# Impact Time Control Guidance > Use when you must compute the impact-time-control-guidance command for a salvo or simultaneous-impact engagement: the proportional-navigation baseline acceleration from the closing speed and the line of sight rate, the PNG time-to-go estimate on the collision course, the impact-time error between the commanded remaining time to go and the natural PNG time, and the time-to-go-error-feedback bias that lengthens or shortens the intercept path so the group arrives at the commanded impact time. Produces the total lateral acceleration command with its PN baseline, bias term, time-to-go estimate and impact-time error. Trigger: impact time control, salvo attack, simultaneous impact, commanded impact time, time to go error feedback, ITCG. - Skill: `ashfordeou/impact-time-control-guidance` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/impact-time-control-guidance` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/impact-time-control-guidance/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - License: Apache-2.0 - Author: ashfordeOU (https://skillmd.com/u/ashfordeou) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/ashfordeou/impact-time-control-guidance --- # Impact-Time-Control Guidance (gnc-autonomy/guidance/impact-time-control-guidance) Use when the task is computing the impact-time-control guidance (ITCG) command for a salvo or simultaneous-impact engagement against a stationary target: the proportional-navigation (PN) baseline from the closing geometry, the leading-order PNG time-to-go estimate on the collision course, the impact-time error between the commanded remaining time-to-go and the natural PNG estimate, and the time-to-go-error-feedback bias that steers the interceptor group to arrive at the commanded impact time. This is the canonical biased-PN impact-time-control structure of the Jeon-Lee-Tahk family (IEEE Transactions on Aerospace and Electronic Systems 42(2):629-641, 2006, summarized by name and paraphrase only, never reproduced). Pairing leaves: proportional-navigation-guidance owns the unaugmented planar PN law, augmented-proportional-navigation the maneuvering-target augmentation; impact-point-prediction is open-loop ballistic prediction; midcourse-guidance handles waypoint steering and handover. ## Domain quick reference - Planar collision-course intercept against a stationary target: closing speed V_c (m/s), line of sight rate lambda_dot (rad/s), range to target R (m), navigation constant N (dimensionless, > 1), commanded remaining time-to-go t_go_des (s). - PN baseline acceleration: a_png = N * V_c * lambda_dot. - PNG time-to-go on the collision course: t_go = R / V_c (exact when the interceptor flies the collision triangle). - Impact-time error: e_t = t_go_des - t_go. - Time-to-go-error-feedback bias: a_b = K_it * V_c * e_t / t_go^2, with the feedback gain K_it scheduled on the engagement state (navigation constant by default). - Total command: a_cmd = a_png + a_b. - A positive error (later arrival commanded than the natural PNG time) gives a positive bias that lengthens the intercept path; a negative error shortens it. ## Workflow 1. Fix the engagement state: closing speed V_c, line of sight rate lambda_dot, range R, navigation constant N and the commanded remaining time-to-go t_go_des. Non-physical inputs are rejected with ValueError (navigation constant at or below 1, non-positive closing speed or range in the estimate, non-positive gain or times in the bias). 2. Compute the PN baseline with png_baseline(nav_constant, closing_speed, los_rate): a_png = N * V_c * lambda_dot. 3. Estimate the natural PNG time-to-go with tgo_estimate_png(closing_speed, range_to_target): t_go = R / V_c. 4. Form the impact-time error e_t = t_go_des - t_go between the commanded remaining time-to-go and the PNG estimate. 5. Compute the time-to-go-error-feedback bias with impact_time_bias(gain, closing_speed, tgo_desired, tgo_actual): a_b = gain * V_c * e_t / t_go^2. The default gain is the navigation constant (K_IT_DEFAULT = 4.0); a custom gain may be passed. 6. Sum the baseline and the bias with itcg_command(nav_constant, closing_speed, los_rate, range_to_target, tgo_desired, gain=None), which returns (a_cmd, a_png, a_b, tgo_png, e_t): the total lateral acceleration command, its PN baseline, the bias term, the time-to-go estimate and the impact-time error. 7. Read the natural (uncontrolled) time to impact with time_to_impact_seconds(range_to_target, closing_speed), the same closed form as the PNG estimate, for the salvo feasibility context. 8. Confirm the deterministic checks with the contract test scripts/test_impact_time_control_guidance.py. ## Worked example All values are REAL outputs of the logic module at the spec anchor state (R = 8000.0 m, V_c = 300.0 m/s, lambda_dot = 0.004 rad/s, N = 4.0, t_go_des = 30.0 s): - png_baseline(4.0, 300.0, 0.004) = 4.800000000000 m/s^2 - tgo_estimate_png(300.0, 8000.0) = 26.666666666667 s - impact time error e_t = 30.0 - 26.666666666667 = 3.333333333333 s - impact_time_bias(4.0, 300.0, 30.0, 26.666666666667) = 5.625000000000 m/s^2 - itcg_command(4.0, 300.0, 0.004, 8000.0, 30.0) = (10.425000000000, 4.800000000000, 5.625000000000, 26.666666666667, 3.333333333333) The natural PNG time to impact is 26.67 s; commanding a 30 s simultaneous arrival produces a positive bias of 5.625 m/s^2 that lengthens the intercept path. Zero-error identity: at t_go_des equal to the PNG estimate the bias is exactly 0 and the command collapses to the pure PN baseline (4.8 m/s^2). The planar fixed-step Euler probe in the contract test shows the bias lengthens the flight time by about 4.1 s at this command. ## Verification - Deterministic stdlib math only; no RNG, no network, no numeric integration in the leaf (the Euler probe lives in the contract test as a test-side identity check). - ValueErrors: navigation constant at or below 1.0; negative closing speed in the baseline; non-positive closing speed or negative range in the time-to-go estimate; non-positive gain, actual time-to-go or desired time-to-go in the bias. - Identities: zero impact-time error gives zero bias and the pure PN command; the natural time to impact equals the PNG time-to-go estimate; doubling the closing speed at constant e_t / t_go^2 doubles the bias; two identical calls return bit-identical results. ## Related leaves - gnc-autonomy/guidance/proportional-navigation-guidance (the unaugmented planar PN law that forms this law's baseline) - gnc-autonomy/guidance/augmented-proportional-navigation (maneuvering- target augmentation of the same baseline) - gnc-autonomy/guidance/midcourse-guidance (waypoint steering, handover, trajectory shaping) - gnc-autonomy/guidance/impact-point-prediction (open-loop unguided ballistic impact prediction) - gnc-autonomy/control/digital-control-design (sampled-data control of the inner loop that would track this command) ## Pitfalls - Do not claim the proportional-navigation law itself: this leaf forms a PN baseline from given engagement geometry but the standalone law, its capture conditions and its variants belong to the PN siblings. - Do not add impact-angle constraints: no leaf in the family claims them and they are out of scope for the time-only law. - The bias formula is deterministic at the given engagement state; this is not a trajectory propagator. Do not present the fixed-step Euler check in the contract test as a leaf capability. - The t_go = R / V_c estimate is the leading-order collision-course form; for wide heading errors the natural PNG time deviates from it, which is exactly the error the feedback term acts on. - Keep the commanded time-to-go positive and the navigation constant above 1.0; both are enforced with ValueError. - Do not use single-word generic tags (guidance, control, navigation, intercept): they would steal corpus tasks from the family router rows. ## Behavior contract (gate 3) The contract test scripts/test_impact_time_control_guidance.py (33 methods, stdlib unittest, offline, deterministic) verifies: the worked-example baseline, time-to-go, error, bias and total command within 1e-9 relative; the zero-error identity (bias zero, command equal to the PN baseline); the ValueError rejections (navigation constant at or below 1, negative closing speed, non-positive closing speed or negative range in the estimate, non-positive gain and non-positive times in the bias); boundary behavior; the linearity of the bias in closing speed; determinism of repeated calls; the natural-time identity; and the planar Euler sign probe showing the bias lengthens the flight time by the anchor margin (between 3.0 and 5.5 s). The test passes under both /usr/bin/python3 and the pyenv 3.13 interpreter; no exact-float equality is asserted on computed sums. ## Compliance STANDARDS-REF, gated false. ARP4754A (reference-only) frames development assurance for guided systems; the ITCG law itself is paraphrased public guidance-theory literature (Jeon, Lee and Tahk 2006) and is never reproduced verbatim.