inverse_dynamics (RNEA / Recursive Newton-Euler Algorithm)#

Overview#

inverse_dynamics computes the inverse dynamics of a robot using the Recursive Newton-Euler Algorithm (RNEA) — given joint positions, velocities, and accelerations, it returns the joint torques required to produce them. GRiD also exposes the per-pass helpers (inverse_dynamics_fpass / inverse_dynamics_bpass) for downstream accelerator pieces that need access to the spatial velocity / acceleration / force intermediates.

Signature#

(c, v, a, f) = rbd.inverse_dynamics(q, qd, qdd=None, GRAVITY=-9.81)

GRAVITY is the signed gravitational acceleration; the default -9.81 is standard downward gravity (matching pinocchio / RBDReference). If qdd is omitted, inverse_dynamics returns the bias term (Coriolis + gravity) used by the forward dynamics composition qdd = Minv·(τ − c).

The gradient#

First-order gradients are available as rbd.inverse_dynamics_gradient(q, qd, qdd, GRAVITY=-9.81), returning np.hstack((dc_dq, dc_dqd)). The second-order tensors are exposed through IDSVA / IDSVA-SO (Inverse Dynamics, Second-Order) (idsva_so_body_frame / idsva_so_world_frame / the idsva_so dispatcher).

Implementation#

The Python reference is RBDReference.inverse_dynamics in RBDReference/RBDReference.py. CUDA codegen lives in grid_codegen/algorithms/_inverse_dynamics.py.

In GRiD#

On every handle, tau = h.inverse_dynamics(q, qd, qdd) takes q at (B, h.nq) and qd, qdd at (B, h.nv), and returns the torques at (B, h.nv). Matrix and derivative outputs are nv-wide as well. See Input / Output ABI (h_q_qd_u) and Python Wrappers (grid-rbd). With qdd omitted it returns the bias c(q, qd) = C(q, qd)·qd + g(q), which is also available as h.nonlinear_effects; h.generalized_gravity is the qd = 0 special case. Optional per-body external forces (f_ext, (B, 6*num_bodies), body-major, [angular; linear] in the body frame) are subtracted from the per-body force, and the signed gravity defaults to -9.81.

Derivatives: h.inverse_dynamics_gradient returns ∂τ/∂(q, qd) as (B, NV, 2*NV) in the tangent space, and IDSVA / IDSVA-SO (Inverse Dynamics, Second-Order) provides the second-order tensors. Inverse dynamics also anchors the inertial-parameter regressor Y(q, qd, qdd) with tau = Y·π (h.inverse_dynamics_regressor) and a generated CUDA regressor-gradient operation. The latter is not a method on the NumPy RobotHandle.

The CUDA host entries are grid::inverse_dynamics and inverse_dynamics_compute_only. RNEA is a short-running operation in the release collection, so dispatch and transfers can be substantial relative to compute time. The choice of C++ host call, NumPy, PyTorch or JAX surface is therefore part of the performance comparison, not just a syntax choice.