4 research outputs found
Unsafe Point Avoidance in Linear State Feedback
International audienceWe propose a hybrid solution for the stabilization of the origin of a linear time-invariant stabilizable system with the property that a suitable neighborhood of a pre-defined unsafe point in the state space is avoided by the closed-loop solutions. Hybrid tools are motivated by the fact that the task at hand cannot be solved with continuous feedback, whereas the proposed hybrid solution induces nominal and robust asymptotic stability of the origin. More specifically, we formulate a semiglobal version of the problem at hand and describe a fully constructive approach under the assumption that the unsafe point to be avoided does not belong to the equilibrium subspace induced by the control input on the linear dynamics. The approach is illustrated on a numerical exampl
A Hybrid Controller for Obstacle Avoidance in an n-dimensional Euclidean Space
For a vehicle moving in an -dimensional Euclidean space, we present a
construction of a hybrid feedback that guarantees both global asymptotic
stabilization of a reference position and avoidance of an obstacle
corresponding to a bounded spherical region. The proposed hybrid control
algorithm switches between two modes of operation: stabilization
(motion-to-goal) and avoidance (boundary-following). The geometric construction
of the flow and jump sets of the hybrid controller, exploiting a hysteresis
region, guarantees robust switching (chattering-free) between the stabilization
and avoidance modes. Simulation results illustrate the performance of the
proposed hybrid control approach for a 3-dimensional scenario.Comment: 8 pages, 3 figures, conferenc
Obstacle Avoidance via Hybrid Feedback
In this paper we present a hybrid feedback approach to solve the navigation
problem of a point mass in the n-dimensional space containing an arbitrary
number of ellipsoidal shape obstacles. The proposed hybrid control algorithm
guarantees both global asymptotic stabilization to a reference and avoidance of
the obstacles. The intuitive idea of the proposed hybrid feedback is to switch
between two modes of control: stabilization and avoidance. The geometric
construction of the flow and jump sets of the proposed hybrid controller,
exploiting hysteresis regions, guarantees Zeno-free switching between the
stabilization and the avoidance modes. Simulation results illustrate the
performance of the proposed hybrid control approach for 2-dimensional and
3-dimensional scenarios