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8: Uncertainty and Error Propagation

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    Robots are systems that combine sensing, actuation, computation, and communication. Except for computation, all of its sub-systems are subject to a high degree of uncertainty. This can be observed in daily life: phone calls often are of poor quality, making it hard to understand the other party, characters are difficult to read from far away, the front wheels of your car slip when accelerating on a rainy road from a red light, or your wireless device has a hard time getting a connection. In robotics, measurements taken by on-board sensors are sensitive to changing environmental conditions and subject to electrical and mechanical limitations. Similarly, actuators are not accurate as joints and gears have backlash and wheels do slip. Finally, communication, in particular, wireless either via radio or infrared, is notoriously unreliable.

    The goals of this chapter are to understand

    • how to treat uncertainty mathematically using probability theory,
    • how measurements with different uncertainty can be combined,
    • how error propagates when taking multiple measurements in a row.

    This chapter requires an understanding of random variables, probability density functions, and in particular the Normal distribution. These concepts are explained in a robotic sensing context in Appendix C.1.

    This page titled 8: Uncertainty and Error Propagation is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Nikolaus Correll via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.