Minimum Sufficient Communication for Independent Behaviour Tree Robot Teams

We present an experimental framework for determining sufficient communication in robot teams running fixed, independent Behaviour Trees with private blackboards. Within a declared policy family, we vary message content and admission frequency and measure traffic in recipient-weighted bits per robot decision. A dense sweep identifies candidate policies for comparison with full-state communication. We retest selected candidates and the reference on fresh, paired scenarios, using one-sided simultaneous confidence bounds to assess whether success remains within five percentage points of the full-state reference. The bounds also assess whether tested cheaper policies can be ruled out as insufficient. Depending on the evidence, the framework reports an exact minimum, a positive bracket, a sufficient upper bound, or an unresolved boundary. Experiments with eight content policies across four warehouse conditions identify zero communication as the exact minimum under low contention. In the scaled condition, the no-release policy at gate $q=0.992222$ is confirmed sufficient, achieving 96.33% success at an estimated rate of 738.55 bits per robot decision, or 0.544% of full-state traffic. The positive minimum remains unresolved. These claims apply only to the declared policy family, sampled gate values and operating conditions.