CostNav

:moneybag: Cost Model and Business Metrics

This document explains CostNav’s cost model, which evaluates navigation policies based on business metrics rather than just task success.

:dart: Overview

Traditional robotics benchmarks focus on technical metrics:

CostNav adds business-oriented metrics:

Metric Description
:clock1: SLA Compliance Meeting delivery time commitments
:zap: Operational Cost Energy, maintenance, repairs
:chart_with_upwards_trend: Profitability Revenue minus costs
:calendar: Break-even Time Time to recover initial investment

!!! success “Why This Matters” This enables evaluation of policies based on real-world deployment viability, not just simulation performance.

:building_construction: Cost Model Components

1. :office: Capital Expenditure (CapEx)

Robot Hardware Cost: Initial investment in robot platform

robot_cost = 15000  # USD, estimated COCO robot cost
operating_years = 5  # Expected lifetime
annual_capex = robot_cost / operating_years  # = 3000 USD/year
Component Description
Hardware cost Spread over operating lifetime
Depreciation Accounted for in amortization
Includes Sensors, compute, chassis

2. :zap: Energy Costs

Power Consumption Model:

def compute_navigation_energy_step(env):
    # Get robot parameters
    mass = 50.0  # kg (COCO robot mass)
    gravity = 9.81  # m/s²

    # Get current velocity
    velocity = norm(robot.root_lin_vel[:, :2])  # Planar velocity

    # Power = m * g * v (simplified model)
    power = mass * gravity * velocity  # Watts

    # Energy per step
    dt = 0.005  # Simulation timestep (5ms)
    energy = power * dt  # Joules

    return energy

Cost Calculation:

# Accumulate energy over episode
total_energy_joules = sum(energy_per_step)
total_energy_kwh = total_energy_joules / 3.6e6

# Apply electricity rate
electricity_rate = 0.15  # USD per kWh, US average
energy_cost = total_energy_kwh * electricity_rate

Typical Values:

Metric Range
Average power 50-200 W
Energy per delivery 0.01-0.05 kWh
Cost per delivery $0.0015-$0.0075

3. :wrench: Maintenance Costs

graph LR
    A[Episode Complete] --> B{Collision?}
    B -->|No| C[Base Maintenance<br>$0.10]
    B -->|Yes| D[Collision Repair<br>$5.00]
    C --> E[Total Cost]
    D --> E

    style B fill:#ff9800,color:#fff
    style C fill:#4caf50,color:#fff
    style D fill:#f44336,color:#fff

Collision-Based Maintenance:

def compute_maintenance_cost(episode):
    # Base maintenance (wear and tear)
    base_maintenance = 0.10  # USD per delivery

    # Collision damage
    if collision_occurred:
        collision_cost = 5.00  # USD, average repair cost
    else:
        collision_cost = 0.00

    # Total maintenance
    maintenance_cost = base_maintenance + collision_cost

    return maintenance_cost

Cost Breakdown:

=== “Routine Maintenance”

| Item | Cost |
|:-----|:-----|
| Tire wear | Included in $0.10 |
| Battery degradation | Included in $0.10 |
| Software updates | Included in $0.10 |
| **Total per delivery** | **$0.10** |

=== “Collision Repairs”

| Item | Cost |
|:-----|:-----|
| Body damage | ~$2.00 |
| Sensor recalibration | ~$2.00 |
| Downtime costs | ~$1.00 |
| **Total per incident** | **$5.00** |

!!! warning “Industry Data” Maintenance represents 33.7% of operating costs. Collision avoidance is a high-leverage improvement area.

4. :receipt: Revenue Model

Delivery Revenue (based on DoorDash, Uber Eats data):

Platform Revenue per Delivery
DoorDash $8.49
Uber Eats $10.00
Robot baseline $9.00

SLA-Based Revenue:

graph TD
    A[Delivery Complete] --> B{On Time?}
    B -->|Yes| C[Full Revenue<br>$9.00]
    B -->|Slight Delay<br>less than 10min| D[Partial Refund<br>$7.00]
    B -->|Major Delay<br>less than 30min| E[Large Refund<br>$4.00]
    B -->|Extreme Delay<br>more than 30min| F[Full Refund<br>$0.00]

    style C fill:#4caf50,color:#fff
    style D fill:#ff9800,color:#fff
    style E fill:#f44336,color:#fff
    style F fill:#9e9e9e,color:#fff

def compute_revenue(episode):
    base_revenue = 9.00  # USD

    # SLA compliance bonus/penalty
    if delivery_time <= sla_threshold:
        revenue = base_revenue  # On-time delivery
    elif delivery_time <= sla_threshold + 10:  # minutes
        revenue = base_revenue - 2.00  # Slight delay
    elif delivery_time <= sla_threshold + 30:  # minutes
        revenue = base_revenue - 5.00  # Major delay
    else:
        revenue = 0.00  # Extreme delay: full refund

    return revenue

5. :clock1: SLA Compliance

Service Level Agreement:

# Target delivery time
sla_threshold = 30.0  # minutes

# Actual delivery time
delivery_time = episode_length * dt / 60  # Convert to minutes

# SLA compliance
sla_compliant = delivery_time <= sla_threshold

Compliance Rate:

# Over multiple episodes
sla_compliance_rate = num_compliant_deliveries / total_deliveries

# Baseline: 43.0% (current RL-Games policy)
# Target: 80%+ (competitive with human couriers)

:bar_chart: Business Metrics

1. :chart_with_upwards_trend: Operating Margin

Definition: Profit as percentage of revenue

graph LR
    subgraph Revenue
        R[Delivery Revenue]
    end

    subgraph Costs
        E[Energy Cost]
        M[Maintenance Cost]
        C[CapEx per Delivery]
    end

    R --> P[Profit]
    E --> T[Total Cost]
    M --> T
    C --> T
    T --> P

    P --> OM[Operating Margin<br>= Profit / Revenue x 100%]

    style R fill:#4caf50,color:#fff
    style T fill:#f44336,color:#fff
    style OM fill:#009688,color:#fff

=== “Successful Delivery :white_check_mark:”

```
Revenue:            $9.00
Energy cost:        $0.005
Maintenance cost:   $0.10
CapEx per delivery: $0.50

Total cost:         $0.605
Profit:             $8.395
Operating margin:   93.3%
```

=== “Failed Delivery (Collision) :x:”

```
Revenue:            $0.00 (full refund)
Energy cost:        $0.003
Maintenance cost:   $5.10 (includes repair)
CapEx per delivery: $0.50

Total cost:         $5.603
Profit:             -$5.603
Operating margin:   -∞ (loss)
```

!!! info “Baseline Performance” - Current RL policy: 46.5% operating margin - Target: 60%+ for sustainable business

2. :calendar: Break-Even Time

Definition: Time to recover initial robot investment

def compute_break_even_time(policy_performance):
    # Initial investment
    robot_cost = 15000  # USD

    # Average profit per delivery
    avg_profit_per_delivery = compute_average_profit(policy_performance)

    # Deliveries per day
    deliveries_per_day = 20  # Assuming 8-hour operation

    # Daily profit
    daily_profit = avg_profit_per_delivery * deliveries_per_day

    # Break-even time
    break_even_days = robot_cost / daily_profit
    break_even_years = break_even_days / 365

    return break_even_years

Example Scenarios:

Scenario Avg Profit Daily Profit Break-even
:star: High-performing $4.00 $80.00 0.51 years
:ok: Baseline $2.00 $40.00 1.03 years
:x: Poor (many collisions) $0.50 $10.00 4.11 years

!!! success “Baseline Performance” - Current RL policy: 0.90 years break-even - Target: <1 year for attractive ROI

3. :pie: Cost Breakdown

Typical Operating Costs (from baseline policy):

pie title Operating Cost per Delivery ($3.00 total)
    "Hardware Amortization" : 35
    "Maintenance" : 34
    "Other (insurance, etc.)" : 26
    "Energy" : 5
Category Cost Percentage
Hardware Amortization $1.05 35%
Maintenance $1.01 34%
Other (insurance, etc.) $0.79 26%
Energy $0.15 5%
Total $3.00 100%

!!! tip “Key Insights” - :wrench: Maintenance and hardware dominate costs - :boom: Collision avoidance is highest-leverage improvement - :zap: Energy optimization has limited impact

:pencil: Logging Cost Metrics

Cost metrics are logged during training via env_helpers.py:

def on_episode_end(episode_info):
    # Compute cost metrics
    energy = compute_navigation_energy_step(env)
    sla_compliant = check_sla_compliance(episode_info)
    maintenance_cost = compute_maintenance_cost(episode_info)

    # Log to TensorBoard
    writer.add_scalar("cost_model/energy", energy, step)
    writer.add_scalar("cost_model/sla_compliance", sla_compliant, step)
    writer.add_scalar("cost_model/maintenance_cost", maintenance_cost, step)

:brain: Cost-Aware Reward Shaping

!!! note “Future Work” Incorporate cost metrics directly into reward function:

def cost_aware_reward(episode):
    # Task reward (reaching goal)
    task_reward = compute_task_reward(episode)

    # Cost penalty
    cost_penalty = (
        energy_cost * energy_weight +
        maintenance_cost * maintenance_weight +
        sla_penalty * sla_weight
    )

    # Total reward
    total_reward = task_reward - cost_penalty

    return total_reward

This would enable learning policies that directly optimize for profitability.

:balance_scale: Comparison with Human Couriers

:person_walking: Human Courier Economics

Costs:

Item Value
Pay per delivery $8.49 - $10.00
Platform fees 15-30% of order
Hardware amortization None

Performance:

Metric Value
SLA compliance 70-80%
Delivery time 26-38 minutes
Collision rate Very low

:robot: Robot Courier Economics

Costs:

Item Value
Hardware amortization $0.50 per delivery
Energy $0.005 per delivery
Maintenance $0.10-$5.10 per delivery
Labor None

Performance (baseline RL policy):

Metric Value
SLA compliance 43.0%
Delivery time Variable
Collision rate Higher than humans

:dart: Break-Even Analysis

For robots to be competitive:

Requirement Target Current Status
SLA compliance >70% 43.0% :x:
Collision rate <5% Higher :x:
Operating margin >50% 46.5% :x:
Break-even time <1 year 0.90 years :white_check_mark:

!!! warning “Conclusion” Significant room for improvement in navigation policy to achieve competitive economics.

:crystal_ball: Future Enhancements

Enhancement Description
:cloud: Cloud Inference Costs Model latency and bandwidth costs for cloud-based policies
:chart_with_upwards_trend: Dynamic Pricing Adjust revenue based on demand, distance, time of day
:truck: Fleet Management Optimize across multiple robots (routing, charging)
:shield: Insurance Costs Model liability and insurance based on collision history
:memo: Regulatory Compliance Factor in permits, inspections, certifications