Trajectory Prediction

These are physics-based models that predict future states by extrapolating current motion using equations of motion. They are deterministic, fast, and require minimal data.

• Constant Velocity (CV) Model: Assumes an agent continues at its current speed and heading. Simple but inaccurate for turning or accelerating agents.
• Constant Acceleration (CA) Model: Incorporates acceleration for better short-term prediction of vehicles changing speed.
• Unicycle/Kinematic Bicycle Model: Adds non-holonomic constraints (e.g., a minimum turning radius) common to wheeled robots and cars, improving realism for curving paths.

Use Case: Provides a low-latency, computationally cheap baseline prediction, often used as an input feature for more complex learning-based models or when sensor data is sparse.

These models predict trajectories by first inferring a high-level goal or intent (e.g., 'turn left at the next intersection', 'proceed to loading dock 3'), then generating a path to that goal.

• Uses a probabilistic framework (e.g., Hidden Markov Models) to estimate the likelihood of possible goals based on observed partial trajectory and map context.
• Crucially depends on a known scene context, such as a semantic map with lanes, intersections, and destinations.
• Output is often a multi-modal distribution, representing the probability of different future paths corresponding to different intents.

Use Case: Essential for predicting the behavior of vehicles at intersections or robots at decision points in a warehouse, where physics alone is insufficient.

These models forecast trajectories by explicitly modeling the interactions between multiple agents, recognizing that their future paths are interdependent.

• Key Insight: An agent's path is influenced by the predicted paths of neighbors (social pooling).
• Common Architectures: Use graph neural networks (GNNs) where agents are nodes and their spatial relationships are edges, or recurrent networks with social pooling layers.
• Captures behaviors like group formation, following, passing, and collision avoidance maneuvers between agents.

Use Case: Critical for dense, dynamic environments like pedestrian zones, busy factory floors, or multi-robot fleets where agents must navigate around each other.

These data-driven models use neural networks to learn complex, non-linear patterns from historical trajectory data without explicit physical rules.

• Long Short-Term Memory (LSTM) Networks: A standard recurrent neural network (RNN) architecture for modeling temporal sequences. They encode a history of positions into a hidden state used for prediction.
• Transformer-Based Models: Increasingly popular, using self-attention mechanisms to weigh the importance of different past time steps and agent interactions more effectively than RNNs.
• Trained on massive datasets of real-world trajectories (e.g., nuScenes, Argoverse) to learn common motion patterns.

Use Case: Provides high-accuracy predictions in complex, real-world scenarios where behavior is not easily captured by simple models, given sufficient training data.

These models address the inherent uncertainty of prediction by generating a probability distribution over possible future trajectories rather than a single 'best guess'.

• Generative Adversarial Networks (GANs): Use a generator to produce realistic trajectory samples and a discriminator to critique them, learning to model the true distribution of future motions.
• Conditional Variational Autoencoders (CVAEs): Learn a latent representation of trajectory patterns and sample from it to produce diverse, plausible futures.
• Output is crucial for risk assessment: A planning system can evaluate the probability of collision across all predicted possibilities.

Use Case: Required for safety-critical applications where accounting for the full spread of possible outcomes (e.g., a pedestrian suddenly jaywalking) is necessary for robust planning.

These models use rich environmental context to constrain predictions to physically feasible and likely paths. They are a fusion of intention-aware and deep learning methods.

• Inputs include: HD maps with lane geometries, traffic rules, and semantic features (crosswalks, stop lines).
• Architectures (e.g., VectorNet) convert map elements and agent histories into a graph of vectors, processed by GNNs.
• Predictions are 'snapped' to plausible lanes and pathways, eliminating physically impossible trajectories.

Use Case: The state-of-the-art for autonomous vehicle prediction, where adherence to lane structure and traffic regulations is paramount. Also vital for AMRs navigating structured warehouses.

The most critical application, where predicted future positions of obstacles are used to compute evasive maneuvers before a conflict becomes imminent. This shifts systems from reactive braking to anticipatory path adjustment.

• Core Input: Combines kinematic predictions with Time to Collision (TTC) and Closest Point of Approach (CPA) metrics.
• Algorithm Integration: Feeds directly into Model Predictive Control (MPC) and Optimal Reciprocal Collision Avoidance (ORCA) planners.
• Impact: Reduces emergency stops by >70% in warehouse simulations, enabling smoother, higher-throughput operations.

Enables cooperative navigation by allowing each agent to anticipate the planned motions of others. This is essential for deadlock prevention and efficient flow in shared spaces like cross-docking stations.

• Mechanism: Predictions create a spatiotemporal occupancy forecast, used by planners like Safe Interval Path Planning (SIPP).
• Requirement: Depends on inter-agent communication protocols or a shared fleet state estimation system.
• Example: An Autonomous Mobile Robot (AMR) yields a corridor intersection by predicting the trajectory of a faster forklift, avoiding a mutual stop.

Predicts the future path of human workers by inferring goal-directed intent from partial motion, not just physics. This enables socially-aware and legible robot behavior.

• Technique: Often uses Social Force Models or LSTM-based neural networks trained on human motion data.
• Application: A robot approaching a shared pick station slows and signals its intent if it predicts a worker is moving toward the same shelf.
• Benefit: Dramatically reduces perceived robot aggression and improves workforce acceptance.

Informs high-level orchestration middleware by forecasting when agents will become available at specific locations. This enables just-in-time task assignment and minimizes idle travel.

• Data Flow: Predicted agent trajectories feed into dynamic task allocation and spatial-temporal scheduling engines.
• Integration: Works with battery-aware scheduling to route low-energy agents to charging stations based on predicted future location.
• Value: Increases effective fleet utilization by optimizing for future state, not just current position.

Acts as the core predictive component within a Runtime Assurance (RTA) or safety monitor architecture. It continuously validates that the primary controller's planned trajectory will not cause a collision within a verified time horizon.

• Function: Provides a formal predictive safety certificate. If a violation is predicted, a verified safe controller (e.g., using Control Barrier Functions) overrides the primary system.
• Critical for: Certifying learning-based or complex controllers in regulated environments.
• Metric: Must operate within a guaranteed Worst-Case Execution Time (WCET).

Generates high-fidelity, predictive models of agent behavior within a digital twin. This is used for stress-testing orchestration logic, sim-to-real transfer learning, and operational forecasting.

• Process: A simulation engine uses trajectory prediction models to generate plausible future states of the entire fleet under various scenarios.
• Output: Identifies systemic bottlenecks and evaluates the robustness of exception handling frameworks before deployment.
• Tooling: Integral to Sim-to-Real pipelines for training Vision-Language-Action Models for robotics in a safe, virtual environment.

A geometric collision avoidance algorithm that defines, for a moving agent, the set of all velocities that would result in a collision with another moving obstacle within a specified time horizon. It is the foundational concept for many predictive avoidance methods.

• Core Mechanism: Constructs a cone in velocity space where any chosen velocity leads to a future intersection with an obstacle's predicted position.
• Application: Used in robotics and autonomous vehicles for local, reactive planning where obstacle trajectories are assumed to be linear over a short time window.

A fundamental risk metric that estimates the time remaining before two objects on a constant relative velocity course will collide if no evasive action is taken. It is a critical input for trajectory prediction and risk assessment systems.

• Calculation: Derived from the relative distance and closing speed between agent and obstacle.
• Usage: Triggers hierarchical safety responses; a low TTC may invoke an Emergency Stop Protocol, while a higher TTC allows for smoother, predictive replanning.

An optimization-based control strategy that repeatedly solves a finite-horizon optimal control problem to compute a sequence of control inputs that satisfies dynamic constraints and avoids predicted collisions.

• Predictive Core: Explicitly uses a trajectory prediction model for obstacles over the optimization horizon.
• Advantage: Can smoothly trade off between goal progression, passenger comfort, and safety by optimizing over future states, not just the immediate next step.

A navigational metric, comprising Distance to CPA (DCPA) and Time to CPA (TCPA), that predicts the minimum future separation distance and time to reach it between two moving objects on their current courses.

• Key Difference from TTC: CPA does not assume a collision will occur; it measures the closest they will get. A small DCPA and TCPA indicate high risk.
• Domain: Extensively used in maritime navigation and aviation for long-range conflict detection.

The algorithmic combination of data from multiple heterogeneous sensors (e.g., LiDAR, radar, cameras) to create a more accurate, reliable, and complete representation of surrounding obstacles. This fused perception is the essential input for any trajectory prediction module.

• Purpose: Mitigates individual sensor weaknesses (e.g., camera poor lighting, LiDAR weather sensitivity).
• Output: Produces a unified list of tracked objects with estimated position, velocity, and classification, forming the basis for predictive models.

A safety architecture that uses a verified safety monitor or controller to override a complex primary controller (e.g., a learning-based planner) if its actions are predicted to violate a safety property like collision avoidance.

• Relation to Prediction: The RTA's safety monitor continuously runs a high-integrity, often simpler, trajectory prediction and collision check.
• Guarantee: Provides a formal safety net, allowing the use of high-performance but less verifiable prediction and planning algorithms in the primary stack.