Feasibility Checker

The core function is to validate a proposed plan against a comprehensive set of hard constraints and soft constraints. This includes:

• Kinodynamic Feasibility: Verifying the plan adheres to the agent's velocity, acceleration, and turning radius limits.
• Collision Avoidance: Ensuring the trajectory maintains a safe distance from static obstacles and other dynamic agents.
• Operational Limits: Checking against battery life, payload capacity, and zone-based access rules. A failure on any hard constraint results in plan rejection.

The checker is embedded within a Model Predictive Control (MPC) or Receding Horizon Control loop. Its position is critical:

1. A planner (e.g., Lattice Planner, RRT*) generates candidate trajectories.
2. The feasibility checker validates each candidate.
3. Only validated plans are passed to the low-level controller for execution. This creates a plan-validate-execute cycle, often running at 10-100Hz, ensuring only safe commands are ever sent to the agent's actuators.

For real-time operation, the checker must provide deterministic (consistent) results with sub-millisecond latency. It cannot be a bottleneck. Techniques include:

• Precomputed Lookup Tables: For common constraint evaluations.
• Efficient Geometric Calculations: Using bounding boxes and signed distance fields for rapid collision checking.
• Parallel Validation: Checking different constraint types simultaneously on multi-core processors. Speed is prioritized over exhaustive search; its role is to filter, not to optimize.

A key architectural principle is the separation of concerns between the planner and the checker.

• Planner/Optimizer: Explores the state space to find a low-cost path (e.g., using A*, MPC). It may use approximations for speed.
• Feasibility Checker: Performs a rigorous, high-fidelity audit of the planner's output. It uses the most accurate models available. This separation allows the planner to be agile and creative, while the checker provides a rigorous, conservative safety layer.

The checker's primary output is a binary feasibility flag (pass/fail). However, for effective plan repair or replanning trigger generation, it must provide rich diagnostics:

• Specific Constraint Violated: e.g., "Acceleration limit exceeded at time t=3.2s."
• Severity Metric: How close the plan was to violating a constraint.
• Suggested Fixes: For example, a region of spacetime to avoid. This diagnostic data is fed back to the planner to generate a better candidate.

In Multi-Agent Path Finding (MAPF) and Heterogeneous Fleet Orchestration, the checker's role expands to validate multi-agent coordination. It must verify:

• Inter-Agent Collision Avoidance: Using concepts like Velocity Obstacles (VO) or Optimal Reciprocal Collision Avoidance (ORCA).
• Temporal Coordination: Ensuring agents respect reserved times at intersections or narrow corridors, as planned by a higher-level Conflict-Based Search (CBS) scheduler.
• Deadlock Prevention: Identifying if a proposed multi-agent move could lead to a gridlock scenario.

The problem of finding a trajectory that satisfies both kinematic constraints (e.g., position, velocity) and dynamic constraints (e.g., acceleration, force/torque limits). A feasibility checker is the primary component that validates whether a candidate trajectory meets these combined kinodynamic feasibility criteria.

• Core Function: Determines if a path is physically executable by the agent's motion model.
• Constraint Types: Includes non-holonomic constraints (e.g., a car cannot move sideways) and actuator limits.
• Relation to Feasibility Checker: The checker implements the mathematical models and inequality checks that define kinodynamic feasibility.

An advanced control method where a dynamic model predicts future system behavior. At each control step, it solves a finite-horizon optimization problem to determine optimal control actions. Feasibility checking is embedded within the MPC solver's constraint satisfaction routine.

• Online Optimization: Continuously solves for a short-term plan.
• Constraint Handling: The optimization problem explicitly includes collision, dynamic, and operational constraints that must be satisfied.
• Checker's Role: The MPC solver's internal feasibility routines validate intermediate solutions during optimization, ensuring the final control sequence is executable and safe.

A mathematical tool used to synthesize controllers that formally guarantee a dynamical system remains within a safe set. It provides a rigorous framework for constraint enforcement, which is the mathematical foundation for a high-assurance feasibility checker.

• Formal Safety Guarantees: Derives conditions that, if satisfied, ensure the system state never leaves the safe region (e.g., stays away from obstacles).
• Runtime Enforcement: Used to filter or modify control inputs in real-time to maintain feasibility.
• Checker Analogy: A CBF provides a continuous, differentiable method for checking and enforcing feasibility, whereas a discrete checker validates a full candidate trajectory.

The continuous process of comparing an agent's actual execution state and sensor readings against its expected plan to detect discrepancies. It works in tandem with the feasibility checker, which validates plans before they are sent to the execution monitor.

• Feedback Loop: Detects when real-world execution deviates from the feasible plan (e.g., wheel slippage, unexpected obstacle).
• Trigger for Rechecking: An execution monitor anomaly is a common replanning trigger, causing the system to generate and feasibility-check a new plan.
• System Integrity: The checker ensures the initial plan is sound; the monitor ensures the world adheres to the plan's assumptions.

Reactive and predictive algorithms (e.g., Velocity Obstacles, Optimal Reciprocal Collision Avoidance) designed to prevent physical conflicts. A feasibility checker must integrate collision constraints as a primary validation criterion.

• Static & Dynamic Obstacles: The checker evaluates the candidate path against a map of static obstacles and predictions of other agents' future positions.
• Safety Margins: Incorporates agent footprint and required buffer zones to ensure a safe, collision-free corridor.
• Hierarchical Validation: Often, a fast, geometric collision check is performed first, followed by more precise kinodynamic validation.

An optimization technique where a solver is initialized with a solution from a previous, similar problem. The feasibility of the warm-start solution is critical; an infeasible warm start can cause solver failure or increased computation time.

• Performance Boost: Using a previously feasible, sub-optimal plan as a starting point dramatically speeds up replanning.
• Checker's Role: Before being passed to an optimizer (e.g., in MPC), the warm-start trajectory is first validated by the feasibility checker. If invalid, it may be repaired or rejected.
• Incremental Replanning: Enables efficient plan repair by checking modifications to the last known feasible plan.