{"product_id":"kinematics-core-3d-differentiable-orca-ip","title":"Kinematics Core - (3D Differentiable ORCA IP)","description":"\u003cp\u003eVLA - 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 \u003cstrong\u003ethree patent-pending extensions\u003c\/strong\u003e that no other published implementation offers:\u003c\/p\u003e\n\u003col\u003e\n\u003cli\u003e\n\u003cstrong\u003eDifferentiable mode.\u003c\/strong\u003e\u003cspan\u003e \u003c\/span\u003eClosed-form analytic gradients of the resolved velocity with respect to every input — drops directly into PyTorch \/ JAX reverse-mode autograd without finite differences.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eHierarchical multi-horizon planning.\u003c\/strong\u003e\u003cspan\u003e \u003c\/span\u003eResolves the classic short-τ-vs-long-τ Pareto trade-off at zero LP-cost overhead.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eComposable differentiable hierarchical mode.\u003c\/strong\u003e\u003cspan\u003e \u003c\/span\u003eGradients chain end-to-end through the per-pair horizon selector.\u003c\/li\u003e\n\u003c\/ol\u003e\n\u003ch3\u003eWhy this matters\u003c\/h3\u003e\n\u003cp\u003eEvery 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.\u003c\/p\u003e\n\u003ch2\u003eVerified Headline Numbers\u003c\/h2\u003e\n\u003ctable\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth\u003eMetric\u003c\/th\u003e\n\u003cth\u003eValue\u003c\/th\u003e\n\u003cth\u003eVerified by\u003c\/th\u003e\n\u003c\/tr\u003e\n\u003c\/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd\u003eCohort tick @ 1024 agents (AVX2 + index + 4-thread OpenMP)\u003c\/td\u003e\n\u003ctd\u003e\u003cstrong\u003e257 µs \/ tick\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd\u003ebench_kinematics\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSpeedup over single-thread scalar baseline\u003c\/td\u003e\n\u003ctd\u003e\u003cstrong\u003e17.6×\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd\u003ebench harness, 4 perf levers compounding\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIndependent oracle agreement (feasible LP cases)\u003c\/td\u003e\n\u003ctd\u003e\u003cstrong\u003e100 % (359\/359)\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd\u003ethird_party\/rvo2_reference.hpp\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAnalytic ↔ finite-difference Jacobian agreement\u003c\/td\u003e\n\u003ctd\u003e\u003cstrong\u003e96 % (177\/184)\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd\u003eproperty-based test §D\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFuzz-tested executions, zero crashes\u003c\/td\u003e\n\u003ctd\u003e\u003cstrong\u003e645,000\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd\u003elibFuzzer @ 90 s × 2 harnesses\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSanitiser coverage (ASan + UBSan, clean)\u003c\/td\u003e\n\u003ctd\u003efull\u003c\/td\u003e\n\u003ctd\u003esanitiser build\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eTest sections passing\u003c\/td\u003e\n\u003ctd\u003e\u003cstrong\u003e12 \/ 12\u003c\/strong\u003e\u003c\/td\u003e\n\u003ctd\u003eproperty-based suite\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/tbody\u003e\n\u003c\/table\u003e\n\u003cblockquote\u003e\u003c\/blockquote\u003e\n\u003ch3\u003eVerified, not asserted\u003c\/h3\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003e257 µs \/ tick\u003c\/strong\u003e\u003cspan\u003e \u003c\/span\u003eat 1024 agents on a 4-thread Intel Xeon (AVX2 + spatial index)\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003e17.6×\u003c\/strong\u003e\u003cspan\u003e \u003c\/span\u003espeedup over the single-thread scalar baseline, via four compounding levers (vectorised gather + spatial index + OpenMP + AVX-512-ready dispatch)\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003e100 %\u003c\/strong\u003e\u003cspan\u003e \u003c\/span\u003eagreement on feasible LP cases against an independent double-precision reference oracle (359 \/ 359 trials)\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003e645,000\u003c\/strong\u003e\u003cspan\u003e \u003c\/span\u003elibFuzzer random-input executions, zero crashes\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eAddressSanitizer \u0026amp; UndefinedBehaviorSanitizer clean\u003c\/strong\u003e\u003cspan\u003e \u003c\/span\u003eacross the full test suite\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003e12 \/ 12\u003c\/strong\u003e\u003cspan\u003e \u003c\/span\u003eproperty-based test sections pass at every build\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eISO\/IEC 14882:2020 (C++20) · MISRA-C++:2023 conformant\u003c\/strong\u003e\u003cspan\u003e \u003c\/span\u003epublic surface\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch3\u003eWhat's in the box\u003cspan\u003e \u003c\/span\u003e\u003cem\u003e(varies by license tier — see below)\u003c\/em\u003e\n\u003c\/h3\u003e\n\u003cul\u003e\n\u003cli\u003eFull C++20 source tree, build system, headers, tests, benchmarks, libFuzzer harnesses\u003c\/li\u003e\n\u003cli\u003eC99 ABI shim · pybind11 NumPy zero-copy Python bindings\u003c\/li\u003e\n\u003cli\u003eAVX2 + AVX-512 SIMD paths · scalar fallback · runtime CPUID dispatch\u003c\/li\u003e\n\u003cli\u003eUniform-grid spatial index · OpenMP multi-threaded driver\u003c\/li\u003e\n\u003cli\u003eDifferentiable kernel with analytic Jacobians · hierarchical multi-horizon kernel\u003c\/li\u003e\n\u003cli\u003eNumerical-analysis whitepaper · patent-disclosure document\u003c\/li\u003e\n\u003cli\u003eConan recipe · CMake export config · CI workflow\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eTwo integration examples (C++ swarm, Python gradient-descent loop)\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Vlaander LTD","offers":[{"title":"Default Title","offer_id":47280803283106,"sku":null,"price":4500.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0703\/1986\/6018\/files\/KinematicsCore.png?v=1779406410","url":"https:\/\/www.vlaander.com\/products\/kinematics-core-3d-differentiable-orca-ip","provider":"Vlaander LTD","version":"1.0","type":"link"}