Trajectory Generator (MATLAB)

Synthetic rigid-body trajectory generator in local ENU (East–North–Up) with lever arms (fixed points rigidly attached to the body, e.g., antennas/sensors).
Produces time series of position/velocity/acceleration for the reference point C and additional points A1–A3, plus attitude as quaternion and DCM.

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Contents

• Features
• Repository layout
• Requirements
• Quick start
• Configuration
• Outputs
• Visualization
• Coordinate frames and conventions
• Citing
• License

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Features

• IMU-rate trajectory generation (dt_INS) with optional GNSS-rate support (dt_GPS).

• Attitude integration on quaternions (robust, no gimbal lock).

• Correct rigid-body kinematics for lever-arm points:

  • Position: r_i = r_C + C_nb * r_i_body
  • Velocity: v_i = v_C + C_nb * (ω × r_i_body)
  • Acceleration: a_i = a_C + C_nb * (ω̇ × r + ω × (ω × r))

• Saves results into Traject.mat for further processing.

• Comet-like 3D animation (simultaneous for all points) using animatedline.

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Repository layout

Typical layout (file names may vary depending on your checkout):

• trajectory_generator.m — main script (trajectory generation + animation + saving Traject.mat)
• quat_from_rotvec.m — quaternion from rotation vector (scalar-first)
• quat_mul.m — quaternion multiplication (Hamilton product, scalar-first)
• quat_to_dcm.m — quaternion → DCM
• skew.m — skew-symmetric cross-product matrix [w]× (optional helper)
• utc2gps.m — UTC→GPS time helper (optional)
• dcm_2vect.m — DCM utility (optional)
• ecef2llh.m, ecef2enu.m, enu2ecef.m — coordinate transforms (optional)

Some helpers may not be called directly by trajectory_generator.m but are included for common navigation/simulation workflows.

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Requirements

• MATLAB R2016b+ recommended.
• No toolboxes required (base MATLAB).

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Quick start

1. Clone the repository and open the project folder in MATLAB.
2. Run the main script:

trajectory_generator

After execution:

• an animation window appears (if enabled in the script),
• Traject.mat is saved in the current folder.

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Configuration

All configuration is done in trajectory_generator.m via the params structure.

Common parameters:

• params.dt_INS — IMU integration step (seconds)
• params.dt_GPS — GNSS step (seconds, optional)
• params.time_mode — how stage durations are interpreted:
  • 'samples' — durations are IMU sample counts
  • 'seconds' — durations in seconds (converted using dt_INS)
• params.module_base — lever-arm baseline size (meters)
• Stage durations:
  • params.Fixed
  • params.Increment_Linear_Velocity
  • params.Without_Increment_Velocity
  • params.Increment_Angular_Velocity
  • params.With_Set_Params
• Motion commands (example):
  • params.a_lin_body — constant linear acceleration during stage 2
  • params.w_ddot_z — yaw angular acceleration during stage 4
• Visualization:
  • params.plot_decim, params.tail, params.pause_dt

Axis convention note (important):
The “forward” direction depends on your Body axes. If forward is +X, use acceleration [a;0;0].
If forward is +Y, use [0;a;0].

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Outputs

The script writes Traject.mat with (main fields):

• dt, dt_INS, dt_GPS, count, t, params
• W_body (3×N) — angular velocity in Body
• W_dot_body (3×N) — angular acceleration in Body
• C_bodyframe2inertial (3×3×N) — C_nb (Body → ENU)
• For points C, A1, A2, A3:
  • R_ENU_* (3×N) — position in ENU
  • V_ENU_* (3×N) — velocity in ENU
  • A_ENU_* (3×N) — acceleration in ENU
• q_nb_hist (4×N) — attitude quaternion (Body → ENU), scalar-first (if saved)

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Visualization

By default, trajectory_generator.m includes a comet-like 3D animation using animatedline.

Tuning knobs:

• params.plot_decim — decimation for plotting
• params.tail — tail length (points)
• params.pause_dt — animation speed (seconds)

If your motion is planar (e.g., U = 0), you can switch to a 2D view (plot / comet) for clearer visuals.

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Coordinate frames and conventions

• ENU is used as the navigation frame: E (x), N (y), U (z).
• Body is a rigid frame attached to the platform.
• Quaternion q_nb is scalar-first ([w x y z]ᵀ) and maps Body → ENU.
• DCM C_nb maps Body → ENU and is stored as C_bodyframe2inertial.

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Citing

If you use this code in a report or publication, cite it as:

Dmitry Kaleev, Trajectory Generator (MATLAB): Rigid Body in ENU with Lever Arms, 2026.

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