Milestone 3: Final Documentation & Analysis

Team: Point Cloud Nine · RAS 598 · ASU · Spring 2026

Milestone 3 presents the scientific dossier for the Semantic Fetch Robot — a rigorous evaluation of system performance, empirical benchmarking across 10 trials, algorithmic analysis of our custom state machine and arm controller, and an ethical impact statement. The report documents what worked, what did not, and why, in accordance with the professor’s guidance to present honest partial demos with detailed technical analysis.

1. Graphical Abstract

flowchart LR
    subgraph MISSION["Fetch Mission"]
        A["🗣️ Operator\nIssues Command"] --> B["🗺️ Navigate to\nObject Location"]
        B --> C["🦾 Arm Grasp\nSequence"]
        C --> D["🔄 Return\nto Operator"]
        D --> E["📦 Deliver\nObject"]
    end

    subgraph STACK["ROS 2 Stack"]
        F["Nav2 + SLAM\nAutonomous Navigation"]
        G["Custom 3-DOF Arm\nJoint Position Control"]
        H["fetch_coordinator\nState Machine"]
        I["noise_injector\nSensor Simulation"]
    end

    subgraph RESULTS["Results"]
        J["✅ Navigation\nVerified in isolation"]
        K["✅ Arm Sequence\nAll 4 poses working"]
        L["⚠️ Integrated Pipeline\nCostmap inflation issue"]
        M["❌ Physical Grasping\nGazebo friction limitation"]
    end

    H --> F
    H --> G
    F --> J
    G --> K
    H --> L
    G --> M

Mission: A mobile manipulator navigates a simulated warehouse, locates a target object at a known map coordinate, executes a pick sequence using a custom 3-DOF arm, and returns the object to the operator.

Key Results: Autonomous navigation and arm sequencing each verified independently. Integrated pipeline blocked by costmap inflation from arm geometry — a documented engineering limitation with a clear solution path.

Demo Videos:

2. Algorithm

2.1 Fetch Coordinator State Machine

The core technical contribution is fetch_coordinator.py — a 6-state mission sequencer that coordinates autonomous navigation and arm manipulation.

State transition function:

\[S_{t+1} = \delta(S_t, e_t)\]

where \(S_t \in \{\text{IDLE}, \text{ARM\_HOME}, \text{NAV\_OBJECT}, \text{GRASP}, \text{NAV\_HOME}, \text{DELIVER}\}\) and \(e_t\) is the outcome event (success/failure) of the current state’s action.

Full state machine:

stateDiagram-v2
    [*] --> IDLE
    IDLE --> ARM_HOME : Mission start
    ARM_HOME --> NAV_OBJECT : Arm settled at home pose
    NAV_OBJECT --> GRASP : NavigateToPose goal succeeded
    NAV_OBJECT --> IDLE : Navigation timeout / abort
    GRASP --> NAV_HOME : Grasp sequence complete
    NAV_HOME --> DELIVER : NavigateToPose goal succeeded
    NAV_HOME --> HOLD : Navigation timeout (hold carry pose)
    DELIVER --> IDLE : Deliver sequence complete

Formal mission execution:

\[\pi = \langle a_1, a_2, a_3, a_4, a_5, a_6 \rangle\] \[a_1: \text{move\_to\_pose}(\theta_{\text{home}})\] \[a_2: \text{NavigateToPose}(x_{\text{obj}}, y_{\text{obj}})\] \[a_3: \text{settle}(\Delta t = 2\text{s})\] \[a_4: \text{grasp\_sequence}(\theta_{\text{pregrasp}} \rightarrow \theta_{\text{grasp}} \rightarrow \theta_{\text{grasp\_close}} \rightarrow \theta_{\text{carry}})\] \[a_5: \text{NavigateToPose}(x_{\text{home}}, y_{\text{home}})\] \[a_6: \text{deliver\_sequence}(\theta_{\text{carry}} \rightarrow \theta_{\text{grasp}} \rightarrow \text{open} \rightarrow \theta_{\text{home}})\]

2.2 Arm Controller — Joint Reliability Algorithm

The second custom contribution is the resend-until-settle pattern in arm_controller.py. Gazebo’s physics step does not guarantee processing of a single published message. Our solution:

\[\forall \theta_i \in \text{pose}: \text{publish}(\theta_i) \times N_{\text{resend}}, \quad \Delta t_{\text{interval}} = 0.4\text{s}\] \[\text{settle}(\tau_{\text{pose}}) \quad \text{before proceeding to next action}\]

where \(N_{\text{resend}} = 10\) and \(\tau_{\text{pose}} \in \{3.0, 3.5, 2.0, 3.0\}\) seconds depending on pose complexity.

Hardcoded pose library (measured empirically from Gazebo joint states):

Pose	\(\theta_1\) (rad)	\(\theta_2\) (rad)	\(\theta_3\) (rad)	Gripper
Home	0.000	0.000	0.000	Closed
Pregrasp	1.043	0.934	0.495	Open
Grasp	1.156	1.163	0.913	Open → Closed
Carry	0.827	0.527	0.299	Closed

2.3 Arm Forward Kinematics

All three joints rotate about the Y axis (pitch), reducing the 3D problem to planar 2D reach:

\[x_{\text{tcp}} = l_1 \sin(\theta_1) + l_2 \sin(\theta_1 + \theta_2) + l_3 \sin(\theta_1 + \theta_2 + \theta_3)\] \[z_{\text{tcp}} = l_1 \cos(\theta_1) + l_2 \cos(\theta_1 + \theta_2) + l_3 \cos(\theta_1 + \theta_2 + \theta_3)\]

where \(l_1 = 0.200\text{m}\), \(l_2 = 0.410\text{m}\), \(l_3 = 0.200\text{m}\).

Maximum reach: \(0.200 + 0.410 + 0.200 = 0.810\text{m}\) from the arm mount point at \(z = 0.475\text{m}\) above the warehouse floor — sufficient to reach the floor when the robot approaches within 0.5m of the target.

2.4 Noise Injector

Zero-mean Gaussian noise injected per sensor reading:

\[\tilde{r}_i = r_i + \mathcal{N}(0, \sigma_{\text{lidar}}^2), \quad \sigma_{\text{lidar}} = 0.02\text{m}\] \[\tilde{p} = p + \mathcal{N}(0, \sigma_{\text{odom}}^2), \quad \sigma_{\text{odom}} = 0.005\text{m}\]

These values approximate RPLIDAR A1 range uncertainty and differential drive wheel slip respectively.

3. Benchmarking & Results

3.1 Subsystem Verification

Before integrated trials, each subsystem was verified independently:

Subsystem	Test	Result	Evidence
Nav2 Navigation	`ros2 action send_goal` to open map coordinates	✅ Passed	Robot reached goal, Feedback: reached, Recoveries: 0
Arm Sequence	`ros2 run semantic_fetch_robot arm_controller`	✅ Passed	All 4 poses executed correctly in Gazebo
Noise Injector	Compare `/bcr_bot/scan` vs `/scan_noisy`	✅ Passed	Values differ by 0.01–0.04m per reading
SLAM Map	Map saved and loaded correctly	✅ Passed	523×517 cell occupancy grid, origin verified

3.2 Integrated Fetch Mission — 10 Trial Results

Configuration:

Object location: Gazebo world (2.2, -2.5, 0.06) — map frame (2.2, -2.5)
Approach pose: map (0.5, -2.5) — 1.7m in front of object
Home pose: map (-2.4, -2.5) — robot spawn location
Navigation timeout: 180 seconds

Trial	Nav to Object	Arm Sequence	Return Home	Total Time	Notes
1	❌ Timeout	—	—	180s	Robot took long path, hit timeout
2	❌ Timeout	—	—	180s	Costmap inflation blocked corridor
3	❌ Timeout	—	—	180s	Robot navigated wrong direction initially
4	❌ Timeout	—	—	180s	Same long-path behavior
5	❌ Abort	—	—	97s	Goal inside obstacle region (error 203)
6	❌ Timeout	—	—	180s	Approached object, stopped 0.3m short
7	❌ Abort	—	—	45s	Nav2 planner could not find path
8	❌ Timeout	—	—	180s	Robot bumped object, box displaced
9	❌ Timeout	—	—	180s	Long path taken around shelving
10	❌ Timeout	—	—	180s	Same behavior as Trial 1

Summary statistics:

Metric	Value
Navigation to object success rate	0 / 10 (0%)
Arm sequence success rate (standalone)	5 / 5 (100%)
Navigation success rate (isolated test)	8 / 10 (80%)
Most common failure mode	Navigation timeout (180s)
Average time before failure	158s

3.3 Root Cause Analysis

The integrated pipeline failed consistently due to costmap inflation from arm geometry. The arm mounted on top of the robot increases the effective collision footprint in the Nav2 costmap. With robot_radius: 0.5m (set to account for arm reach), Nav2 inflates obstacles by 0.5m in all directions, making the approach corridor to the object appear too narrow to traverse.

Evidence:

Navigation succeeds at 80% when goals are set in the open warehouse center
Navigation fails consistently when the goal is near shelving (approach corridor width < 1.0m)
Isolated arm sequence succeeds 100% of the time
The failure is reproducible and consistent — not random

Root cause: The robot_radius parameter in nav2_params.yaml is set to accommodate the arm’s physical reach, but this causes the costmap to reject valid approach corridors near obstacles. A narrower robot_radius for navigation combined with a separate arm-aware footprint would resolve this.

Solution path (not implemented due to time constraints):

Use a polygon footprint in Nav2 that accounts for the arm’s actual swept volume
Reduce robot_radius to 0.3m for navigation, accept slightly closer obstacle clearance
Alternatively, fold the arm to a compact home pose verified to clear all obstacles before navigating

When navigation was tested in isolation (no integrated fetch mission), results were significantly better:

Test	Goal	Result	Time
Open corridor goal	`(-2.5, -2.5)` → `(1.5, -1.0)`	✅ Success	24s
Diagonal traversal	`(-2.5, -2.5)` → `(0.0, 0.0)`	✅ Success	18s
Near-obstacle goal	`(-2.5, -2.5)` → `(1.0, -2.5)`	✅ Success	121s
Return to home	`(1.0, -2.5)` → `(-2.4, -2.5)`	✅ Success	133s
Inside obstacle	`(-2.5, -2.5)` → `(-10.0, -8.0)`	❌ Abort	2s

These results confirm the navigation stack is functional — the failure in integrated trials is specifically the approach corridor width issue, not a fundamental navigation failure.

4. Ethical Impact Statement

Privacy

The Semantic Fetch Robot uses a 2D LiDAR and depth camera for environment perception. In its current simulation form, no personal data is collected. However, in a real warehouse deployment, the depth camera would capture continuous video of the environment, potentially including images of workers. Future iterations must implement on-device processing with no cloud transmission of raw video, automatic blurring of human faces and identifiable features, and data retention policies that delete sensor logs after task completion. From a Utilitarian perspective, the efficiency gains of autonomous fetch robots benefit the majority of warehouse workers by reducing physical strain, but must be weighed against privacy intrusions for individuals captured by the sensor suite. A Justice framework requires that workers be informed of all data collection and given meaningful consent — not merely buried in employment contracts.

Safety

The bcr_bot with mounted arm has a combined mass of approximately 3-4 kg and operates at up to 0.5 m/s. Kinetic energy at maximum speed: \(KE = \frac{1}{2}mv^2 = \frac{1}{2}(4)(0.5)^2 = 0.5\text{J}\). While low, the arm’s sweeping motion during grasp sequences creates an unpredictable collision envelope. Nav2’s collision monitor and costmap inflation provide software-level safety, but physical deployments require hardware emergency stops, speed limiting near human zones, and arm position interlocks that prevent movement during navigation. During our testing, the robot bumped the target object in Trial 8 and displaced it — demonstrating that even at low speeds, unintended contact occurs. This must be addressed with force-torque sensing on the arm and contact detection logic in the fetch coordinator.

Bias

The current system hardcodes the object location as a known map coordinate. A future YOLOWorld-based semantic detection system would introduce algorithmic bias: the object detector trained on internet imagery may fail to recognize objects in warehouse lighting conditions, objects with unconventional colors, or objects partially occluded by other items. LiDAR-based localization also fails near glass surfaces and highly reflective materials — common in modern warehouses. These failures disproportionately affect edge cases that may be more common in certain operational contexts. From an Engineering Justice perspective, the system should be validated across diverse warehouse environments before deployment, with explicit failure mode documentation provided to operators.

5. Custom Module Code Links

Module	File	Key Logic	GitHub Link
Fetch Coordinator	`fetch_coordinator.py`	State machine `run()` method	fetch_coordinator.py
Arm Controller	`arm_controller.py`	`POSES` dict + `move_to_pose()` resend logic	arm_controller.py
Noise Injector	`noise_injector_node.py`	Gaussian noise injection on scan + odom	noise_injector_node.py
Navigate to Goal	`navigate_to_goal.py`	Nav2 action client	navigate_to_goal.py
Combined URDF	`bcr_bot_with_arm.urdf.xacro`	Custom 3-DOF arm geometry + Gazebo controllers	bcr_bot_with_arm.urdf.xacro
Full Demo Launch	`full_demo.launch.py`	Single-command launch with Nav2 + timing	full_demo.launch.py

Key Line References

fetch_coordinator.py — State machine run() method: The 6-step mission sequence starting at approximately line 132. Each step calls either navigate_to() (Nav2 action client) or self._arm.move_to_pose() (arm controller).

arm_controller.py — Resend logic: The move_to_pose() method resends each joint command resend_count=10 times at resend_interval=0.4s before waiting for the settle time. This custom logic was developed to overcome Gazebo’s physics step timing — a single published message was frequently dropped.

noise_injector_node.py — Gaussian injection:

noise = np.random.normal(0, self.lidar_std, ranges.shape)
noisy.ranges = (ranges + noise).tolist()

6. Individual Contribution & Audit Appendix

Team Member	Primary Technical Role	Key Contributions	Files / Commits
Suyash Dhir	Simulation, Navigation & Manipulation Lead	Simulation environment setup · SLAM mapping · Nav2 bringup and parameter tuning · TF frame debugging · Combined robot URDF with custom 3-DOF arm · Arm joint axis redesign (Z→Y) for ground reach · Arm pose calibration (all poses measured from Gazebo joint states) · `arm_controller.py` · `fetch_coordinator.py` · `navigate_to_goal.py` · Launch file development · `full_demo.launch.py` · All trial runs · Demo video recording	`semantic_fetch_robot/arm_controller.py` · `semantic_fetch_robot/fetch_coordinator.py` · `bcr_bot_with_arm/` · Commit: `a8a612a`
Divyaraj Nakum	Documentation & Architecture Lead	`milestone3.md` full report · `milestone2.md` · `milestone1.md` revision · Kinematics derivation · System architecture diagrams · Ethical impact statement · Benchmarking analysis · MathJax rendering setup	`milestone3.md` · `milestone2.md` · `milestone1.md` · `_includes/head_custom.html` · Commit: `26c146d`

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Semantic Fetch Robot · RAS 598 Mobile Robotics · Team: Point Cloud Nine · Arizona State University · 2026