Abstract
The implementation of SMC-based techniques in Chap. 2 strictly required the uncertainties in the system to be bounded [1, 2]. However, considering these state-dependent uncertainties to be bounded can be regarded as a conservative assumption for practical scenarios. Furthermore, these approaches depend upon the viscous friction model to compute the nominal friction forces which is essential for determining the control effort. For situations where this analytical friction model doesn’t hold, tracking accuracy would eventually be further compromised. Hence, to relax such assumptions and circumvent the dependence on the friction model, an artificial-delay-based methodology has been proposed in this chapter to solve the tracking problem for a planar snake robot. Time-Delayed Control (TDC) is a robust control method applied to solve the trajectory tracking problem for systems with model as well as parametric uncertainties and disturbances without assuming them to be bounded, utilizing input and output measurements from a delayed time. The implementation of TDC is based on the assumption that the uncertainties should vary slowly over time. As practical snake robots are known to travel slowly through their surroundings, the uncertainty in the ground condition or the frictional forces, do evolve at a slow rate making TDC a natural and fitting choice to accomplish satisfactory tracking performance for a snake robot.
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Notes
- 1.
The solutions of system \(\dot{\mathbf {x}} = \mathbf {f}(\mathbf {x},t)\) remain Uniformly Ultimately Bounded with ultimate bound b [15], if \(\exists ~a,~b,~c,~T \in \mathbb {R}^{+}\) such that for \(0< a < c\) and \(\left\Vert \mathbf {x}(0)\right\Vert \le a\), \(\left\Vert \mathbf {x}(t)\right\Vert \le b~\forall ~t \ge T\).
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Mukherjee, J., Kar, I.N., Mukherjee, S. (2021). Time-Delayed Control for Planar Snake Robots. In: Adaptive Robust Control for Planar Snake Robots. Studies in Systems, Decision and Control, vol 363. Springer, Cham. https://doi.org/10.1007/978-3-030-71460-4_3
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