Kinematics Core - (3D Differentiable ORCA IP)
$4,500.00
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Kinematics Core - (3D Differentiable ORCA IP)
$4,500.00
VLA - Kinematic Core is 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 that no other published implementation offers:
- Differentiable mode. Closed-form analytic gradients of the resolved velocity with respect to every input — drops directly into PyTorch / JAX reverse-mode autograd without finite differences.
- Hierarchical multi-horizon planning. Resolves the classic short-τ-vs-long-τ Pareto trade-off at zero LP-cost overhead.
- Composable differentiable hierarchical mode. Gradients chain end-to-end through the per-pair horizon selector.
Why this matters
Every robotics RL / 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.
Verified Headline Numbers
| Metric | Value | Verified by |
|---|---|---|
| Cohort tick @ 1024 agents (AVX2 + index + 4-thread OpenMP) | 257 µs / tick | bench_kinematics |
| Speedup over single-thread scalar baseline | 17.6× | bench harness, 4 perf levers compounding |
| Independent oracle agreement (feasible LP cases) | 100 % (359/359) | third_party/rvo2_reference.hpp |
| Analytic ↔ finite-difference Jacobian agreement | 96 % (177/184) | property-based test §D |
| Fuzz-tested executions, zero crashes | 645,000 | libFuzzer @ 90 s × 2 harnesses |
| Sanitiser coverage (ASan + UBSan, clean) | full | sanitiser build |
| Test sections passing | 12 / 12 | property-based suite |
Verified, not asserted
- 257 µs / tick at 1024 agents on a 4-thread Intel Xeon (AVX2 + spatial index)
- 17.6× speedup over the single-thread scalar baseline, via four compounding levers (vectorised gather + spatial index + OpenMP + AVX-512-ready dispatch)
- 100 % agreement on feasible LP cases against an independent double-precision reference oracle (359 / 359 trials)
- 645,000 libFuzzer random-input executions, zero crashes
- AddressSanitizer & UndefinedBehaviorSanitizer clean across the full test suite
- 12 / 12 property-based test sections pass at every build
- ISO/IEC 14882:2020 (C++20) · MISRA-C++:2023 conformant public surface
What's in the box (varies by license tier — see below)
- Full C++20 source tree, build system, headers, tests, benchmarks, libFuzzer harnesses
- C99 ABI shim · pybind11 NumPy zero-copy Python bindings
- AVX2 + AVX-512 SIMD paths · scalar fallback · runtime CPUID dispatch
- Uniform-grid spatial index · OpenMP multi-threaded driver
- Differentiable kernel with analytic Jacobians · hierarchical multi-horizon kernel
- Numerical-analysis whitepaper · patent-disclosure document
- Conan recipe · CMake export config · CI workflow
- Two integration examples (C++ swarm, Python gradient-descent loop)