Optimal control principles to explain 3D eye movement Carlos - - PowerPoint PPT Presentation

Computer and Robot Vision Lab

Optimal control principles to explain 3D eye movement

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Carlos Aleluia June 2019

Computer and Robot Vision Lab

Outline

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• 1. Problem, Motivation and Approach
• 2. Models and Methods
• 3. Implementation
• 4. Experiments and Results
• 5. Conclusions and Future Work

Computer and Robot Vision Lab

Problem

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Human eye has 6 muscles (grouped in antagonistic pairs that generate 3 DOF) However, only 2 DOF are needed to fixate on a plane Purpose of the mechanisms that deal with this issue still remain unknown

Computer and Robot Vision Lab

Motivation

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Eye orientation abides certain rules (Listing’s Law) Understanding of these principles is crucial

Computer and Robot Vision Lab

Apply optimal control methods to a simulator that resembles the real robotic model, trying to obtain similar dynamic properties as the human eye Define set of cost functions and respective trade-offs under which the system behaves similarly to the human eye, which may include: i) Orientation accuracy ii) Time spent iii) Energy consumed iv) Motor effort

Approach

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Input - motor rotation (in degrees) Output - eye orientation (represented by a rotation vector)

Non-linear Model

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Dependencies are non-linear due to rotations, deadzone...

insertion points on the eye insertion points on the motor plates string/elastic force

Computer and Robot Vision Lab

It’s possible to approximate the non-linear model by a linear system, using system identification methods In our case, identified model is a discrete time-invariant state space model:

Linearization

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2nd order system in each direction: 𝑚=2𝘯

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Optimal Control

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input sequence saccade duration

accuracy cost energy cost duration cost

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Optimal Control

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Energy Cost: Proportional to motor velocity:

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Optimal Control

Duration Cost: Parameter 𝛾 has to be tuned

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Computer and Robot Vision Lab

Optimal Control

Approach 1: Planned Trajectory

Listing’s plane is implicitly defined: imposes a restriction on 𝑠x for all time

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Optimal Control

Approach 2: Fixed Final Orientation

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This approach imposes a restriction on 𝑠x only for final time

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Optimal Control

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Approach 3: Free Torsion

This approach does not impose any restriction on 𝑠x

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Non-linear Model - Simulink

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The forces and corresponding torques are computed for each iteration Output is obtained by integrating the equations of motion

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Non-linear Model - Simulink

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Experiments

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1) Study statistics on 𝑠x using output for all possible saccades, starting from straight ahead 2) Study the same statistics on 𝑠x but this time doing all saccades in sequence 3) Analyze the dependencies of saccade duration and peak velocity on saccade amplitude

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1- Saccades starting from origin

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Approach 𝞽rx (°) Planned Trajectory 0.6195 Fixed Final Orientation 0.5217 Free Torsion 1.3659

𝑦𝑨 and 𝑧𝑨 planes for fixed final orientation approach

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2- Saccades done in sequence

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𝑦𝑨 and 𝑧𝑨 planes for fixed final orientation approach

Approach 𝞽rx (°) Planned Trajectory 1.4065 Fixed Final Orientation 1.4921 Free Torsion 2.8762

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3- Dependencies on saccade amplitude

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Saccade duration is expected to increase with amplitude Peak velocity is expected to saturate

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Conclusions and Future Work

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Reasonably good results were achieved so far using the trade-off found Despite the nonlinearities, overall optimization works fine Next steps in this work: ○ attempt to reduce 𝞽rx ○ analyze feasibility of aggregation of different linear models ○ study effects of minimization of motor effort ○ test on real system (possibly even the new one being built?)

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Thank you! Questions?

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