ashfordeOU Proportional Navigation (gnc-autonomy/guidance/proportional-navigation)
Use when the task is proportional navigation guidance for a planar intercept: closing velocity, line of sight rate, and the commanded acceleration from the navigation constant.
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).
- Closing velocity: vc = -(rxvx + ryvy) / r in m/s; positive when the range is decreasing, negative when the target recedes.
- Line of sight rate: lam_dot = (rxvy - ryvx) / r^2 in rad/s; the rotation rate of the interceptor-to-target line.
- Commanded acceleration: a_c = N * vc * lam_dot in m/s^2, perpendicular to the line of sight. N is the navigation constant, typically 3 to 5, with 4 the common baseline.
- Pure pursuit steers straight at the target and needs a lead angle; proportional navigation nulls the line of sight rate and needs no explicit lead.
- Units: m, m/s, rad/s, m/s^2; angles are radians throughout.
- ARP4754A (reference-only) frames development assurance for aircraft systems; the PN law is 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 closing_velocity(rx, ry, vx, vy) and confirm it is positive, so the range is decreasing.
- Compute line_of_sight_rate(rx, ry, vx, vy) in rad/s; this is the rotation rate the guidance law acts to null.
- Compute commanded_acceleration(rx, ry, vx, vy, n_nav) with N between 3 and 5; the result is the lateral acceleration to command, perpendicular to the line of sight.
- Bundle the full state with guidance_command(rx, ry, vx, vy, n_nav=4.0), which returns range, closing velocity, LOS rate, acceleration command, and N in one dict.
Pitfalls
- Reading the closing speed magnitude instead of the signed closing velocity; a receding target must flip the sign of the command.
- Mixing degrees and radians for the LOS rate; the formulas require radians.
- Feeding filtered range and range rate that are inconsistent with the raw relative vectors; both PN formulas must share one (rx, ry, vx, vy) set.
- Accepting N <= 0; the module raises ValueError, and N below 3 typically nulls the line of sight rate too slowly.
- Commanding the acceleration without the perpendicular-to-LOS check; a_c is the lateral component, not the total acceleration vector.
Behavior contract (gate 3)
The closing velocity, line of sight rate, commanded acceleration, and bundled guidance command are exercised by the gate 3 contract test: scripts/test_proportional_navigation.py against scripts/proportional_navigation_logic.py (stdlib unittest, offline). Run: python3 scripts/test_proportional_navigation.py
Compliance
- ARP4754A is proprietary (SAE); name and paraphrase only per standards-map.yaml, reference-only: true.
- compliance: STANDARDS-REF, gated: false.