Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Optimal Control of Sensor-Induced Illusions on Robotic Agents

Lorenzo Medici, Steven M. LaValle, Basak Sakcak

TL;DR

The paper addresses manipulating a robotic receiver’s perceived location to achieve a producer-defined goal using sensor-level illusion control. It formalizes the interaction with intrinsic and extrinsic models, information states, and plausibility/illusion notions, enabling the application of standard control tools. A constructive solution leverages a bijection between receiver I-states and tower intensities, proving controllability and designing a producer policy through a discrete-time Riccati framework; the approach extends to advanced receivers with disturbances via receding-horizon quadratic programming. Numerical results for simple and advanced receivers validate convergence to the producer’s target while maintaining plausible receiver states, highlighting trade-offs between speed and plausibility under disturbances.

Abstract

This paper presents a novel problem of creating and regulating localization and navigation illusions considering two agents: a receiver and a producer. A receiver is moving on a plane localizing itself using the intensity of signals from three known towers observed at its position. Based on this position estimate, it follows a simple policy to reach its goal. The key idea is that a producer alters the signal intensities to alter the position estimate of the receiver while ensuring it reaches a different destination with the belief that it reached its goal. We provide a precise mathematical formulation of this problem and show that it allows standard techniques from control theory to be applied to generate localization and navigation illusions that result in a desired receiver behavior.

Optimal Control of Sensor-Induced Illusions on Robotic Agents

TL;DR

The paper addresses manipulating a robotic receiver’s perceived location to achieve a producer-defined goal using sensor-level illusion control. It formalizes the interaction with intrinsic and extrinsic models, information states, and plausibility/illusion notions, enabling the application of standard control tools. A constructive solution leverages a bijection between receiver I-states and tower intensities, proving controllability and designing a producer policy through a discrete-time Riccati framework; the approach extends to advanced receivers with disturbances via receding-horizon quadratic programming. Numerical results for simple and advanced receivers validate convergence to the producer’s target while maintaining plausible receiver states, highlighting trade-offs between speed and plausibility under disturbances.

Abstract

This paper presents a novel problem of creating and regulating localization and navigation illusions considering two agents: a receiver and a producer. A receiver is moving on a plane localizing itself using the intensity of signals from three known towers observed at its position. Based on this position estimate, it follows a simple policy to reach its goal. The key idea is that a producer alters the signal intensities to alter the position estimate of the receiver while ensuring it reaches a different destination with the belief that it reached its goal. We provide a precise mathematical formulation of this problem and show that it allows standard techniques from control theory to be applied to generate localization and navigation illusions that result in a desired receiver behavior.

Paper Structure

This paper contains 14 sections, 2 theorems, 23 equations, 4 figures, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Related work
  3. Preliminary Definitions
  4. Agents in a universe
  5. Producer and receiver agents
  6. Defining plausibility and illusions
  7. Optimal Control of Sensor-Induced Illusions
  8. Problem Description
  9. Proposed Solution
  10. Extending to advanced receivers
  11. Numerical Results
  12. A simple receiver
  13. An advanced receiver
  14. CONCLUSION

Key Result

Proposition 1

The preimage of $y^r_k$ under $h^r$ is a singleton if and only if $r_k^{(i)} \leq s_{c}^{(i)}$ for all $i=1,2,3$ and the intersection of the three circles centered at $t^{(i)}$ with radius $d_i = \sqrt{{s_c^{(i)}}/{r_k^{(i)}}-1}$ for $i=1,2,3$ is not empty. Otherwise, it is the empty set.

Figures (4)

  • Figure 1: Localization illusions. (a) A receiver is placed at $\omega^r_k$ and the signal intensity is set to $s^{(i)}$ at the source for towers at $t^{(i)}$ for $i=1,2,3$. Considering the model of signal transmission with the signal intensity at source as $s_c$, the measured intensity at receiver position results in erroneous position estimate (intersection of red dashed circles). (b) Models of signal intensity as a function of distance from tower position (source). Blue line is the receiver model. Changing the signal intensity to different values leads to the perceived distance to the tower be different than the actual distance (see the intersection of the black line with the actual model and the receiver model).
  • Figure 2: Producer and receiver agents coupled to the same universe.
  • Figure 3: Simulation results considering a simple receiver. (Left) Trajectories corresponding to receiver position $w^r_k$ (blue) and receiver I-state ${\iota}_k^r$ (orange). (Right) Producer actions $u^p_k = [u^p_{k,1} \: u^p_{k,2}]^T$ as a function of stages.
  • Figure 4: Simulation results considering an advanced receiver. (Left) Trajectories corresponding to receiver position $w^r_k$ (blue) and receiver I-state ${\iota}_k^r$ (orange). (Right) Producer actions $u^p_k = [u^p_{k,1} \: u^p_{k,2}]^T$ as a function of stages.

Theorems & Definitions (12)

  • Definition 1: Intrinsic model
  • Definition 2: Agent
  • Definition 3: Extrinsic model
  • Definition 4: Receiver
  • Definition 5: Producer
  • Definition 6: Correspondence
  • Definition 7: Plausibility
  • Definition 8: Reality
  • Definition 9: Illusion
  • Proposition 1
  • ...and 2 more