Multi-Regime Manipulator Dynamics
Free-space slew, contact approach, and loaded manipulation — three stiffness regimes, one solver configuration, zero re-tuning.
- 0
- SolvSRK divergences at contact transition
- 3/5
- RK45 divergences at contact transition
- <1 µm
- Near-equilibrium residual vs LSODA
- 10⁶
- Eigenvalue ratio at contact (7-DOF)
The scenario
Set the picture
A 6-DOF industrial manipulator arm picks components from a conveyor (free-space slew, low stiffness), approaches a fixture (contact approach, rising stiffness as compliance controllers engage), inserts and fastens a part (loaded manipulation, high stiffness from Hertzian contact forces). The dynamics cross three stiffness regimes in a single pick-and-place cycle.
The same multi-regime challenge appears in welding robots (arc ignition → seam tracking → crater fill), CNC tool changers, collaborative robots handling variable payloads, and surgical manipulators transitioning between free motion and tissue contact.
Cost today
Standard ODE solvers (RK45, Dormand-Prince) are tuned for one stiffness regime. When the manipulator transitions from free-space to contact, the eigenvalue ratio jumps by 3–4 orders of magnitude. The solver either takes thousands of tiny steps (simulation runs 50–100× slower than real time) or diverges entirely.
Industrial practice: switch between separate solver profiles at regime boundaries, detected by hand-coded heuristics. Each profile needs separate tuning. Each transition needs a guard condition. The guard conditions are where the crashes hide.
What changes with SolvSRK
SolvSRK handles stiffness transitions internally — no external guard conditions, no profile switching, no per-regime tuning.
On SCARA 4-DOF and 7-DOF manipulator benchmarks with Hertzian contact forces, SolvSRK maintained impedance parity with LSODA (the gold-standard stiff solver) across the full workspace — including the contact transition where RK45 diverges.
Near-equilibrium precision: sub-micron positional agreement with LSODA at the insertion dwell point, where the manipulator holds position under contact load.
Measurable outcome
What we claim — and how it survives review
Each line below maps to a captured number in the demo section. Every number is reproducible from the benchmark suite.
- Impedance parity with LSODA across free-space, contact approach, and loaded manipulation regimes.
- Zero divergences at stiffness transitions (RK45: diverges at contact onset in 3 of 5 benchmark trajectories).
- Single solver configuration — no per-regime tuning profiles, no guard-condition heuristics.
- Sub-micron near-equilibrium precision at the insertion dwell point.
- Validated on SCARA 4-DOF and 7-DOF manipulator models with Hertzian contact.
The demo
What was tested. How. What the simulation printed.
SCARA 4-DOF pick-and-place cycle: free-space slew (0.8 s), contact approach with compliance (0.3 s), loaded insertion with Hertzian contact (0.4 s), retract (0.5 s). 7-DOF variant with higher stiffness ratio (10⁶). Both benchmarks run against LSODA (reference), RK45 (standard), and SolvSRK.
Measured: max position error vs LSODA, divergence count, wall-clock time, near-equilibrium residual at the insertion dwell point.
Captured benchmark output
The numbers the simulation actually printed.
| Solver | 4-DOF max err | 7-DOF max err | Divergences | Near-eq residual |
|---|---|---|---|---|
| LSODA (reference) | — | — | 0 / 5 | — |
| SolvSRK | 0.8 µm | 1.2 µm | 0 / 5 | 0.4 µm |
| RK45 | 12.3 µm* | diverged | 3 / 5 | n/a |
* RK45 4-DOF error on the 2 trajectories where it did not diverge. 7-DOF: diverged on all contact-transition trajectories.
Composes with
Where this POC sits in the benchmark suite
POC 01
Self-Regulating Process Control Under Sensor Degradation
Self-regulating control provides the uncertainty-aware gain scheduling for the manipulator's compliance controller.
POC 03
Predictive Maintenance with Edge-Cloud Parity
Predictive maintenance uses the digital twin of the manipulator for bearing-wear detection.
POC 04
Model-Free Sensor Anomaly Detection on Process Instruments
Sensor anomaly detection catches force-torque sensor faults during contact.
Evidence pointers
Where the claims live in the evidence register
These are the validation sources a reviewer should trace to verify every number on this page.
- Robotics vertical — multi-regime dynamics validation complete
- 7-DOF manipulator dynamics benchmark suite
- SolvSRK dynamics validation — SCARA 4-DOF benchmark
- SolvSRK stability under stiffness — eigenvalue ratio 10⁶
Previous · POC 01
Self-Regulating Process Control Under Sensor Degradation
Next · POC 03
Predictive Maintenance with Edge-Cloud Parity
Want to see these numbers on your plant?
Run the benchmark on your actual process model.
Two weeks, fully credited. No production integration needed. Every claim above traces back to a simulation you can verify.