Battery Constraint Solver

The solver treats battery limits as inviolable mathematical boundaries, not soft suggestions. This includes:

• Minimum Charge Threshold: No agent is ever assigned a task that would drop its SoC below a safety buffer.
• Station Capacity: The solver never schedules more agents to charge than there are physical charging bays available.
• Charging Window Adherence: Tasks are only assigned if they can be completed within the agent's available energy and time windows. This guarantees that the output schedule is physically executable without stranding agents.

The solver balances competing operational goals simultaneously using a weighted cost function. It can optimize for:

• Minimizing Task Tardiness: Ensuring SLAs are met.
• Maximizing Throughput: Completing the highest number of tasks per shift.
• Minimizing Energy Cost: Shifting charging loads to off-peak tariff windows.
• Minimizing Battery Degradation: Avoiding deep discharges and high C-Rates. The output is a Pareto-optimal schedule that represents the best possible trade-off between these conflicting objectives.

The solver does not assume a flat energy-per-meter rate. It integrates a physics-based or data-driven consumption model that accounts for:

• Payload Weight: Heavier loads increase current draw.
• Terrain and Inclines: Ramps require significantly more energy than flat ground.
• Acceleration Profiles: Frequent stop-start traffic consumes more energy than constant velocity.
• Regenerative Braking Estimates: Energy recovered during deceleration is credited back to the battery budget. This precision prevents the solver from creating an optimistic plan that fails in the real world.

The solver synchronizes the where and when of charging with the task schedule. It sequences tasks so that an agent naturally arrives at a charging station with a low SoC just as a slot becomes available. Key capabilities include:

• Opportunity Charging Insertion: Automatically inserting short, partial charges during idle windows to extend operational range without a full cycle.
• Charge Queue Prediction: Forecasting future contention for charging stations and pre-emptively adjusting agent routes to avoid bottlenecks.
• Deadlock Prevention: Ensuring no circular dependency occurs where Agent A is waiting for Agent B's charger, and vice versa.

Beyond just solving for today, the solver incorporates a Battery Degradation Model to extend fleet lifespan. It operationalizes this by:

• Limiting Depth of Discharge (DoD): Avoiding full 100%-to-0% cycles in favor of shallower, less damaging partial cycles.
• C-Rate Governance: Respecting maximum charge and discharge rates to prevent accelerated chemical aging from excessive current.
• State of Health (SoH) Balancing: Distributing heavy workload cycles across the fleet to prevent a single high-value asset from degrading prematurely. This shifts the paradigm from purely reactive energy management to proactive asset preservation.

The solver is not a static batch processor. It operates within a closed-loop orchestration system that triggers replanning on exception:

• Unexpected Energy Drain: If an agent's actual SoC diverges from the predicted model (e.g., due to headwind or a stuck wheel), the solver recomputes a feasible recovery plan, potentially reassigning its remaining tasks to other agents.
• Charger Outage: If a charging station goes offline, all agents assigned to it are rerouted to alternative stations, with their task sequences re-optimized around the new energy budget.
• Hot-Order Insertion: A new urgent task is inserted into the live schedule only if a feasible energy window exists for an agent to complete it without violating its minimum charge threshold.