Ensuring Tolerances for Trajectory Tracking of Non-Holonomic Robots under Disturbance and Measurement Delay
Controls and Robotics Seminar Series
Frank Lawless
April 1st, 2022
Robotics and Controls Seminar
1
4/01/2022
COAR LAB
Trajectory Planning for Robotic Systems
Applications
Robotics and Controls Seminar
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E. Masehian and N. Mohamadnejad, "Path planning of nonholonomic flying robots using a new virtual obstacle method"
Overview
Robotics and Controls Seminar
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Trajectory Tracking for Mobile Robots
Robotics and Controls Seminar
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Reference Trajectory
Robot Trajectory
Robot Trajectory
Previous Works
Robotics and Controls Seminar
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K. Shojaei, A. M. Shahri, A. Tarakameh, and B. Tabibian, “Adaptive trajectory tracking control of a differential drive wheeled mobile robot,” 2011
Plamen Petrov and Ivan Kralov, “A Look-ahead approach to mobile robot path tracking based on distance-only measurements,” 2019
R. L. S. Sousa, M. D. do Nascimento Forte, F. G. Nogueira and B. C. Torrico, "Trajectory tracking control of a nonholonomic mobile robot with differential drive," 2016
Adaptive Feedback Linearization
Look-ahead Feedback Linearization
Feedforward Control
Compensate for parametric uncertainty
The Problem
-Develop a controller such that the tracking error E(t) converges to zero. �-Develop a controller to track any human provided reference trajectory.
-Maximum error
-Maximum velocities
-Develop a controller such that E(t) converges non-exponentially
-E(t) converges in a linear manner at high error and exponentially after a user defined threshold
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Robotics and Controls Seminar
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Control
Control II
Control I
Exponential
Non-
Exponential
Differential Drive Robots
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Centroid Dynamics
Base-point Dynamics
Controller I Design
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Proposed state-feedback controller
Reference Vs. Robot Trajectory
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D = 1
D = 10
Control I Velocity Bounds
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-Maximum Linear and Angular Velocities
Control I Velocity Bounds
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Bounded velocities
Simulation Results of Control I
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Reference Trajectory
Control II Design
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Proposed High Error controller
Control I
Control II
Through Lyapunov analysis
Control II Velocity Bounds
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Bounded velocities
Transition Model
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Control II
Control I
Control
m = 1
m = .1
Simulation Results of Control I&II
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Control I
Control I&II
Introducing noise
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Two main ways for noise to be introduced into the system:
-Error tolerance must be decided by user
-High noise might result in the robot to veer off the reference trajectory causing operational and safety concerns
Delay
Robotics and Controls Seminar
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Estimated heading angle
When current position cannot be determined the heading angle must be estimated.
Bounded heading angle error
Estimated heading angle error
Initial heading angle
Inaccurate guess
Better guess
Finding the error in heading angle
Lyapunov Stability for control I
Lyapunov function
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Prove E(t) converges to zero with noise and delay
Lyapunov Stability for control I
Lyapunov function
Through Young’s inequality we can bound our relationship
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To guarantee E(t) to converge to zero
Prove E(t) converges to zero with noise and delay
Error Bounds
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Error with high noise
Error with low noise
Bounded error with noise
Noise and Delay Simulation Results
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Conclusion and Future Works
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Thank you�Q&A
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