for Autonomous Driving among Many Pedestrians
Yuanfu Luo, Panpan Cai, Aniket Bera, David Hsu, Wee Sun Lee, Dinesh Manocha
TL;DR
Autonomous vehicles need to navigate safely and smoothly among many pedestrians despite uncertain, unobserved intentions and variable local interactions. The paper develops PORCA to model both factors and integrates it into a POMDP planner. Experiments report more accurate prediction and safe, efficient, smooth robot-vehicle driving among pedestrians.
Problem
Pedestrian intentions are not directly observable, interactions vary, and motion models must capture both intentions and local interactions for robust planning.
Method
The system extends ORCA into PORCA and embeds the model in a POMDP that plans vehicle control under uncertain pedestrian intentions and interactions.
Results
The system predicts pedestrian motions more accurately than prior models and enables safe, efficient, and smooth driving among many pedestrians.
Takeaways & Limitations
Combining pedestrian motion prediction with POMDP planning enables robot vehicles to drive safely, efficiently, and smoothly among crowds.
Takeaways & Limitations
The original ORCA model has limitations including the freezing pedestrian problem and violation of non-holonomic constraints.
Abstract
from arXiv · showhide
This paper presents a planning system for autonomous driving among many pedestrians. A key ingredient of our approach is PORCA, a pedestrian motion prediction model that accounts for both a pedestrian's global navigation intention and local interactions with the vehicle and other pedestrians. Unfortunately, the autonomous vehicle does not know the pedestrian's intention a priori and requires a planning algorithm that hedges against the uncertainty in pedestrian intentions. Our planning system combines a POMDP algorithm with the pedestrian motion model and runs in near real time. Experiments show that it enables a robot vehicle to drive safely, efficiently, and smoothly among a crowd with a density of nearly one person per square meter.
I. INTRODUCTION
Autonomous driving among many pedestrians requires motion prediction that captures both global intentions and local interactions, while planning must handle intentions that are uncertain and unobservable. The paper combines PORCA with a POMDP to support intention- and interaction-aware vehicle planning.
- Motivation: Dense pedestrian environments challenge autonomous vehicles because motions, environments, sensing, and robot control are uncertain and constantly changing.The target capability is driving safely, efficiently, and smoothly in places such as airport terminals, shopping malls, and hospital complexes.
- Motivation: Accurate pedestrian motion prediction must model both global navigation intentions and local interactions with obstacles, vehicles, and other pedestrians.Intentions alone do not fully determine movement, so both global and local factors are needed to capture pedestrian motion at multiple scales.
- Motivation: Pedestrian intentions are hidden, interactions vary across individuals, and robust planning must account for these uncertainties.Intentions must be inferred rather than directly observed, while interaction behavior differs with factors including age, gender, and risk propensity.
- Approach: The system conditions a pedestrian motion model on intentions and interactions, then embeds it in a POMDP for vehicle control under uncertainty.The POMDP uses PORCA in its state-transition function and maintains a probability distribution over possible pedestrian intentions.
- Approach: PORCA extends ORCA by encouraging pedestrians to escape freezing states and by accounting for the vehicle’s more restricted collision-avoidance capability.ORCA can cause agents to slow or stop in head-on encounters, and its homogeneous-agent assumption is inadequate for pedestrian–vehicle interaction.
- Results: Experiments report more accurate pedestrian prediction and vehicle behavior that avoids collisions while reaching goals more efficiently and smoothly.The paper contrasts its intention- and interaction-aware planning with prior approaches that ignore interactions or assume simpler pedestrian motions.
B. Pedestrian Motion Modeling
The pedestrian motion model builds on ORCA while addressing vehicle non-holonomy and unnatural interaction behavior. The broader system combines belief tracking, path planning, and POMDP-based speed planning, using PORCA to predict pedestrian behavior during lookahead search.
- Pedestrian Motion Modeling: Existing pedestrian motion models include social-force, data-driven, and geometric approaches, while many do not explicitly model interactions with non-holonomic vehicles.Prior crosswalk-specific approaches handle pedestrian–vehicle interactions but do not apply to general scenes.
- Pedestrian Motion Modeling: PORCA develops from ORCA by accounting for non-holonomic vehicle motion and enhancing the objective function to simulate more natural interactions.The model targets limitations of treating all agents homogeneously and of producing unnatural pedestrian responses.
- System Architecture: The system overview contains a belief tracker, a hybrid-A* path planner, and a speed planner.The belief tracker updates pedestrian-intention beliefs, while hybrid A* produces a non-holonomic driving path.
- ORCA Foundation: ORCA represents agents as discs and uses velocity obstacles to identify relative velocities that would cause collisions within a time window.Collision-free relative velocities lie outside the corresponding velocity obstacle.
- System Architecture: The speed planner embeds PORCA in an intention POMDP and uses belief-tree lookahead to select vehicle speed actions.The vehicle executes the first action of the plan after the search evaluates predicted pedestrian behaviors.
IV. PEDESTRIAN MOTION PREDICTION
The pedestrian motion model extends ORCA to predict more natural pedestrian–vehicle and pedestrian–pedestrian interactions using pedestrian and vehicle intentions. ORCA represents collision avoidance through velocity obstacles, half-plane constraints, and reciprocal velocity sets.
- The model uses pedestrian and vehicle intentions to simulate interactions and predict pedestrian motions.
- ORCA generates half-planes of collision-avoiding velocities for each agent and selects an optimal velocity from their intersection.
- The velocity obstacle contains relative velocities that would cause a collision between two agents before a time horizon τ.
- The Minkowski difference inflates one agent’s geometry by the other’s, allowing the first agent to be treated as a point; for discs, the resulting radius is rA + rB.
- Velocities outside the velocity obstacle guarantee collision-free motion for at least τ time.
- When the other agent selects velocities from a set VB, agent A must choose a velocity outside the velocity obstacle combined with VB.
2) Collision-Avoiding Velocity Set:
ORCA constructs reciprocal collision-avoiding velocity sets for interacting agents and chooses velocities close to their optimization velocities. It assigns collision-avoidance responsibility symmetrically between agents.
- A collision-avoiding velocity set for A excludes velocities that could collide with B given B’s possible velocity set.
- Velocity sets are reciprocal collision-avoiding when each agent’s set lies within the other agent’s collision-avoiding set.
- Reciprocal maximal velocity sets are the largest reciprocal collision-avoiding sets under the stated inclusion relation.
- ORCA computes a reciprocal collision-avoiding set for each agent in every interacting pair, guided by optimization velocities.
- Optimization velocities may represent preferred velocities corresponding to intentions or the agents’ current velocities.
- ORCA finds the smallest relative-velocity change that avoids collision within τ and divides responsibility equally between the two agents.
- In the freezing pedestrian example, ORCA’s computed velocity for A is much smaller than its preferred velocity, so A slows substantially instead of detouring.
4) Computing the New Velocity:
ORCA selects a new velocity for an agent by choosing the feasible collision-avoiding velocity closest to its preferred velocity, using linear programming.
- The agent constructs a collision-avoiding velocity set induced by all other agents.
- It selects a new velocity closest to its preferred velocity from that feasible set.
- This velocity-selection problem can be solved efficiently using linear programming.
B. Limitations of ORCA
ORCA has two stated limitations: freezing pedestrians and violating non-holonomic motion constraints. These arise from selecting velocities near goal-directed preferred velocities and assuming agents can change direction freely.
- ORCA’s two limitations are the freezing pedestrian problem and violation of non-holonomic constraints.
- Freezing Pedestrians: Minimizing distance to a goal-directed preferred velocity can make obstructed pedestrians walk very slowly or remain stationary.
- Freezing Pedestrians: Human pedestrians generally maintain speed and detour around obstacles, unlike the freezing behavior produced in some ORCA simulations.
- Non-Holonomic Constraints: ORCA assumes holonomic agents can freely change direction, but real vehicles are usually non-holonomic and cannot do so.
- Non-Holonomic Constraints: This assumption can cause pedestrians to anticipate unrealistic side-wise vehicle avoidance and respond unnaturally near vehicles.
2) Violation of Non-holonomic Constraints:
PORCA addresses ORCA’s freezing-pedestrian problem and vehicle interaction constraints by adding low-overhead patience modeling and distance-dependent responsibility allocation.
- 1) Objective Function with Patience:: PORCA introduces a low-computation solution to ORCA’s freezing-pedestrian problem, avoiding the costly multiple-step lookahead or global replanning alternatives.The added objective penalizes unintended slowing while retaining efficient computation during planning cycles.
- 1) Objective Function with Patience:: The patience variable ϱA penalizes unintended slowing and encourages pedestrians to explore directions that allow faster movement.Patience decreases when an intending pedestrian moves below the speed threshold ς and is restored when speed exceeds ς.
- 1) Objective Function with Patience:: The patience mechanism makes pedestrians increasingly impatient when they remain stationary or move slowly, reflecting their preference to maintain current speed.For pedestrians intending to stay put, patience remains fixed at 1.
- 1) Objective Function with Patience:: When ϱ<1, the objective is no longer convex, but speeds below ς occur only occasionally, so ϱ remains 1 most of the time.The authors report that PORCA can therefore still be solved efficiently.
- 2) ORCA with Changing Responsibilities:: PORCA shifts more collision-avoidance responsibility to pedestrians near vehicles, helping vehicle velocities stay closer to current velocity and comply with non-holonomic constraints.Responsibility increases linearly as distance falls within threshold d, reaching maximum R at zero distance; experiments use d=1.5 and R=0.95.
V. INTENTION-AWARE AND INTERACTION-AWARE AUTONOMOUS DRIVING
The system uses a POMDP to plan vehicle actions while treating pedestrian intentions as hidden state variables and updating beliefs over them during search.
- V. INTENTION-AWARE AND INTERACTION-AWARE AUTONOMOUS DRIVING: The policy maps beliefs to actions to maximize expected discounted rewards over uncertain state transitions and observations.The discount factor γ places greater preference on immediate rewards as γ decreases.
- V. INTENTION-AWARE AND INTERACTION-AWARE AUTONOMOUS DRIVING: POMDP planning searches a belief tree that branches over actions and observations, updating child beliefs with Bayes’ rule.The search outputs a policy conditioned on the initial belief.
- V. INTENTION-AWARE AND INTERACTION-AWARE AUTONOMOUS DRIVING: The POMDP represents pedestrian intentions as hidden variables and reasons over probability distributions, or beliefs, rather than directly observed intentions.Its transition model captures imperfect robot control and uncertain environment dynamics.
- V. INTENTION-AWARE AND INTERACTION-AWARE AUTONOMOUS DRIVING: The planning system’s uncertainty-aware formulation supports intention- and interaction-aware autonomous-vehicle planning.Pedestrian intentions are represented by goal locations in the environment.
1) State Modeling:
The model separates vehicle and pedestrian state transitions, uses discrete speed-control actions, and predicts pedestrian motion from intentions, positions, and interactions.
- 1) State Modeling:: The planner chooses among ACCELERATE, DECELERATE, and MAINTAIN actions to avoid collisions and navigate efficiently and smoothly.These discrete actions control vehicle speed along the planned path.
- 1) State Modeling:: Vehicle observations include position and speed, while pedestrian observations include all pedestrian positions; the model treats these observations as fully observable.The formulation focuses uncertainty modeling on pedestrians’ hidden intentions.
- 1) State Modeling:: Vehicle and pedestrian transitions are modeled separately, with the vehicle following a hybrid A* path under non-holonomic constraints and noisy control dynamics.The vehicle drives for fixed duration Δt after each discrete action.
- 1) State Modeling:: PORCA computes pedestrian velocities and next-step positions from intended goals, pedestrian positions, and vehicle position, speed, and interactions.A stop intention with preferred velocity 0 models stationary pedestrians, while Gaussian noise represents interaction uncertainty.
- 1) State Modeling:: The reward function penalizes collisions and encourages the vehicle to drive safely, efficiently, and smoothly.Collision penalty varies with driving speed, and reaching the goal receives a reward.
5) Reward Modeling:
The evaluation compares pedestrian prediction and autonomous-driving planners across simulated crowd scenarios, emphasizing safety, efficiency, and smoothness. POMDP-PORCA models pedestrian intentions, interactions, and uncertainty, outperforming safety-achieving baselines in the reported comparisons.
- Pedestrian Prediction: PORCA predicts detours around a moving vehicle and uniquely predicts that the pedestrian maintains speed during the detour in the example scene.Const-Vel and Pref-Vel predict straight trajectories leading to collisions, while ORCA and PORCA predict detours.
- Simulation Scenarios: Three simulated scenarios test stationary pedestrians, pedestrians walking toward the vehicle, and 150 pedestrians walking toward seven goals.The first two scenarios require a straight 16-meter drive, while Scenario 3 plans the vehicle path in real time.
- Evaluation Criteria: 300 trials per scenario evaluate safety, efficiency, and smoothness using collision rate, success rate, travel time, and acceleration/deceleration counts.Average collision rate, travel time, and acceleration/deceleration counts use only successful trials; success means reaching the goal within 6 minutes.
- Planning Results: POMDP-PORCA guarantees safety and outperforms safety-achieving Reactive-Controller and POMDP-Pref-Vel baselines in efficiency and smoothness.Const-Speed and Dynamic-Hybrid-A* produce collisions in the reported comparison.
- Planning Results: Reactive-Controller never reaches its goal in Scenario 1 because it waits for stationary pedestrians, whereas POMDP-PORCA slowly advances as pedestrians give way.POMDP-Pref-Vel achieves relatively higher success rates than Reactive-Controller but requires more travel time and drives less smoothly than POMDP-PORCA.
C. Autonomous Driving with A Robot Scooter
The system is deployed on a robot vehicle equipped with laser, inertial, and wheel-encoder sensors for pedestrian detection, localization, and vehicle-state estimation. In repeated campus-plaza trials, it reached its goal efficiently and smoothly while avoiding pedestrians, while future work targets vehicle constraints, richer pedestrian models, and more efficient planning.
- Robot Platform: The robot vehicle uses two LIDARs, an IMU, and wheel encoders, with a maximum speed set to 1m/s for safety.The top-mounted LIDAR supports pedestrian detection, while the bottom-mounted LIDAR supports localization.
- Robot Platform: Pedestrians are detected by K-means clustering and tracked across adjacent laser frames, while adaptive Monte Carlo localization combines LIDAR, IMU, and wheel-encoder data.The planning system runs on ROS and an Ethernet-connected laptop.
- Real-World Evaluation: Across repeated campus-plaza trials, the vehicle reached its goal efficiently and smoothly while avoiding pedestrians successfully in all trials.The experiment used the autonomous driving system on a real robot vehicle.
- Future Work: Future work includes incorporating non-holonomic vehicle constraints into ORCA velocity sets, using more sophisticated pedestrian models, and exploiting the POMDP-lite structure for efficiency.The current POMDP model is described as a POMDP-lite whose hidden variables are constant or deterministically changing.