ashfordeOU Pursuit Guidance (gnc-autonomy/guidance/pursuit-guidance)
Use when the task is pursuit guidance for a planar intercept: the pure pursuit or lead pursuit aim heading, the guidance error, the capture condition, and comparison with proportional navigation.
Domain quick reference
- Geometry: (rx, ry) is the relative position of the target from the interceptor in the inertial plane (m); (vx, vy) is the relative velocity (m/s). Range is r = sqrt(rx^2 + ry^2).
- Line of sight angle: lam = atan2(ry, rx) in rad; the direction of the interceptor-to-target line.
- Pure pursuit: the interceptor velocity points at the target's current position, so the commanded heading equals the line of sight angle: psi_cmd = atan2(ry, rx).
- Guidance error (heading error): eta = wrap(psi_cmd - psi) into [-pi, pi]; the pursuit law turns to null eta, so the velocity aligns with the line of sight.
- Capture condition: with constant speeds, pure pursuit captures a non-maneuvering target on a straight course only when the interceptor is faster, Vi > Vt; at Vi <= Vt a receding target cannot be caught.
- Tail chase intercept time: t_i = r / (Vi - Vt) in s when the target is directly ahead and receding; valid only for Vi > Vt.
- Lead pursuit: aim at a point ahead of the target. For a constant velocity collision course the lead angle is lam_lead = asin((Vt / Vi) * sin(beta)) in rad, where beta is the angle between the line of sight and the target velocity vector. The aim heading is psi_cmd = lam + lam_lead. The arcsin argument must lie in [-1, 1]; otherwise the interceptor is too slow and no collision course exists.
- On a perfect collision course the line of sight does not rotate (lam_dot = 0), the same steady state proportional navigation seeks.
- Comparison with PN: proportional navigation commands lateral acceleration a_c = N * Vc * lam_dot perpendicular to the line of sight; pure pursuit commands a turn toward the line of sight and keeps lam_dot nonzero until intercept. PN nulls the line of sight rate directly and needs no explicit lead; pure pursuit is simpler but less efficient and more sensitive to target maneuvers.
- Units: m, m/s, rad, rad/s, m/s^2; angles are radians throughout.
- ARP4754A (reference-only) frames development assurance for aircraft systems; pursuit guidance laws are common guidance-theory knowledge.
Workflow
- Form the relative geometry: rx = xt - xi, ry = yt - yi, vx = vxt - vxi, vy = vyt - vyi in the inertial plane, SI units, angles in radians.
- Compute line_of_sight_angle(rx, ry); this is the pure pursuit aim heading.
- Compute heading_error(psi, rx, ry) between the current heading and the aim heading, wrapped to [-pi, pi]; the pursuit law turns to null it.
- For lead pursuit, compute lead_angle(v_target, v_interceptor, beta) and add it to the line of sight angle for the aim heading. Confirm the arcsin argument is within [-1, 1], or the interceptor is too slow for a collision course.
- Check capture_possible(v_interceptor, v_target): pure pursuit captures only when Vi > Vt.
- For a tail chase, compute intercept_time(r, v_interceptor, v_target) as r / (Vi - Vt).
- For comparison, compute pn_acceleration(rx, ry, vx, vy, n_nav=4.0) with N between 3 and 5; the result is the lateral acceleration proportional navigation would command.
Pitfalls
- Using the range instead of the vector components for the aim heading; atan2(ry, rx) needs the signed relative position.
- Leaving the heading error unwrapped; the wrapped value in [-pi, pi] is the angle the turn must null, not the raw difference.
- Taking a lead angle arcsin outside [-1, 1]; that geometry has no collision course at the given speed ratio.
- Forgetting the speed condition Vi > Vt; a slower interceptor never captures a receding straight-course target in pure pursuit.
- Confusing the lead angle with the line of sight angle; the aim heading is their sum, not either alone.
- Mixing degrees and radians; all formulas require radians.
Behavior contract (gate 3)
The line of sight angle, wrapped heading error, lead angle, capture condition, intercept time, and the proportional navigation comparison command are exercised by the gate 3 contract test: scripts/test_pursuit_guidance.py against scripts/pursuit_guidance_logic.py (stdlib unittest, offline). Run: python3 scripts/test_pursuit_guidance.py
Compliance
- ARP4754A is proprietary (SAE); name and paraphrase only per standards-map.yaml, reference-only: true.
- compliance: STANDARDS-REF, gated: false.