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An adaptive optimal control approach to monocular depth observability maximization

Tochukwu Elijah Ogri, Muzaffar Qureshi, Zachary I. Bell, Kristy Waters, Rushikesh Kamalapurkar

Abstract

This paper presents an integral concurrent learning (ICL)-based observer for a monocular camera to accurately estimate the Euclidean distance to features on a stationary object, under the restriction that state information is unavailable. Using distance estimates, an infinite horizon optimal regulation problem is solved, which aims to regulate the camera to a goal location while maximizing feature observability. Lyapunov-based stability analysis is used to guarantee exponential convergence of depth estimates and input-to-state stability of the goal location relative to the camera. The effectiveness of the proposed approach is verified in simulation, and a table illustrating improved observability is provided.

An adaptive optimal control approach to monocular depth observability maximization

Abstract

This paper presents an integral concurrent learning (ICL)-based observer for a monocular camera to accurately estimate the Euclidean distance to features on a stationary object, under the restriction that state information is unavailable. Using distance estimates, an infinite horizon optimal regulation problem is solved, which aims to regulate the camera to a goal location while maximizing feature observability. Lyapunov-based stability analysis is used to guarantee exponential convergence of depth estimates and input-to-state stability of the goal location relative to the camera. The effectiveness of the proposed approach is verified in simulation, and a table illustrating improved observability is provided.
Paper Structure (10 sections, 2 theorems, 25 equations, 6 figures, 1 table)

This paper contains 10 sections, 2 theorems, 25 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Camera Motion Model
  3. ICL-Based Observer Design
  4. Design of feature observability maximizing Velocity
  5. Stability Analysis
  6. Analysis of Camera ICL Observer Error system
  7. Analysis of position error system
  8. Simulation Study
  9. Results
  10. Conclusion

Key Result

Theorem 1

Provided Assumptions ass:trackableFeatures-ass:sufficientExcitation hold, the update laws defined in eq:d1H, eq:d2H, and eq:d3H ensure that the origin of the observer error system is globally exponentially stable and the trajectories of the estimation errors $\tilde{\vartheta}(\cdot)$ converge expon

Figures (6)

  • Figure 1: Camera tracking four planar features on an object while moving from $\mathscr{C}$ to $\mathscr{G}$.
  • Figure 2: Trajectory of the distance error of the features of the object relative to the camera.
  • Figure 3: Trajectory of the distance error of the features of the object relative to the goal.
  • Figure 4: Trajectory of the distance error of the goal relative to the camera.
  • Figure 5: The trajectories of the actual goal position relative to the camera expressed in $\mathscr{W}$.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Remark 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof