Three Axis Gyroscope — Robotics/Navigation Sensors

Three-axis Gyroscope

Robotics / Navigation Sensors

What a three-axis rate gyroscope reads: the body angular rates, passed through a scale-factor and cross-coupling matrix, a bias, a g-sensitive bias driven by the acceleration the sensor feels, an optional second-order sensor response and output limits.

ω_meas = sat( H( SFCC · ω + bias + g_s · G ) ), the g-sensitive term taken entry by entry, with H(s) = ω_n² / (s² + 2ζω_ns + ω_n²) on each axis

Ports

• w – ω, the body angular rates p, q, r in rad/s, a [3,1] column.
• G – the acceleration the sensor feels, in g, a [3,1] column; it reaches the output only through the G-sensitive Bias.
• w_meas – ω_meas, the measured rates, always a [3,1] column.

The port order is the Simulink block's own. Both inputs must be [3,1] columns.

Parameters

• Second-order Dynamics – whether the sensor has a response:
  • on – each axis passes through H(s) above (default).
  • off – the sensor is instantaneous: ω_meas = sat(SFCC · ω + bias + g_s · G).
• Natural Frequency (rad/s) – ω_n, a scalar greater than zero. Default 190.
• Damping Ratio – ζ, a scalar of zero or more. Default 0.707.
• Scale Factors and Cross-coupling – the [3,3] matrix SFCC. The identity (default) is a perfect sensor; the diagonal holds the scale factors and the off-diagonal entries the cross-axis sensitivities.
• Measurement Bias – three numbers added after the matrix and before the dynamics. Default [0 0 0].
• G-sensitive Bias – g_s, three numbers in rate per g, each multiplying its own entry of G and added before the dynamics. Default [0 0 0], which makes the G port inert.
• Update Rate (s) – how the dynamics are realized, and the Simulink block's own "Update rate":
  • 0 (default) – continuous. Under a continuous solver the response is integrated as it stands; when the block is stepped – the discrete solver, and every code export – it is the exact zero-order-hold discretization at the block's period, which is what the continuous sensor computes from inputs that hold across each sample.
  • greater than 0 – a discrete sensor updating every that many seconds, with the Tustin (bilinear, unwarped) discretization of H(s) – exactly what the Simulink block builds for a positive rate. The block then runs at its own period, which must be this same value: set Sampling Time (s) to it, or leave that at zero with the model's sampling time equal to it. A mismatch is reported and stops the run.
• Lower and Upper Output Limits – six numbers, the three lower limits then the three upper ones, applied last. -inf and inf (default on all six) mean no limit. Each lower limit must not exceed its upper one.
• 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. Every parameter is baked in at export time, and so is the discretization: the section coefficients are computed for the block's period (or its update rate) and printed at full precision. All ten are rendered from the one description of the arithmetic the block's own simulation runs, so they perform the same operations in the same order.

The three HDL targets are simulation-only: they carry the whole model in real arithmetic and quantize only at the ports. At a period short against the sensor's response the section's poles sit close to z = 1, where Q16.16 coefficients lose the filter's DC gain, and the default limits are infinite, which fixed point cannot hold. VHDL keeps the arithmetic in a function of its own, called once per value it returns.

Simulink bridge

Import and export, mapped to Aerospace Blockset's aerolibnav/Three-axis Gyroscope. Second-order Dynamics ↔ dtype_g (on/off, 1:1), Natural Frequency (rad/s) ↔ w_g, Damping Ratio ↔ z_g, Scale Factors and Cross-coupling ↔ g_sf_cc, Measurement Bias ↔ g_bias, G-sensitive Bias ↔ g_sen, Update Rate (s) ↔ g_Ts, Lower and Upper Output Limits ↔ g_sat, all passing their values through unchanged.

g_rand ("Noise on") is always off (see Notes); a model importing it on is reported rather than silently changed. The block has no SampleTime, so Sampling Time (s) stays on the ICore side and the rate crosses as g_Ts instead – which is not the same thing: a rate of −1 in g_Ts makes the Simulink block's filter diverge.

Notes

• Stateful with the dynamics on: two states per axis, starting at zero. With Update Rate (s) at 0 the output has no direct feedthrough (it reads the response state); with a positive rate, or with the dynamics off, it does.
• No sensor noise. The Simulink block can add white noise from its own random number generator; no generated code can reproduce that sequence, so no test could confirm a noisy export, and the option is not offered. To model noise, add a Band-Limited White Noise per axis after this block – it lands after the output limits rather than before them.
• Linear in its inputs until the limits clamp, but the limits make it nonlinear, so the block carries no state space and model reduction reports it as unmergeable.
• The Three-axis Inertial Measurement Unit is this block and the Three-axis Accelerometer in one, with G taken from the body acceleration.