ashfordeOU Command to Line of Sight Guidance (gnc-autonomy/guidance/command-to-line-of-sight)
Use when the task is command to line of sight guidance for a missile intercept: the tracker to target line, the LOS error of the missile, the steering command proportional to the error and its rate, and the cross track offset verdict.
Domain quick reference
- Geometry: the tracker sits at the origin of the inertial plane. (xt, yt) is the target position (m) and (xm, ym) the missile position (m). The tracker to target line is the line the missile must ride.
- Line of sight angle: lam = atan2(y, x) in rad, the direction of the tracker to point line, used for the target (lam_t) and the missile (lam_m).
- LOS error: eps = wrap(lam_t - lam_m) in rad, wrapped into [-pi, pi]; the signed angular deviation of the missile from the tracker target line. The CLOS law commands a turn to null it.
- Line of sight rate: lam_dot = (xvy - yvx) / r^2 in rad/s, the rotation rate of the tracker to target line, with range r = sqrt(x^2 + y^2).
- Steering command: a_c = k_error * eps + k_rate * lam_dot in m/s^2, the lateral acceleration proportional to the LOS error and its rate. Gains are non-negative; k_error in 1/s^2 and k_rate in 1/s. The error-only case (k_rate = 0) is the beam riding law.
- Cross track offset: d = (xtym - ytxm) / r_t in m, the signed perpendicular offset of the missile from the tracker target line, positive on one side of the line. The missile is on line when |d| is within the tracking tolerance.
- On line verdict: on_line(d, tol) is True when |d| < tol, the tracking tolerance in meters.
- CLOS steers the missile onto the tracker target line directly; proportional navigation instead nulls the line of sight rate and pursuit guidance points the velocity at the target or a lead point. CLOS needs no target speed estimate but is sensitive to tracker measurement noise.
- Units: m, m/s, rad, rad/s, m/s^2; angles are radians throughout.
- ARP4754A (reference-only) frames development assurance for aircraft systems; CLOS guidance laws are common guidance-theory knowledge.
Workflow
- Form the geometry: the tracker at the origin, the target at (xt, yt) and the missile at (xm, ym), SI units, angles in radians.
- Compute the target line of sight angle with los_angle(xt, yt) and the missile line of sight angle with los_angle(xm, ym).
- Compute the LOS error with los_error(lam_t, lam_m), wrapped to [-pi, pi]; this is the angular deviation the steering law acts to null.
- Compute the line of sight rotation rate with los_rate(xt, yt, vx, vy) using the target velocity, to track the moving target.
- Compute the steering command with steering_command(eps, lam_dot, k_error, k_rate); the result is the lateral acceleration to command, perpendicular to the line. Use k_rate = 0 for the beam riding law.
- Compute the cross track offset with cross_track_offset(xm, ym, xt, yt) and the on line verdict with on_line(d, tol) before gating the tracking assessment.
Pitfalls
- Mixing up the target and missile line of sight angles in the LOS error; eps = wrap(lam_t - lam_m) is the missile deviation from the target line, and the sign flips if the order is reversed.
- Leaving the LOS error unwrapped; the wrapped value in [-pi, pi] is the angle the steering law must null.
- Using the range instead of the vector components for the line of sight angle; atan2(y, x) needs the signed position.
- Taking the line of sight rate at zero range; the tracker to target line is undefined when r = 0.
- Using negative gains in the steering command; the CLOS law is stabilizing only for non-negative k_error and k_rate.
- Confusing the cross track offset with the LOS error; the offset is a perpendicular distance in meters, the error is an angle in radians.
- Using a non-positive tracking tolerance; the on line verdict is undefined for tol <= 0.
Behavior contract (gate 3)
The line of sight angle, wrapped LOS error, line of sight rate, steering command, cross track offset, and on line verdict are exercised by the gate 3 contract test: scripts/test_command_to_line_of_sight.py against scripts/command_to_line_of_sight_logic.py (stdlib unittest, offline). Run: python3 scripts/test_command_to_line_of_sight.py
Compliance
- ARP4754A is proprietary (SAE); name and paraphrase only per standards-map.yaml, reference-only: true.
- compliance: STANDARDS-REF, gated: false.