Cooperative Interceptor 2v2 (straight-line)

ADVANTAGES1 · dim 12

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 2-target cooperative PN guidance with deconfliction. Per-vehicle state [x,y,theta] (dim=12). 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 = 2
  • N_total = 4
  • 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 = 12
  • omega_t = 0
Initial condition
y(0) = [-100, 0, 1.57079632679, 100, 0, 1.57079632679, -150, 3000, -1.57079632679, 150, 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 2v2 (straight-line) (cooperative-interceptor-2v2-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%
10.150625 ms0.860
2SciPy DOP853SciPy
100%
8.54349 ms0.822
3SciPy RadauSciPy
100%
8.31,15336 ms0.818
4Vern9external
100%
8.26583.97 s0.814
5SciPy BDFSciPy
100%
7.445216 ms0.795
6CVODE BDFexternal
100%
7.121616 ms0.789
7Vern7external
100%
7.04523.97 s0.786
8FBDFexternal
100%
7.05585.01 s0.786
9SciPy LSODASciPy
100%
7.02124 ms0.786
10SciPy RK23SciPy
100%
6.942210 ms0.783
11Tsit5external
100%
6.5342795 ms0.775
12SciPy RK45SciPy
100%
6.42906 ms0.772
13TRBDF2external
100%
5.89105.28 s0.756
14CVODE Adamsexternal
100%
5.722112 ms0.755

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_2v2_straight_line_2026,
  title        = {Resonix Evidence Portal: Cooperative Interceptor 2v2 (straight-line)},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonix.tech/evidence/problems/cooperative-interceptor-2v2-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