Kinematics Core - (3D Differentiable ORCA IP)

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.