Midcourse Guidance

Midcourse Guidance (gnc-autonomy/guidance/midcourse-guidance)

Use when the task is steering a guided vehicle or interceptor through the midcourse phase between launch and terminal handover: reaching a planned waypoint or constraint geometry, shaping the trajectory, sizing the speed deficit and the miss distance of the closing geometry, and deciding when terminal guidance takes over.

Domain quick reference

Midcourse guidance steers to a planned intermediate condition (a waypoint, a constraint corridor, a handover geometry) rather than to the target directly; a terminal law (proportional navigation, pursuit, command-to-line-of-sight) then owns the final intercept. Planar model: vehicle at position p = (px, py) with speed V and heading psi, waypoint w = (wx, wy), turn-rate limit omega_max, guidance step dt. Angles are radians; units are m, s, m/s, rad, rad/s, m/s^2.

• Desired course: psi_d = atan2(wy - py, wx - px). Worked anchor: p = (0, 0), w = (1000, 500) gives psi_d = 26.565 deg.
• Course error: e = wrap(psi_d - psi) into (-pi, pi]. Same anchor with psi = 0 gives e = +26.565 deg; with psi = 45 deg gives e = -18.435 deg (the wrap keeps the short way around).
• Turn-rate-limited steering: psi_c = psi + clamp(e, -omega_max * dt, +omega_max * dt). Anchor: omega_max = 5 deg/s, dt = 1 s clamps the commanded turn to 5 deg per step although e = 26.565 deg; omega_max = 30 deg/s lets the full error through and psi_c = psi_d in one step.
• Velocity-to-be-gained: vgo = max(0, V_target - V * cos(e)), the speed deficit along the desired course after the heading error is removed. Anchor: V = 250 m/s, e = 20 deg, V_target = 300 m/s gives vgo = 300 - 234.92 = 65.08 m/s; at e = 0 the same anchor gives vgo = 50 m/s.
• Zero-effort-miss for a constant-velocity closing geometry: relative position rho = r_t - r_i, relative velocity v_rel = v_t - v_i, time-to-go t_go = -(rho . v_rel) / |v_rel|^2 clamped to >= 0, and ZEM = |rho + v_rel * t_go|, the miss distance at closest approach if nothing changes. Anchor: interceptor at (0, 0) at 300 m/s along +x, stationary target at (6000, 150) gives t_go = 20 s and ZEM = 150 m; target at (9000, 0) at 100 m/s along +x gives t_go = 45 s and ZEM = 0 (perfect intercept geometry).
• Handover condition: hand off to terminal guidance when the closing range reaches the handoff range R_ho, or when t_go falls below the terminal acquisition time. Anchor: closing speed Vc = 1000 m/s and seeker acquisition at 8 km gives handover at t_go = 8 s; the midcourse law must have driven ZEM inside the seeker capture radius by then.
• Gravity-compensated ascent shaping: normal acceleration to track a flight path angle program, a_c = V * gamma_dot_c + g * cos(gamma), the second term holding the climb up against gravity. Anchor: V = 300 m/s, gamma_dot_c = 0.5 deg/s, gamma = 30 deg, g = 9.81 m/s^2 gives a_c = 2.62 + 8.50 = 11.11 m/s^2.
• FAR-25 and CS-25 (reference-only) frame flight control system certification context for transport airplanes; the shaping laws themselves are common guidance knowledge.

Workflow

1. Confirm the phase: midcourse steers to a planned intermediate condition. If the task is direct target capture, use the terminal law leaves (proportional-navigation, pursuit-guidance, command-to-line-of-sight) instead.
2. Define the geometry: waypoint or constraint positions in meters, headings in radians.
3. Compute desired_heading(position, waypoint) and course_error(position, waypoint, heading); the error is wrapped to (-pi, pi].
4. Apply the turn-rate limit with commanded_heading(position, waypoint, heading, omega_max, dt); while the error exceeds omega_max * dt the vehicle banks at the limit and the error shrinks step by step.
5. Compute velocity_to_be_gained(speed, course_error_angle, speed_target) for the speed deficit along the course, and zero_effort_miss(interceptor_pos, interceptor_vel, target_pos, target_vel) to check the intercept line before handover.
6. Check handover_check(interceptor_pos, target_pos, handoff_range); hand off only when ZEM is already inside the terminal capture radius, otherwise the terminal law starts with a large miss.
7. For ascent phases add the gravity compensation term gravity_compensated_accel(speed, flight_path_rate, flight_path_angle, g) and state the model limits: flat earth, no drag, no wind; real trajectories need a 3-DOF or 6-DOF simulation.

Pitfalls

• Confusing midcourse guidance with proportional-navigation: PN is the terminal law commanding acceleration from closing velocity and line-of-sight rate at the target; midcourse steers to a planned intermediate condition and hands off before PN takes over.
• Confusing with pursuit-guidance: pursuit aims the interceptor velocity at the target with a capture condition; midcourse never aims at the target during the shaping phase.
• Confusing with command-to-line-of-sight: CLOS holds the missile on the tracker-to-target line; midcourse steering has no tracker line.
• Confusing with impact-point-prediction: that leaf is open-loop ballistic geometry for where an unguided round lands; midcourse guidance is closed-loop steering of a guided vehicle.
• Confusing with lqr-design: LQR derives an optimal state-feedback gain from cost weights over a linear model; midcourse shaping laws are simple explicit steering and energy functions, not optimal controllers.
• Forgetting the wrap: the course error must be wrapped to (-pi, pi], or a small geometric error turns the vehicle the long way around.
• Mixing degrees and radians: atan2, the turn clamp, and the wrap all work in radians.
• Negative velocity-to-be-gained: clamp vgo at zero; a vehicle already faster than the speed target has nothing to gain.
• t_go sign in ZEM: for a receding geometry (rho . v_rel > 0) the closest approach is in the past; clamp t_go to >= 0 and report the ZEM at the current point.
• Handing off too early or too late: handover before ZEM is inside the capture radius gives the terminal law a large initial miss; handover after the acquisition time wastes seeker tracking.
• Dropping gravity compensation in ascent: without the g * cos(gamma) term the shaped climb droops under gravity.

Behavior contract (gate 3)

The waypoint steering law, velocity-to-be-gained, zero-effort-miss, turn-rate clamping, gravity-compensated ascent acceleration, handover check, and the demonstration are exercised by the gate 3 contract test: scripts/test_midcourse_guidance.py against scripts/midcourse_guidance_logic.py (stdlib unittest, offline). Run: python3 skills/gnc-autonomy/guidance/midcourse-guidance/scripts/test_midcourse_guidance.py

Compliance

• FAR-25 (US government work, public domain) and CS-25 (EASA, free-download) are referenced by id only per standards-map.yaml, reference-only: true; no text is copied.
• compliance: STANDARDS-REF, gated: false.