Ultrasonic Distance-Sensor Crosstalk in Student-Built Engineering Education Mobile Robots: A Multi-Echo Time-of-Flight Benchmark Linking Transducer Ringing to Collision-Avoidance Reliability Bounds

Ultrasonic rangefinding is the default obstacle-detection modality in student-built mobile robots, yet the same low-cost transducers that make it affordable also produce multi-echo returns whose timing depends on transducer ringing, cross-sensor acoustic crosstalk and the geometry of nearby surfaces. A multi-echo time-of-flight model is stated in which each transducer emits a ringing envelope, the environment returns a superposition of echoes, and the receiver thresholds the envelope to produce a range estimate; crosstalk between co-mounted transducers is represented as an additive interference term whose magnitude depends on inter-sensor spacing and firing schedule. From the model, three propositions are derived: a ringing-induced lower bound on resolvable range, a crosstalk-induced bias in the reported range that grows as inter-sensor spacing shrinks, and a collision-avoidance reliability bound that translates range error into the probability of failing to stop before contact at a given approach speed. The propositions are evaluated against a declared benchmark configuration spanning cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points, with 2000 replications per cell and an intraclass correlation of 0.64. The benchmark is methodological rather than empirical: it specifies the quantities a student laboratory must report if its collision-avoidance claims are to be comparable across builds, and it identifies the ringing and crosstalk parameters that dominate the reliability bound.