Composable Dynamics for Cooperative Humanoids: A RoboCompiler Extension

Mehdi Heydari Shahna; Jouni Mattila

cs.ROOct 9, 2026

Composable Dynamics for Cooperative Humanoids: A RoboCompiler Extension

Authors: Mehdi Heydari Shahna, Jouni Mattila

Organizations: Faculty of Engineering and Natural Sciences, Tampere University, Tampere, Finland

Abstract

Physically connected humanoids need consistent dynamics for internal actuator loops, inter-robot forces, and changing ground supports. We extend RoboCompiler with member-wise dynamics assembly, compiling reduced dynamics from rigid bodies, moving actuator parts, and reflected rotor inertias. Compiled body Jacobians and analytic constraint curvature yield an explicit Coriolis factor satisfying the power identity for floating-base quasi-velocities. A two-level reduction retains reusable robot models while composing their supports and hand connections; local inertial updates have rank at most six, and prescribed-acceleration constraint wrenches are affine in actuator efforts. These interfaces support actuator-aware tracking, coupled force allocation, payload updates, and support-mode switching for five hand-linked humanoids. Across 264 feasible states in eight humanoid configurations, normalised acceleration discrepancies remain within $1.6\!\times\!10^{-10}$ against a hard-constraint reference and $1.4\!\times\!10^{-10}$ against a compiler-independent reference; MuJoCo simulations achieve 0.73~mm root-mean-square (RMS) pelvis error in the ring dance and complete side steps through 20 support-mode changes.

Figures & tables

Fig. 1: (a) Five closed-chain humanoids dance hand in hand on the realistic MuJoCo plant; from the logged states. (b) One humanoid with the moving actuator parts: the screw barrels and rods of knees, ankles and elbows and the universal-joint crosses of the ankle struts contribute explicitly to the dynamics alongside the links and reflected rotor inertias.

Fig. 2: RoboCompiler generates the lift

v=Eu

. The extension adds analytic rates and state-dependent robot modules; the composer

G

closes supports and hand links. Member edits and prescribed-acceleration wrench maps serve downstream consumers. MuJoCo and Pinocchio views share the record.

System, mode	Bodies	Joints	Chords	Ports	$d$	$d_{1}$
Humanoid, no support	42	49	8	21	27	–
Humanoid, one sole	42	49	9	21	21	–
Humanoid, two soles	42	49	10	21	15	–
Ring of five, all soles	210	245	55	105	60	5 $\times$ 27
Ring, left soles	210	245	50	105	90	5 $\times$ 27
Ring, actuator space	210	245	55	105	60	5 $\times$ 27

TABLE I: Humanoid closure modes: massive bodies, record joints, chords (loops, supports, hand links), actuator ports, independent speeds

d

and level-1 speeds per robot

d_{1}

Fig. 3: State-wise dynamics consistency across humanoid configurations and two additional mechanisms. Humanoid state-wise accelerations against the 50-digit hard-constraint reference (

\delta_{a}

, max over the states of each mode). Maximal coordinates: normalised body-acceleration discrepancy

\delta_{b}

against the compiler-independent solve. Proposed: member-wise assembly with two-level composition. No curvature, no actuator inertia and per-robot models remove one ingredient of the model.

Fig. 4: Executed motions on the realistic plant, rendered from the logged states. Top: ring (hand wave), semicircle (sway and twist) and line (bow). Bottom: travelling ring, one side-step cycle, and the sole trajectories of all ten feet seen from above: grey curves show the references and coloured curves the executed left/right sole paths.

	$d$	Proposed	Projected		Pinocchio
System			analytic	FD	KKT
Humanoid	15	1.99	1.71	2.97	0.88
Ring of five	60	3.46	5.11	9.19	18.4
Ring, new closure mode (build and prepare): 15.6
Ring, payload edit (rank 6): 0.035

TABLE II: Humanoid evaluation times in ms. Member-wise assembly with two-level composition, including

C

and analytic curvature. Projected: ( 3 ) with analytic or finite-difference (FD) curvature. Pinocchio: proximal constrained dynamics [ 12 ] (tolerance

10^{-13}

, regularisation

\mu=10^{-9}

, 200-iteration limit; pin chords use two point pairs).

	Ring, realistic plant						Ring, ideal plant			Realistic, pelvis
Policy	pelvis	palm	link $F$	sole $F$	min $F_{z}$	infeas.	pelvis	palm	link $F$	semicircle	line
	mm	mm	err. N	err. N	N	%	mm	mm	err. N	mm	mm
Proposed	0.73	1.92	2.2	30	55	0	0.029	0.080	0.01	0.72	0.72
Projected tree ( 3 )	0.73	1.92	–	–	55	0	–	–	–	–	–
Per-robot models	0.76	2.00	–	39	21	11	0.191	0.223	–	0.71	0.72
No curvature	0.73	2.09	2.3	30	54	0	0.053	0.725	0.53	0.72	0.72

TABLE III: Thirty-second dances: RMS position and force-prediction errors, minimum sole normal force, and allocation steps with slack above 0.1. Force statistics exclude the first 0.5 s. Dash: unavailable or inapplicable; “fell”: fall time.

Fig. 5: Closed-loop dances. (a) Largest palm error over ten palms, 0.2 s moving RMS; shading indicates choreography. (b) RMS pelvis error across formations and plants; colours follow (a), green denotes per-robot models, gold massless actuators, and

\times

a fall. (c) Measured and predicted hand-link force magnitudes, 0.1 s moving means over raw signals.

Multibody Dynamics

Multibody dynamics studies how connected rigid or flexible bodies move and interact under forces, constraints, impacts, and friction.

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Sep 28, 2026J/K move · Enter open · S save

RoboCompiler: Graph-Native Compilation of Closed-Chain Robots for Consistent Modeling, Control, and Simulation

Mehdi Heydari Shahna, Joongheon Kim, Jouni Mattila

Faculty of Engineering and Natural Sciences, Tampere University, Tampere, Finland

Robotic Control Robotics Simulation Multibody Dynamics Robotics

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Robots with kinematic loops, coupled actuators, and changing contacts require consistent models of configuration, motion, force, and dynamics. Yet these interfaces are often reconstructed separately for control and simulation, making closure and actuation consistency difficult to maintain. This paper presents RoboCompiler, a graph-native framework that compiles a canonical mechanism graph into a shared mechanical interface. From bodies, joints, frames, inertias, and actuator ports, it constructs closure paths and analytic residual Jacobians, then assembles feasible configurations through rank-checked continuation and correction. A tangent lift maps independent velocities to full robot and task motion, while paired actuator-port maps preserve virtual work. A constraint-curvature correction extends the reduction to accelerations and projected rigid-body dynamics, including floating-base and support modes. Cycle-local evaluation, generated Jacobians, and dependency-aware reuse enable localized updates when closure inputs change. We evaluate physical loops and task-induced constraints on a industrial excavator, Unitree Go2, Franka Panda, Kangaroo, and a six-UPS Stewart platform. High-precision constrained-dynamics and independent Pinocchio checks confirm mechanical consistency; MuJoCo and Isaac Sim/PhysX executions demonstrate task performance and model reuse under native contact. For Kangaroo, compilation reduces residual-and-Jacobian evaluation time by 96.7% and closed-loop rollout wall time by 66.8%, with dynamics and control held fixed.

Abstract

Multibody Dynamics

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