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Motor Mixing Matrix — Custom 8-Thruster 6-DOF

The motor mixing matrix defines how high-level pilot commands (roll, pitch, yaw, throttle, forward, lateral) are decomposed into individual thrust commands for each of the 8 motors. This is the core of Encore's omnidirectional maneuverability.

Matrix Definition

Defined in AP_Motors6DOF.cpp under SUB_FRAME_CUSTOM (frame string: SUB_FRAME_ENCORE):

Motor Position Roll Pitch Yaw Throttle Forward Lateral
MOT_1 Front-Right-Top +0.071 +0.2625 −0.3335 +0.525 +0.7875 +0.454
MOT_2 Front-Left-Top −0.071 +0.2625 +0.3335 +0.525 +0.7875 −0.454
MOT_3 Rear-Right-Top +0.071 −0.2625 +0.3335 +0.525 +0.7875 +0.454
MOT_4 Rear-Left-Top −0.071 −0.2625 −0.3335 +0.525 +0.7875 −0.454
MOT_5 Front-Right-Bottom −0.071 −0.2625 −0.3335 −0.525 +0.7875 +0.454
MOT_6 Front-Left-Bottom +0.071 −0.2625 +0.3335 −0.525 +0.7875 −0.454
MOT_7 Rear-Right-Bottom −0.071 +0.2625 +0.3335 −0.525 +0.7875 +0.454
MOT_8 Rear-Left-Bottom +0.071 +0.2625 −0.3335 −0.525 +0.7875 −0.454

Column Semantics

Each column in the add_motor_raw_6dof() call maps to a degree of freedom:

add_motor_raw_6dof(
    motor_num,      // Motor index (1-8)
    roll_fac,       // Roll torque contribution (+/- 1.0)
    pitch_fac,      // Pitch torque contribution (+/- 1.0)
    yaw_fac,        // Yaw torque contribution (+/- 1.0)
    throttle_fac,   // Vertical thrust contribution (+/- 1.0)
    forward_fac,    // Forward/backward thrust contribution (+/- 1.0)
    lat_fac,        // Lateral (strafe) thrust contribution (+/- 1.0)
    testing_order   // Motor test sequence index
);

Design Rationale

Why a Custom Matrix?

Stock ArduSub frame types assume planar thruster arrangements (e.g., BlueROV2's 6-thruster vectored layout). Encore's frame uses 8 thrusters in a 3D omnidirectional configuration — 4 top-mounted and 4 bottom-mounted at opposing cant angles. No stock frame type supports this geometry.

Thruster Geometry

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The 8 thrusters are arranged in vertically mirrored pairs — each top motor has a corresponding bottom motor at the same X/Y position but with inverted throttle polarity. This geometry provides:

  • Full 6-DOF control: Independent authority over roll, pitch, yaw, heave, surge, and sway
  • Symmetric thrust envelope: Equal thrust capability in all directions
  • Redundant vertical control: Loss of any single vertical motor is partially compensated by its pair

Factor Tuning

  • Roll factors (±0.071): Intentionally low magnitude. The thruster moment arms for roll are short (thrusters are close to the roll axis), so small factors prevent roll overshoot.
  • Pitch factors (±0.2625): Moderate magnitude reflecting the longer fore/aft moment arm relative to the pitch axis.
  • Yaw factors (±0.3335): Tuned to balance yaw authority against cross-coupling into roll/pitch.
  • Throttle factors (±0.525): Top motors positive, bottom motors negative. Opposing signs create net vertical thrust; equal magnitudes ensure zero vertical bias at neutral throttle.
  • Forward factors (+0.7875): All motors contribute equally to forward thrust. The high magnitude reflects the canted thruster geometry's effective forward projection.
  • Lateral factors (±0.454): Left/right motors have opposing signs. Magnitude tuned to account for the lateral force projection angle of the canted thrusters.

Stabilization Path

The mixing matrix integrates into two stabilization functions:

output_armed_stabilizing() (Default Path)

Standard linear superposition:

thrust[i] = roll × roll_factor[i]
           + pitch × pitch_factor[i]
           + yaw × yaw_factor[i]
           + throttle × throttle_factor[i]
           + forward × forward_factor[i]
           + lateral × lateral_factor[i]

Final output is clamped to [-1.0, +1.0] and multiplied by motor direction.

output_armed_stabilizing_vectored_6dof() (6-DOF Normalized Path)

Separates the mixing into two independently-normalized groups to prevent saturation:

  • RPT group (Roll + Pitch + Throttle): Attitude stabilization axes
  • YFL group (Yaw + Forward + Lateral): Translation axes

Each group is normalized independently before summation:

thrust[i] = (rpt[i] / rpt_max) + (yfl[i] / yfl_max)

This prevents a maxed-out forward command from starving the attitude stabilization loop of motor headroom.

Thrust-to-PWM Conversion

int16_t calc_thrust_to_pwm(float thrust_in) {
    int16_t range_up = pwm_max - 1500;
    int16_t range_down = 1500 - pwm_min;
    return 1500 + thrust_in * (thrust_in > 0 ? range_up : range_down);
}
  • Neutral: 1500 µs (zero thrust)
  • Full forward: pwm_max µs
  • Full reverse: pwm_min µs
  • Asymmetric scaling: Accounts for ESCs with different forward/reverse deadbands

[INSERT DETAILS HERE: ESC model, PWM range (min/max µs), thruster model and specs (thrust curve, max thrust in kgf)]