Designing Robust Linear Output Feedback Controller based on CLF-CBF framework via Linear~Programming(LP-CLF-CBF)

TL;DR

This work considers the problem of designing output feedback controllers that use measurements from a set of landmarks to navigate through a cell-decomposable environment using duality, control Lyapunov function and control barrier function, and linear programming.

Abstract

We consider the problem of designing output feedback controllers that use measurements from a set of landmarks to navigate through a cell-decomposable environment using duality, Control Lyapunov and Barrier Functions (CLF, CBF), and Linear Programming. We propose two objectives for navigating in an environment, one to traverse the environment by making loops and one by converging to a stabilization point while smoothing the transition between consecutive cells. We test our algorithms in a simulation environment, evaluating the robustness of the approach to practical conditions, such as bearing-only measurements, and measurements acquired with a camera with a limited field of view.

Figures (4)

• Figure 1: The polygonal environment in Fig .\ref{['g1']} is decomposed to 8 convex sections Fig .\ref{['g2']}, blue arrows indicate the exit direction and green arrows indicate the inverse exit direction for each cell, the corresponding graph is shown in Fig . \ref{['g3']}
• Figure 2: a) Bearing direction measurements. Landmarks are shown by blue circles, and the robot is shown by a black circle. We assume the robot measures the bearing to landmarks directly and they are shown by blue arrows. The position of landmarks is known, and bearing direction measurements between landmarks are shown by purple, green, and orange arrows. b) As bearing measurements are unit vectors, the robot sees all the landmarks within 1 unit from itself. c) modify bearing measurements by assuming the landmark $l_2$ is fixed.
• Figure 3: Converging to a point while changing variable $\eta$. The black circle shows the starting point, while the black diamond represents the converging point. In Fig. \ref{['fig:stationary_share']}, all cells share the same landmarks shown by blue squares. In Fig. \ref{['fig:stationary_diff']}, Upper cells with orange edges use the orange landmarks, and lower cells with black edges use blue landmarks. For both cases, increasing variable $\eta$ makes the path smoother.
• Figure 4: Making loops changing variable $\eta$. The black circle shows the starting point. In Fig. \ref{['fig:o2-shared']}, all cells share the same set of landmarks which are shown by blue squares. In Fig. \ref{['fig:o2-diff']}, Upper cells with orange edges use the orange landmarks, and lower cells with black edges use blue landmarks. For both cases, increasing variable $\eta$ makes the path smoother.

Theorems & Definitions (37)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Proposition 1: HCBF, hcbf
• Proposition 2
• Definition 6
• Definition 7
• Remark 1