Kinematics Core - (3D Differentiable ORCA IP)
Sold once. One buyer acquires the complete IP outright — every line of source, every test, every audit artefact — and it is then denied to every other party. No licence, no recurring, no second buyer.
Acquire — begin due diligence →Technical Ledger
| SKU | VLA-GEN-KIN-V1.0 |
|---|---|
| Vendor | Vlaander LTD |
| Classification | Engineering Asset |
| Variant | Default Title |
| Availability | ProvisionedPASSING |
Provenance & integrity.
| Language | C++20 · MISRA-C++:2023 |
|---|---|
| Build | CMake · Conan recipe · CI workflow |
| SIMD dispatch | AVX2 · AVX-512 · scalar fallback · runtime CPUID |
| Sanitizers | ASan · UBSan cleanPASSING |
| Fuzzing | 645,000 executions · 2 harnesses · zero crashesPASSING |
| Oracle agreement | 100% on feasible LP cases (359/359)PASSING |
| Tests | 12/12 property-test sectionsPASSING |
| Signing scheme | ed25519 signed releases |
| Signing key | Publishing 2026-Q3 |
| SHA-256 | Publishing 2026-Q3 |
| Release | Publishing 2026-Q3 |
| External audit | Publishing 2026-Q3 |
Value, in your metrics.
| Metric you track | Magnitude |
|---|---|
| Gradient accuracy in training | Closed-form analytic Jacobians replace finite-difference wrappers — the noise floor and the per-tick allocation cost are both eliminated. |
| Production / training code reuse | One kernel: the production planner and the differentiable training-time primitive are the same implementation. |
| Cohort resolution latency | 257 µs/tick at 1,024 agents — 17.6× over the single-thread scalar baseline (AVX2, spatial index, 4-thread OpenMP). |
| Correctness assurance | 100% agreement with an independent double-precision oracle on feasible LP cases (359/359); 645,000 fuzz executions, zero crashes. |
| Framework integration | Drops into PyTorch or JAX reverse-mode autograd via zero-copy pybind11 NumPy bindings; a C99 ABI shim binds everything else. |
Build-vs-buy basis.
Reproducing this in-house: approximately 12–22 engineer-months for a senior team familiar with differentiable optimization, ORCA collision avoidance, and SIMD numerical kernels for robotics. At a loaded cost of $25,000 per engineer-month, that is $300,000–$550,000, or $715,000 after a 30% risk premium for scope overrun. Purchasing the source: $250,000 plus approximately 3 weeks of integration effort. Stated biases: we compare against the high end of the build estimate, apply a 30% risk premium for scope overrun, and exclude opportunity cost. Editable assumptions: engineer-months (12–22), loaded cost per month ($25,000), risk premium (30%). Flip any of these and the comparison adjusts accordingly — the model is yours to defend, not ours to dictate.
Risk allocation.
| Risk | Borne by | Basis | Buyer’s recourse |
|---|---|---|---|
| IP cleanliness | Vlaander LTD | Source warranted as original work, clean of third-party IP at point of sale. | Indemnification capped at the purchase price paid. |
| Benchmark performance | Vlaander LTD | Published numbers must reproduce on the documented hardware. 30-day inspection window from delivery. | Refund of the purchase price within the inspection window. |
| Integration into buyer’s stack | Buyer | Integration footprint published on every product page. No warranty extends to bespoke environments outside the documented targets. | Use the published footprint as the integration spec; engage Vlaander engineering at sales@vlaander.com for paid support. |
| Regulatory compliance in buyer’s jurisdiction | Buyer | Export classified EAR99. Buyer self-screens against restricted jurisdictions and parties under their own legal counsel. | Request a pre-sale export review at sales@vlaander.com — provided at no charge. |
| Vendor continuity | Buyer | No vendor can warrant its own continuation. Source delivered without licence server, kill-switch, or expiry — risk transferred to buyer by the outright-sale model. | Self-maintain in perpetuity using the delivered source; fork freely under the Sale terms. |
| Source-code escrow | Joint | Source is delivered to the buyer at sale, so escrow is structurally unnecessary. Available on request when buyer counsel mandates a third-party deposit. | Request escrow at sales@vlaander.com — buyer-funded; Vlaander participates without charge. |
| Security disclosure post-sale | Joint | Vlaander acknowledges security reports within 24 hours and honours coordinated disclosure indefinitely on shipped versions. Buyer applies remediation in their environment. | Report to sales@vlaander.com — disclosure policy published at /security. |
Scope & maturity.
- The full two-case ORCA solver with three patent-pending extensions: differentiable mode (closed-form analytic Jacobians), hierarchical multi-horizon planning, and the composable differentiable-hierarchical mode.
- AVX2 and AVX-512 SIMD paths with a scalar fallback and runtime CPUID dispatch, a uniform-grid spatial index, and an OpenMP multi-threaded driver.
- The verification surface: 100% independent-oracle agreement on feasible cases, 645,000 fuzz executions, ASan/UBSan-clean builds, and 12/12 property-test sections.
- A C99 ABI shim, zero-copy pybind11 NumPy bindings, a numerical-analysis whitepaper, and the patent-disclosure document.
- Three-dimensional ORCA velocity-obstacle resolution — not a full motion-planning stack (no global planner, perception, or dynamics integration).
- Analytic Jacobians agree with finite differences in 96% of property cases (177/184); the residual cases are constraint-boundary degeneracies where finite differencing is itself ill-conditioned.
- The patent-pending extensions are filed, not yet granted; the buyer inherits the patent options on outright sale.
System Abstract
Institutional-grade C++20 mathematical IP for real-time three-dimensional multi-agent kinematic resolution. It implements the full two-case Optimal Reciprocal Collision Avoidance (ORCA) algorithm with three patent-pending extensions no other published implementation offers: a differentiable mode that emits closed-form analytic gradients of the resolved velocity with respect to every input — dropping directly into PyTorch or JAX reverse-mode autograd with no finite differences; hierarchical multi-horizon planning that resolves the classic short-τ-versus-long-τ Pareto trade-off at zero LP-cost overhead; and a composable differentiable-hierarchical mode whose gradients chain end-to-end through the per-pair horizon selector.
Every robotics RL or differentiable-MPC pipeline integrating ORCA today writes its own finite-difference wrapper, accepting the noise floor and the per-tick allocation cost as the price of admission. This asset eliminates both: the same kernel that ships into your production planner doubles as the differentiable training-time primitive for the controller above it — one implementation for production and training, with analytic gradients instead of finite-difference noise.
Delivered as source: the full C++20 tree with build system, headers, tests, benchmarks, and libFuzzer harnesses; a C99 ABI shim and zero-copy pybind11 NumPy bindings; AVX2 and AVX-512 SIMD paths with a scalar fallback and runtime CPUID dispatch; a uniform-grid spatial index and OpenMP multi-threaded driver; the differentiable kernel with analytic Jacobians and the hierarchical multi-horizon kernel; plus a numerical-analysis whitepaper and the patent-disclosure document. Verified, not asserted: 257 µs/tick at 1,024 agents (17.6× over the single-thread scalar baseline), 100% agreement with an independent double-precision oracle on feasible LP cases (359/359), 645,000 fuzz executions with zero crashes, AddressSanitizer and UndefinedBehaviorSanitizer clean, and 12/12 property-test sections passing — on an ISO/IEC 14882:2020 (C++20), MISRA-C++:2023-conformant public surface.