UR5e Payload Research · Transportation and Nominal Control

UR5e Heavy-Payload Transport & Control

A physics-based Cartesian transportation benchmark connecting workspace constraints, two-parabola trajectory design, computed-torque PD versus MPC selection, and independent ROS 2–Isaac Sim validation before learning is introduced.

UR5eCartesian TrajectoryComputed-Torque PDMPCROS 2 HumblePhysXPayload Mismatch

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3.0 sPhysically motivated Cartesian transfer
25 + 30PD and MPC configurations screened
1.195 mmG025 matched 3 kg PhysX Cartesian RMSE
Engineering question: can a UR5e execute a demanding and physically interpretable Cartesian payload-transportation task with an accurate nominal controller, and does that controller remain dependable after transfer from a numerical plant to ROS 2–PhysX?
Heavy-Payload Transportation and Nominal Control
UR5e Cartesian transport demonstration, including the accepted trajectory and ROS 2–PhysX controller execution.

1. Task-Driven Workspace Design

Instead of prescribing an arbitrary set of joint angles, this study defines a transport mission between two workstations. The pick target uses approximately 80% of the nominal horizontal reach and the place target approximately 95%. The elevated destination introduces a 350 mm difference in tabletop height. The payload is rigidly attached, allowing the investigation to isolate free-space transportation dynamics rather than grasp acquisition or release.

Task quantityPickPlace
Tool0 position (m)(0.4648, −0.4959, 0.0050)(0.5520, 0.5889, 0.3550)
Tabletop height (m)−0.0500.300
Horizontal distance / nominal reach≈ 0.80≈ 0.95
Figure 1 — Pick-Station Configuration
Figure 1 — Pick-Station ConfigurationThe initial payload and UR5e configuration in the Isaac Sim workcell.
Figure 2 — Place-Station Configuration
Figure 2 — Place-Station ConfigurationExtended destination geometry used to probe configuration-dependent torque and reach constraints.

2. Three-Second Two-Parabola Cartesian Reference

The reference couples continuous horizontal motion with an ascent and descent formed by two parabolic vertical segments. The path is continuous in position and first derivative but changes vertical second derivative at normalized progress s = 2/3. A nonuniform time law reduces the progress rate near that curvature transition; it does not eliminate the acceleration discontinuity mathematically.

x(s) = 0.4648 + 0.0872s,   y(s) = −0.4959 + 1.0848s
z(0) = 0.005 m,   z(2/3) = 0.500 m,   z(1) = 0.355 m

The prescribed task lasts 3.0 s, with the join occurring at approximately 1.7944 s. Peak recorded joint speed is approximately 71.78°/s, below the cited 180°/s manufacturer maximum. This is a reference-feasibility result, not a measured hardware response.

Figure 3 — Accepted Cartesian Transfer Path
Figure 3 — Accepted Cartesian Transfer PathThe ascent–descent transportation path used unchanged across the nominal and residual-learning comparisons.
Figure 4 — Reference Motion and Joint Trajectory
Figure 4 — Reference Motion and Joint TrajectoryThe selected Cartesian path and its six-joint inverse-kinematics representation.

3. Nominal-Controller Screening: PD and MPC

Two model-based controller families were evaluated under common reference conditions. Computed-torque PD uses reference inverse dynamics and current-state tracking feedback; locally linearized MPC optimizes correction effort over a finite horizon with constraints on the complete commanded torque. The comparison tested 25 PD configurations and 30 MPC configurations, rather than choosing gains solely by intuition.

τG025 = sat[τff(qr,q̇r,q̈r) + M(q)(Kpe + Kdė)]
Offline candidateCartesian RMSEEngineering observation
PD G0221.099 mmLowest offline PD Cartesian error
PD G0251.127 mmStronger terminal damping; selected for PhysX comparison
MPC best screened2.470 mmBest within tested local linearized MPC grid
Figure 5 — Computed-Torque PD Gain Screening
Figure 5 — Computed-Torque PD Gain ScreeningThe 25-condition search compares Cartesian accuracy and controller parameters.
Figure 6 — MPC Parameter Search
Figure 6 — MPC Parameter SearchTwo-stage search across prediction horizon and state/effort weights; the tested objective exhibited nonmonotonic parameter sensitivity.

4. Independent ROS 2–PhysX Deployment

The transfer to Isaac Sim was treated as an independent experiment rather than a visual demonstration of offline trajectories. The six-joint effort command was published on /joint_command, with joint state returned on /joint_states. The simulation used a nominal 2 ms PhysX step and a requested 20 ms ROS controller interval; these were not proven to form a perfectly synchronized hard real-time loop.

Before robust tracking could be measured, gravity preload, active return, a two-second stabilization gate, and controlled trajectory arming were introduced. Without effective holding effort, the manipulator moved under gravity even though the intended reference had not begun. This was a commissioning issue, not evidence that the nominal dynamics equations were intrinsically incorrect.

Figure 7 — PhysX Transportation Execution
Figure 7 — PhysX Transportation ExecutionThe independently executed articulation follows the prescribed Cartesian task through the ROS 2 effort-control interface.
Figure 8 — PhysX Tool Path Projections
Figure 8 — PhysX Tool Path ProjectionsRecorded joint states are mapped to tool position using the validated analytical forward-kinematics implementation.

5. Nominal Controller Validation and G025 Selection

The final G025 controller used Kp = 256 and Kd = 41.6. G022 ranked slightly better in the offline PD sweep, but G025 achieved the lowest recorded Cartesian RMSE among the three selected controllers in PhysX. The difference illustrates why the final controller was not chosen by numerical search alone.

ControllerPhysX Cartesian RMSEJoint RMSE
G0131.4539 mm0.170°
G0221.2335 mm0.125°
G0251.1951 mm0.115°
Figure 9 — Cartesian Tracking Accuracy in PhysX
Figure 9 — Cartesian Tracking Accuracy in PhysXTime-resolved Tool0 tracking error for G013, G022, and G025; the accepted initial perturbation contributes to early peaks.
Figure 10 — Joint Torque During Transportation
Figure 10 — Joint Torque During TransportationNominal joint-effort behavior under the accepted physics simulation and torque-command configuration.

6. Payload Mismatch and the Motivation for Learning

The nominal 3 kg model produced highly accurate tracking when the plant also carried 3 kg. Retaining that model while increasing actual payload to 5 kg raised the measured PhysX Cartesian RMSE to 10.560 mm, compared with 1.195 mm in the matched condition. The controller remained mathematically intact, but its feedforward calculation no longer represented the actual loaded dynamics.

ΔτID = ΔM(qr)q̈r + Δc(qr,q̇r) + Δg(qr)

This result motivates the next project: retaining a functioning nominal controller and investigating whether bounded learned compensation can address the particular discrepancy rather than replacing established physics.

7. Engineering Boundaries

Scope: the reported 1.195 mm is a PhysX trajectory RMSE reconstructed from joint states, not hardware positioning accuracy or a verified payload-to-table clearance. The simulated joint effort limits are asset configuration values, not independently verified continuous actuator ratings. Grasp mechanics, release, and formal closed-loop safety remain outside this study.

Project Resources

Source Code & Experiment Records

UR5e analytical modeling, nominal control, ROS 2–PhysX implementation, residual RL training, evaluation routines, and recorded experiment data.

Open Part 3 on GitHub

Technical Reports

The complete integrated investigation and a concise engineering version are provided as two separate PDF files.

Condensed ReportFull Report
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Project by Sooyong Kim · Robotics & Autonomous Systems Portfolio