Cooperative Interceptor 2v1 (straight-line)

ADVANTAGES1 · dim 9

SolvSRK wins. At the comparison noise level, SolvSRK beats the best baseline by at least 10 percentage points of survival, or by at least 0.05 balanced score when survival is tied. Use SolvSRK for this class of problem. All verdicts →

2-interceptor vs 1-target cooperative PN guidance with deconfliction. Per-vehicle state [x,y,theta] (dim=9). Target maneuver: straight-line. d_miss=2m terminal cutoff. Inter-interceptor repulsive potential at d_safe=50m.

Defense autonomy

Problem definition

Zarchan, 'Tactical and Strategic Missile Guidance', Ch. 8; Shima & Rasmussen, 'Cooperative Interceptor Guidance'

Canonical RHS excerpt from the registered callable used for this benchmark cell. Expand it to verify the state equations; it is not a standalone runnable fixture.

Show canonical RHS excerpt
def rhs(t: float, y: np.ndarray) -> np.ndarray:
    d = np.zeros(dim)

    positions = np.empty((N_total, 2))
    for k in range(N_total):
        bk = k * _STATES_PER_VEHICLE
        positions[k, 0] = y[bk + 0]
        positions[k, 1] = y[bk + 1]

    for i in range(N_interceptors):
        bi = i * _STATES_PER_VEHICLE
        x_m, y_m, th_m = y[bi + 0], y[bi + 1], y[bi + 2]

        vx_m = V_m * np.cos(th_m)
        vy_m = V_m * np.sin(th_m)

        d[bi + 0] = vx_m
        d[bi + 1] = vy_m

        tgt_idx = N_interceptors + (i % N_targets)
        bt = tgt_idx * _STATES_PER_VEHICLE
        x_t, y_t, th_t = y[bt + 0], y[bt + 1], y[bt + 2]

        dx = x_t - x_m
        dy = y_t - y_m
        r_sq = dx * dx + dy * dy

        if r_sq > d_miss_sq:
            r = np.sqrt(r_sq) + _EPS_RANGE
            vx_t = V_t * np.cos(th_t)
            vy_t = V_t * np.sin(th_t)
            dlam_dt = (dx * (vy_t - vy_m) - dy * (vx_t - vx_m)) / (r * r)
            V_c = -(dx * (vx_t - vx_m) + dy * (vy_t - vy_m)) / r
            a_pn = N_pn * V_c * dlam_dt
        else:
            a_pn = 0.0

        a_deconf_x = 0.0
        a_deconf_y = 0.0
        for j in range(N_interceptors):
            if j == i:
                continue
            bj = j * _STATES_PER_VEHICLE
            dxij = y[bi + 0] - y[bj + 0]
            dyij = y[bi + 1] - y[bj + 1]
            dist_sq = dxij * dxij + dyij * dyij

            if dist_sq < d_gate_sq:
                dist = np.sqrt(dist_sq) + _EPS_RANGE
                separation = max(dist - d_safe, 0.1)
                repulsion = 50.0 / (separation * separation)
                repulsion = min(repulsion, 200.0)
                a_deconf_x += repulsion * dxij / dist
                a_deconf_y += repulsion * dyij / dist

        a_total = a_pn + (a_deconf_x * np.sin(th_m) - a_deconf_y * np.cos(th_m))
        d[bi + 2] = np.clip(a_total, -50.0, 50.0) / V_m

    for j in range(N_targets):
        bj = (N_interceptors + j) * _STATES_PER_VEHICLE
        th_t_j = y[bj + 2]

        d[bj + 0] = V_t * np.cos(th_t_j)
        d[bj + 1] = V_t * np.sin(th_t_j)
        d[bj + 2] = omega_t

    return d
Parameters
  • N_interceptors = 2
  • N_pn = 3
  • N_targets = 1
  • N_total = 3
  • V_m = 100
  • V_t = 30
  • _EPS_RANGE = 1e-06
  • _STATES_PER_VEHICLE = 3
  • d_gate_sq = 10000
  • d_miss_sq = 4
  • d_safe = 50
  • dim = 9
  • omega_t = 0
Initial condition
y(0) = [-100, 0, 1.57079632679, 100, 0, 1.57079632679, 0, 3000, -1.57079632679]
Horizon
t ∈ [0, 60]

Canonical RHS excerpt captured from the same registered callable used for the published benchmark. Frozen closure values are summarized below; helper imports and solver settings are intentionally omitted.

Fingerprint

Spread: low

Default noise: medium

Recommendation snapshot

Clean best: SolvSRK

Noisy best: SolvSRK

Coverage

14 solver arms · clean + 5 noise levels

Ranked on survival, precision, and speed

Versions & freeze

Methodology →
Freeze
2026-08-13
libsolvsrk
2.3.0
SciPy
1.14
SUNDIALS
CVODE (bundled backend)

20 seeds/cell default · 14 arms · TRL 4–5 · simulation-lab validated · this page: Cooperative Interceptor 2v1 (straight-line) (cooperative-interceptor-2v1-straight-line)

Governed SolvTune benchmark freeze; per-arm medians only. RHS definitions and raw trial rows are not published.

Self-reported by Resonix Labs · not independently verified

Results matrix

Pick an objective and a noise level to rank all arms on survival, median SCD, median nfev, and median wall time. Medians across seeds.

Objective

Best overall trade-off of survival, precision, and speed.

Noise level

#SolverSurvivalSCDnfevWallScore
1SolvSRK
100%
9.33,53059 ms0.840
2SciPy RadauSciPy
100%
6.94,399154 ms0.783
3SciPy LSODASciPy
100%
6.41,82334 ms0.771
4FBDFexternal
100%
6.01,9345.72 s0.763
5SciPy BDFSciPy
100%
5.72,381105 ms0.755
6Vern9external
100%
5.55,2824.79 s0.749
7SciPy DOP853SciPy
100%
5.53,21868 ms0.749
8SciPy RK23SciPy
100%
5.53,04171 ms0.749
9CVODE BDFexternal
100%
5.41,35944 ms0.748
10Vern7external
100%
5.13,3024.66 s0.740
11SciPy RK45SciPy
100%
4.91,56834 ms0.736
12Tsit5external
100%
4.92,0401.06 s0.736
13CVODE Adamsexternal
100%
4.894034 ms0.733
14TRBDF2external
100%
3.13,2295.88 s0.693

At Clean, best balanced arm is SolvSRK.

Values are medians across seeds, measured by Resonix Labs on Resonix hardware and not independently verified; nfev and wall are on reference lab hardware (indicative). Under injected noise only SolvSRK and the SciPy arms are run. How we measure accuracy → · Verification status →

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Cite this page

Replace the access date. Pin the freeze ID and library versions when comparing against a later export. Cite it as what it is — a self-reported vendor benchmark, not an independently verified result. The note field says so; please keep it.

@misc{resonix_evidence_cooperative_interceptor_2v1_straight_line_2026,
  title        = {Resonix Evidence Portal: Cooperative Interceptor 2v1 (straight-line)},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonix.tech/evidence/problems/cooperative-interceptor-2v1-straight-line}},
  note         = {Self-reported vendor benchmark; internally generated by Resonix Labs and not independently verified. Accessed YYYY-MM-DD. Freeze 2026-08-13; libsolvsrk 2.3.0; SciPy 1.14.}
}

Related

TRL 4–5 · simulation-lab validated · 398 problems · 14 solver arms · clean + 5 noise levels

Freeze: 2026-08-13 · scipy 1.14 · libsolvsrk 2.3.0 · Methodology

Self-reported by Resonix Labs · not independently verified · Verification status