Abstract
The generation of motion for robots obeys classically to a two-step paradigm. The first step is the planning, where the typical problem is to find a geometric path that allows the robot to reach the desired configuration starting from the current position while ensuring obstacle avoidance and enforcing the satisfaction of kinematic constraints. Motion planning lays its grounding on the decidability properties of this classic geometrical problem. Moreover, the traditional approaches that are used to find solutions rely on the global probabilistic certainty of the convergence of path construction stochastically sampled in the configuration-space. The second step of motion generation is the control, where the robot has to perform the planned motion while ensuring the respect of dynamical constraints. Motion control seeks primarily for local controllability or at least the stability of the motion. The basic instances of this problems have long been tackled using local state-space control. However, the typical nonlinearity of the dynamics, together with the non controllability of its linearization, lead more and more solutions to resort to model predictive control. These methods make it possible to predict the outcome of a control strategy in a future horizon and to improve it accordingly, commonly by using numerical optimizations which take into account the safety constraints and efficiency intents. However, since few years, the improvement of computational capabilities and numerical algorithms allows more and more to deal with complex dynamical systems and for longer horizons. This allows then these approaches to untighten the local nature of their applications and progressively start wider explorations of their reachable space. This evolution brings us to the question of the rising overlap between planning and control. Today, most planning problems would take too much time to be solved online with numerical approaches. Does that imply that the generation of motion will theoretically never be free of the necessity of a prior planning? Or on the contrary, is planning only a numerical issue?
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Notes
- 1.
Sometimes it is called also model preview control, but this latter designation seems restrained to linear systems.
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Benallegue, M., Laumond , JP., Mansard, N. (2017). Robot Motion Planning and Control: Is It More than a Technological Problem?. In: Laumond, JP., Mansard, N., Lasserre, JB. (eds) Geometric and Numerical Foundations of Movements . Springer Tracts in Advanced Robotics, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-51547-2_1
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