Differential-drive robots built in engineering technology programmes accumulate heading and position error during dead-reckoning navigation because wheel slip converts commanded wheel rotation into unmodelled translation and rotation. The model separates systematic slip bias from random slip noise and expresses the growth of heading variance as a function of path curvature, wheelbase and per-revolution slip variance. A benchmark protocol is specified in which ground-truth trajectory data are used to estimate the slip parameters and to compute the probability that a robot reaches a goal region within a stated tolerance. The analysis yields closed-form expressions for the heading-error standard deviation after a path of given length and curvature, and for the maximum path length that keeps the probability of exceeding a heading tolerance above a chosen reliability level. The contribution is a design-oriented bound that links measurable wheel-slip statistics to navigation reliability, allowing instructors and student designers to specify encoder resolution, wheel material and path planning rules from a target reliability rather than from trial and error. The paper is methodological and theoretical; no empirical data are reported, and the benchmark is presented as a protocol for future ground-truth measurement.
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Nkusi et al. (2026) studied this question.
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