Model Predictive Control (MPC) for Collision Avoidance

At each control step, MPC solves a constrained optimization problem over a finite future time window (the prediction horizon). The algorithm computes a sequence of control inputs that minimizes a cost function (e.g., tracking error, energy use) while explicitly respecting dynamic constraints (vehicle physics) and collision constraints (maintaining safe distances). Only the first control input of the optimized sequence is executed before the process repeats, enabling continuous adaptation.

MPC's mathematical formulation allows for the direct, explicit inclusion of hard and soft constraints as part of the optimization problem. This is critical for safety.

• Hard Constraints: Non-negotiable limits like actuator saturation (max steering angle) or strict safety margins that define a collision-free region.
• Soft Constraints: Desirable limits (like lane boundaries) that can be temporarily violated with a penalty, preventing the optimizer from becoming infeasible in tight situations. This provides a principled way to trade off safety and performance.

MPC's core advantage is its predictive capability. Using an internal dynamic model of the ego-agent and prediction models for other obstacles, it simulates (rolls out) potential future states. It evaluates these simulated trajectories against collision constraints, allowing it to anticipate and avoid conflicts before they become imminent. This contrasts with purely reactive methods like the Dynamic Window Approach (DWA) that only consider immediate sensor data.

The MPC optimizer is guided by a cost function that balances competing objectives, making it highly adaptable. Typical terms include:

• Path Tracking: Minimize deviation from a global reference path.
• Control Effort: Minimize steering and acceleration for smooth, efficient motion.
• Collision Risk: Incorporate a penalty based on predicted Time to Collision (TTC) or inverse distance to obstacles.
• Comfort: Penalize high jerk or lateral acceleration. The weights on these terms dictate the agent's driving style, from aggressive to conservative.

MPC operates in a receding horizon fashion. After solving the optimization and applying the first control command, the prediction horizon shifts forward one time step, and the process repeats with new sensor measurements. This feedback mechanism compensates for model inaccuracies, disturbances, and unexpected obstacle behavior. It transforms an open-loop plan into a closed-loop, robust control policy that continuously corrects for prediction errors.

MPC functions as a local, short-term controller within a hierarchical architecture. It receives a target trajectory or waypoints from a higher-level global path planner (e.g., using Safe Interval Path Planning (SIPP)). MPC's role is to faithfully track this plan while dynamically avoiding local, unpredicted obstacles. This separation of concerns allows for efficient long-range planning and precise, safe short-term execution, a common pattern in Heterogeneous Fleet Orchestration.

A motion planning approach that generates collision-free trajectories by simultaneously satisfying both kinematic constraints (like minimum turning radius) and dynamic constraints (like acceleration limits). Unlike geometric planners, it produces physically feasible paths that an agent's actuators can execute, making it a critical precursor or component within an MPC optimization problem.

• Key Constraint: Ensures planned velocity and acceleration profiles are within the agent's physical capabilities.
• Relation to MPC: MPC often uses a kinodynamic model as the core prediction model within its finite-horizon optimization.

The process of forecasting the future states (position, velocity) of dynamic obstacles. Accurate prediction is essential for the predictive aspect of MPC, as the controller optimizes actions based on where obstacles will be, not just where they are.

• Methods: Ranges from simple constant velocity models to complex neural network-based predictors.
• MPC Integration: The predicted trajectories of other agents form the collision constraints in the MPC's optimization problem. Poor prediction directly degrades MPC safety.

A mathematical tool for safety-critical control that formally guarantees a system's state will remain within a predefined safe set. A Predictive CBF extends this guarantee over a future time horizon.

• Safety Filter: Can be used as a runtime assurance layer to correct an MPC's output if it risks constraint violation.
• Alternative to Hard Constraints: Sometimes integrated directly into the MPC formulation to provide robust safety guarantees despite model uncertainty, acting as a soft constraint that is always satisfied.

Geometric, reactive collision avoidance algorithms. The Velocity Obstacle (VO) defines the set of velocities an agent must avoid to prevent a future collision. Optimal Reciprocal Collision Avoidance (ORCA) is a decentralized, cooperative extension.

• Comparison to MPC: VO/ORCA are typically reactive and instantaneous, selecting a safe velocity from a set. MPC is predictive and optimization-based, computing a sequence of optimal control inputs. MPC can incorporate more complex dynamics and constraints but is computationally heavier.

Fundamental risk assessment metrics that feed into collision avoidance logic. Time to Collision (TTC) estimates the time until impact if courses remain unchanged. Closest Point of Approach (CPA), defined by Distance (DCPA) and Time (TCPA), predicts the minimum future separation.

• MPC Input: These metrics are used to trigger or weight the collision avoidance constraints within the MPC's cost function. A low TTC or DCPA would make the collision constraint extremely costly to violate.

A safety architecture where a simple, verifiable safety monitor or controller oversees a complex primary controller (like an MPC or learning-based system). If the primary controller's action is predicted to cause a collision, the RTA layer overrides it with a guaranteed-safe action.

• Defense in Depth: Provides a fail-safe layer for MPC systems, crucial for certification in safety-critical applications (e.g., aviation, autonomous vehicles).
• Works with WCET: The RTA monitor must have a bounded Worst-Case Execution Time (WCET) to guarantee timely intervention.