[Paper Review] Temporal changes in stimulus perception improve bio-inspired source seeking

Alejandro Pequeño-Zurro, Danish Shaikh+1 more|arXiv (Cornell University)|Mar 25, 2019

Insect Pheromone Research and ControlAgricultural and Biological Sciences21 references3 citations

TL;DR

This paper proposes a bio-inspired source-seeking controller for Braitenberg vehicle 3a that incorporates the temporal derivative of the stimulus into velocity control, resolving a circular dependency between motion and perception. Theoretical and simulation results show that including stimulus dynamics improves convergence speed, trajectory stability, and reduces oscillations compared to the standard model.

ABSTRACT

Braitenberg vehicles are well known qualitative models of sensor driven animal source seeking (biological taxes) that locally navigate a stimulus function. These models ultimately depend on the perceived stimulus values, while there is biological evidence that animals also use the temporal changes in the stimulus as information source for taxis behaviour. The time evolution of the stimulus values depends on the agent's (animal or robot) velocity, while simultaneously the velocity is typically the variable to control. This circular dependency appears, for instance, when using optical flow to control the motion of a robot, and it is solved by fixing the forward speed while controlling only the steering rate. This paper presents a new mathematical model of a bio-inspired source seeking controller that includes the rate of change of the stimulus in the velocity control mechanism. The above mentioned circular dependency results in a closed-loop model represented by a set of differential-algebraic equations (DAEs), which can be converted to non-linear ordinary differential equations (ODEs) under some assumptions. Theoretical results of the model analysis show that including a term dependent on the temporal evolution of the stimulus improves the behaviour of the closed-loop system compared to simply using the stimulus values. We illustrate the theoretical results through a set of simulations.

Motivation & Objective

• To address the circular dependency between robot velocity and perceived stimulus changes in bio-inspired navigation.
• To model and analyze a new velocity-based control mechanism that uses the time derivative of the stimulus for improved source seeking.
• To demonstrate that including temporal stimulus dynamics enhances convergence speed and trajectory stability over standard Braitenberg 3a.
• To provide a theoretical foundation for controllers relying on motion-dependent sensory inputs such as optical flow or event cameras.

Proposed method

• Formal modeling of a dynamic Braitenberg vehicle using differential-algebraic equations (DAEs) that capture the interdependence between motion and stimulus perception.
• Conversion of the DAE system into non-linear ordinary differential equations (ODEs) under specific assumptions to enable analytical stability analysis.
• Incorporation of the stimulus time derivative into the forward velocity control law, modulating speed based on the gradient of the stimulus and its rate of change.
• Linearization of the system around a straight-line trajectory to analyze local stability and eigenvalue behavior.
• Use of simulations with varying initial conditions to compare trajectory performance between standard and dynamic Braitenberg controllers.
• Application of band-pass filtering principles to address noise sensitivity in real-world implementations, though not fully modeled in the current work.

Experimental results

Research questions

• RQ1 How does including the time derivative of the stimulus in the control law affect the convergence speed and stability of a Braitenberg vehicle?
• RQ2 What is the impact of stimulus dynamics on trajectory shape and oscillation amplitude near the optimal path?
• RQ3 How does the forward speed vary when the vehicle points away from the source in the dynamic model compared to the standard model?
• RQ4 Can the circular dependency between motion and perception be analytically resolved using a simplified closed-loop model?
• RQ5 What are the implications of this controller for robotics systems using motion-dependent sensors like event cameras or optical flow?

Key findings

• The dynamic controller with stimulus derivative inclusion achieves faster convergence to the source compared to the standard Braitenberg 3a, as shown in simulations with initial pose x = -6, y = 0.
• Trajectories of the dynamic model exhibit reduced oscillation amplitudes and shorter path lengths, especially when starting near the linearized trajectory (x = -6, y = 1).
• The real part of the eigenvalues for the linearized system becomes more negative with the dynamic controller, indicating faster convergence to the straight-line solution.
• When pointing directly away from the source, the dynamic controller reduces forward speed, promoting sharper turns and improved path efficiency, as demonstrated in the x = -2, y = 1, θ = arctan(-1/2) simulation.
• The imaginary part of the eigenvalues is smaller in the dynamic model, suggesting reduced oscillatory behavior around the reference trajectory.
• Theoretical analysis confirms that the inclusion of stimulus dynamics enhances system stability and performance, even under the assumption of high signal-to-noise ratio.