EOM 6DOF Euler Angles — Robotics/Equations Of Motion
Robotics/Equations_Of_Motion/EOM_6DOF_Euler_Angles · 2 input / 6 output port(s) at insert · exports to Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog, PLC Structured Text
Description#
The block's own DESCRIPTION_HTML, rendered verbatim — the same text the config dialog's info panel and the library navigator show. Fix a wrong sentence in the block's .cpp (R-D9), never here.
EOM 6DOF Euler Angles
Robotics / Equations Of Motion
The six-degree-of-freedom equations of motion of a rigid body of fixed mass, carried in body axes with the attitude as the Euler angles roll φ, pitch θ and yaw ψ (the 3-2-1 sequence). With the body velocity Vb = [u; v; w], the body rates ω = [p; q; r], the inertia tensor I and the flat-earth position Xe:
- Vb' = F/m − ω × Vb
- ω' = I−1(M − ω × (Iω))
- φ' = p + (q·sin φ + r·cos φ)·tan θ, θ' = q·cos φ − r·sin φ, ψ' = (q·sin φ + r·cos φ)/cos θ
- Xe' = DCMbeT Vb
Ports
- F – the applied force in body axes, [3,1].
- M – the applied moment about the centre of gravity in body axes, [3,1].
- Ve – the velocity in the flat-earth frame, DCMbeT Vb, [3,1].
- Xe – the position in the flat-earth frame, [3,1].
- Euler – the Euler angles [φ; θ; ψ] in radians, [3,1].
- DCMbe – the direction cosine matrix from the flat-earth frame to body axes, [3,3].
- Vb – the velocity in body axes [u; v; w], [3,1].
- wb – the body rates [p; q; r] in rad/s, [3,1].
Parameters
- Units – Metric (MKS) (the default) or English (velocity in ft/s). The two are the same arithmetic, so the choice only says which units the numbers are in.
- Initial Position [Xe Ye Ze] – three values. Defaults to [0 0 0].
- Initial Velocity [U V W] – the initial body velocity, three values. Defaults to [0 0 0].
- Initial Euler Angles [phi theta psi] – in radians, three values, with |θ| below 90°. Defaults to [0 0 0].
- Initial Body Rates [p q r] – in rad/s, three values. Defaults to [0 0 0].
- Mass – m, a scalar > 0. Defaults to 1.
- Inertia – the inertia tensor I, a [3,3] with a nonzero determinant. Defaults to eye(3).
- Integration Substeps – M, how many fourth-order Runge-Kutta steps a sample is integrated with on the discrete solver and in exported code, a whole number of 1 or more. Defaults to 100. No Simulink counterpart.
- Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.
Code export
All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. A core holds the twelve states, publishes the six outputs from them, and integrates one sample with the inputs held and M Runge-Kutta substeps – with M = 100, the same computation as Simulink's fixed-step ode4 at one hundredth of the sample time. The mass and the inertia's inverse are folded to constants.
The three HDL targets are simulation-only real
arithmetic, quantized at the port: a sine of a state has no Q16.16 form. The cores
simulate correctly and are not offered as synthesizable.
Simulink bridge
Import and export, mapped to Aerospace Blockset's
aerolib6dof2/6DOF (Euler Angles): Units →
units (the two offered values 1:1), Initial Position [Xe Ye Ze]
→ xme_0, Initial Velocity [U V W] →
Vm_0, Initial Euler Angles [phi theta psi] →
eul_0, Initial Body Rates [p q r] → pm_0,
Mass → mass_0 and Inertia →
inertia. Always emitted with mtype = Fixed
and vre_flag and mass_flag off: each of those moves that
block's port list, and this block has one. The knots unit system is not offered
– it converts velocities inside the integration – and an imported one
is reported. "Sampling Time (s)" does not cross: the Simulink block is
continuous and defines no SampleTime.
Notes
- Stateful, continuous and nonlinear: twelve continuous states. The outputs are states or functions of them, so the block has no direct feedthrough and a loop through it is not an algebraic loop.
- θ = ±90° is the Euler kinematics' singularity (gimbal lock): tan θ and 1/cos θ grow without bound there, in this block as in Simulink's. EOM 6DOF Quaternion-style attitude has no such point.
- The inertia's inverse is formed once, at configuration load, from the adjugate; the Simulink block solves the same system each step. The two agree to rounding.
Code facts#
| Fact | Value |
|---|---|
| registered type | Robotics/Equations_Of_Motion/EOM_6DOF_Euler_Angles |
| family | Robotics/Equations_Of_Motion |
| solver environment class | ICoreBlock_0_Robotics_1_Equations_Of_Motion_2_EOM_6DOF_Euler_Angles |
| source | src/ICoreBlocks/ICoreBlockLibrary/Blocks/Robotics/Equations_Of_Motion/EOM_6DOF_Euler_Angles/ICoreBlock_0_Robotics_1_Equations_Of_Motion_2_EOM_6DOF_Euler_Angles.cpp |
| header | src/ICoreBlocks/ICoreBlockLibrary/Blocks/Robotics/Equations_Of_Motion/EOM_6DOF_Euler_Angles/ICoreBlock_0_Robotics_1_Equations_Of_Motion_2_EOM_6DOF_Euler_Angles.h |
| default size on canvas | 150 × 150 px |
| ports at insert | 2 in, 6 out |
| code generators implemented | Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog, PLC Structured Text |
Ports#
| # | Direction | Signal type | Description label |
|---|---|---|---|
| 1 | in | ICoreDouble | F |
| 2 | in | ICoreDouble | M |
| 3 | out | ICoreDouble | Ve |
| 4 | out | ICoreDouble | Xe |
| 5 | out | ICoreDouble | Euler |
| 6 | out | ICoreDouble | DCMbe |
| 7 | out | ICoreDouble | Vb |
| 8 | out | ICoreDouble | wb |
Ports the constructor creates. A block whose port list changes with its configuration adds or removes ports at load time; the count above is the one a freshly inserted block has.
Configuration variables#
| Config variable | Default | Simulink parameter |
|---|---|---|
Units | Metric (MKS)%~%English (velocity in ft/s)~~Metric (MKS) | units |
Initial Position [Xe Ye Ze] | [0 0 0] | xme_0 |
Initial Velocity [U V W] | [0 0 0] | Vm_0 |
Initial Euler Angles [phi theta psi] | [0 0 0] | eul_0 |
Initial Body Rates [p q r] | [0 0 0] | pm_0 |
Mass | 1.0 | mass_0 |
Inertia | [1 0 0; 0 1 0; 0 0 1] | inertia |
Integration Substeps | 100 | not crossed |
Every block also carries Sampling Time (s) from ICoreBlockSolverEnvironment: zero or less inherits the solver's rate, a positive value runs the block at that period.
Simulink bridge#
| support | Support::Both |
| Simulink path | aerolib6dof2/6DOF (Euler Angles) |
| port-count rule | PortsParam::None |
SampleTime parameter | no — the counterpart defines none; the rate stays on the ICore side |
| deliberately not crossed | Integration Substeps |
| always set | mtype = Fixed, vre_flag = off, mass_flag = off |
| ICore config | Simulink parameter | Value translation |
|---|---|---|
Units | units | Metric (MKS) → Metric (MKS), English (velocity in ft/s) → English (velocity in ft/s) |
Initial Position [Xe Ye Ze] | xme_0 | passes through |
Initial Velocity [U V W] | Vm_0 | passes through |
Initial Euler Angles [phi theta psi] | eul_0 | passes through |
Initial Body Rates [p q r] | pm_0 | passes through |
Mass | mass_0 | passes through |
Inertia | inertia | passes through |
Caveat (shown to the user): aerolib6dof2/6DOF (Euler Angles) is continuous and has NO SampleTime parameter (verified against the R2026a block dialog). mtype, vre_flag and mass_flag are pinned because each moves that block's port list; the kts unit system is not offered because it converts velocities inside the integration; "Integration Substeps" is how this block integrates a sample and has no counterpart
Catalog contract: src/ICoreBlocks/ICoreCoder/ICoreCommandSystem/SimulinkBridge/ICoreSimulinkBlockCatalog.h
Description vs code#
The lists agree. check_block_descriptions.py finds no disagreement between the description's Ports, Parameters, Code export and Simulink bridge lists and the code's.
The verdict above is
tools/docs/check_block_descriptions.py(P7.1), which compares LISTS. It cannot read a sentence: "stateless" on a block with a state, an initial-value semantic the recursion does not implement, a "not synthesizable" caveat the HDL banner contradicts. That is the agent audit (P7.3) on BLOCK_DESCRIPTION_AUDIT.md, and this tool's green is not a substitute for one.
File banner (developer view)#
The top comment of the block's .cpp — the maths, the realization and the export strategy, addressed to whoever changes it. It must not contradict the description above (P7.5).
6DOF (Euler Angles) -- rigid-body equations of motion, fixed mass, Euler-angle attitude State [Vb (u v w), omega (p q r), (phi theta psi), Xe (xe ye ze)], inputs F and M ([3,1] each, body axes):
Vb' = F/m - omega x Vb omega' = I^-1 (M - omega x (I omega)) [phi' theta' psi'] = [1 sin(phi)tan(theta) cos(phi)tan(theta) 0 cos(phi) -sin(phi) 0 sin(phi)/cos(theta) cos(phi)/cos(theta)] omega Xe' = DCMbe' Vb
⚠ MEASURED AGAINST R2026a, and the block cannot be read: aerolib6dof2/6DOF (Euler Angles) is a compiled EOM6DOFBodyEuler block. Integrated with ode4 at 1e-4 for 0.5 s from a state with every component nonzero, under constant force and moment and an ASYMMETRIC inertia, the equations above reproduce Vb and omega to every printed digit and the angles and position to ~1e-16. What else the measurement settled:
- Six outputs, in the order Ve (= DCMbe' Vb), Xe, [phi theta psi], DCMbe [3,3], Vb, omega.
No acceleration outputs: the accelerations are the 6DOF Acceleration blocks.
- DCMbe is the earth-to-body matrix of the 3-2-1 rotation (first row cos(theta)cos(psi),
cos(theta)sin(psi), -sin(theta)) -- checked element by element against the block's output.
- Its sibling 6DOF (Quaternion) returns the same trajectory to ~1e-15 from the same dialog.
omega' uses the inertia's INVERSE, formed once at config load from the adjugate, where the Simulink block solves; the two agree to an ULP per step. "Metric" and "English (velocity in ft/s)" are the same arithmetic (no gravity inside); kts is not offered (it converts velocities inside the integration). mtype, vre_flag and mass_flag move the Simulink port list; pinned.
A continuous block with a real derivative; the discrete path and every exported core run ICoreEomRk4's map, which at M = 100 substeps is Simulink's fixed-step ode4 at Ts/100. ⚠ theta = +/-90 deg is the Euler kinematics' singularity (1/cos(theta)), exactly as in Simulink.
Sample results#
Plotted: vector — Sine Wave, [3,1]: amplitudes 1/2/3 at 2 rad/s (tried only because every scalar stimulus was refused)
Category dynamic · sample time 0.1 · 60 steps · commit b3a2977ca · produced by docsSample --out <folder> --blocks EOM_6DOF_Euler_Angles --steps 60 · data docs/generated/samples/Robotics__Equations_Of_Motion__EOM_6DOF_Euler_Angles.json · the SVG is generated from those numbers by tools/docs/plot_svg.py, so it is a run and not a drawing (R-D10).