Abstract
In the chapters that follow we will make use of elementary control functions to construct our control solutions for the problems introduced in Chap. 3. These control functions will be referred to as control primitives and will be the subject of this chapter. In particular, we will review consensus controllers for single integrators in \(\mathbb {R}^2\) and rotational integrators in \(\mathsf {SO}(2)\) as they are required to develop control solutions for kinematic unicycles. The control solutions for flying robots will instead make use of consensus controllers for double integrators in \(\mathbb {R}^3\) and rotating rigid bodies in \(\mathsf {SO}(3)\).
©2019 IEEE. Reprinted, with permission, from (Roza et al., 2019). Reused text from Sects. 4.1.1 and 4.3.2.
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Notes
- 1.
If \(x=\sigma (s)\) is an arc length parametrization of \(\mathcal {C}\), then we define the unit vector tangent to \(\mathcal {C}\) by \(\bar{r}(x)=\bar{r}(\sigma (s)) = (d/ds)\sigma (s)\).
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Roza, A., Maggiore, M., Scardovi, L. (2022). Control Primitives. In: Distributed Coordination Theory for Robot Teams. Lecture Notes in Control and Information Sciences, vol 490. Springer, Cham. https://doi.org/10.1007/978-3-030-96087-2_4
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DOI: https://doi.org/10.1007/978-3-030-96087-2_4
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