Abstract
This paper presents a framework of path following via set stabilization for mobile manipulator systems. The mobile manipulator is modelled as a single redundant dynamic system. The mobile base considered belongs to a large class of wheeled ground vehicles, including those with nonholonomic constraints. Kinematic redundancies are resolved by designing a controller that solves a suitably defined constrained quadratic optimization problem, which can be easily tuned by the designer to achieve various desired poses. By employing partial feedback linearization, the proposed path following controller has a clear physical meaning. The desired path to be followed is a spline in the output space of the system. The controller simultaneously controls the manipulator and mobile base. The result is a unified path following controller without any trajectory planning performed on the mobile base. The approach is experimentally verified on a 4-degree-of-freedom (4-DOF) manipulator mounted on a differential drive mobile platform.
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Notes
- 1.
The results of this paper do not rely on the assumption that the state space be Euclidean. One could replace \(\mathbb R^N\) by a smooth Riemannian manifold. Nonetheless, we assume \(x\in \mathbb R^N\) to avoid unnecessarily cumbersome notation.
- 2.
Invariance: if for some time \(t=0\) the state x(0) is appropriately initialized with \(y=H(x(0)) \in \mathscr {P}\), then \((\forall t \ge 0) \; H(x(t)) \in \mathscr {P}\). Attractiveness: for initial conditions x(0) such that the output H(x(0)) is in a neighbourhood of the desired path \(\mathscr {P}\), \(H(x(t)) \rightarrow \mathscr {P}\) as \(t \rightarrow \infty \).
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Gill, R., Kulić, D., Nielsen, C. (2018). Path Following for Mobile Manipulators. In: Bicchi, A., Burgard, W. (eds) Robotics Research. Springer Proceedings in Advanced Robotics, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-60916-4_30
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