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Topics in Trajectory Generation for Robots

Ghazaei, Mahdi LU (2015)
Abstract
A fundamental problem in robotics is generating the motion for a task. How to translate a task to motion or a series of movements is a non-trivial problem. The complexity of the task, the structure of the robot, and the desired performance determine the sequence of movements, the path, and the course of motion as a function of time, namely the trajectory. As we discuss in this thesis, a trajectory can be acquired from a human demonstration or generated by carefully designing an objective function. In the first approach, we examine a number of robotic setups which are suitable for human demonstration. More notably, admittance control as a new dimension to the robot-assisted teleoperation is investigated. We also describe a free-floating... (More)
A fundamental problem in robotics is generating the motion for a task. How to translate a task to motion or a series of movements is a non-trivial problem. The complexity of the task, the structure of the robot, and the desired performance determine the sequence of movements, the path, and the course of motion as a function of time, namely the trajectory. As we discuss in this thesis, a trajectory can be acquired from a human demonstration or generated by carefully designing an objective function. In the first approach, we examine a number of robotic setups which are suitable for human demonstration. More notably, admittance control as a new dimension to the robot-assisted teleoperation is investigated. We also describe a free-floating behavior which makes robust lead-through programming possible. As a way to utilize these setups, we present some ideas for developing a high-level language for an event-based programming common to assembly tasks.



Since immediate reaction to variations in the target state and/or robot state is desirable, we reformulate the trajectory generation problem as a controller design problem. Using the Hamilton-Jacobi-Bellman equation, we derive a closed-loop solution to the fixed-time trajectory-generation problem with a minimum-jerk cost functional. We show that the resulting trajectory coincides with a fifth-order polynomial function of time that instantaneously updates due to changes in the reference signal and/or the robot states.



A short comparison is made between kinematic and dynamic models for generating optimal trajectories. The conclusion is that given conservative kinematic constraints, both models behave in a similar way. Having this in mind, we derive an analytic solution to the problem of fixed-time trajectory generation with a quadratic cost function under velocity and acceleration constraints. The advantage of the analytic solution compared to an on-line optimization approach lies in the efficiency of the computation.



To extend the idea of closed-loop trajectory generation, we adapt the Model Predictive Control (MPC) framework. MPC is traditionally applied to tracking problems, i.e., when there is an explicit reference signal. Thus, it is a common practice to have a separate layer that generates the reference signal. We propose an integrated approach by introducing a final state constraint in the formulation. Additionally, we give the interpretation that the difference between tracking and point-to-point trajectory-planning problems is in the density of the specified desired reference signal. We utilize a strategy to reduce the discretization time successively. This way, we respect the real-time constraints for computation time while the accuracy of the solution is gradually improved as the deadline approaches. We have verified our proposed MPC approach to trajectory generation in a ball-catching experiment. (Less)
Please use this url to cite or link to this publication:
author
supervisor
organization
publishing date
type
Thesis
publication status
published
subject
pages
120 pages
publisher
Department of Automatic Control, Lund Institute of Technology, Lund University
project
LCCC
PRACE
language
English
LU publication?
yes
id
34df53b3-d949-4a76-b23d-786a98d05052 (old id 5148838)
date added to LUP
2015-03-06 09:32:09
date last changed
2016-09-19 08:44:49
@misc{34df53b3-d949-4a76-b23d-786a98d05052,
  abstract     = {A fundamental problem in robotics is generating the motion for a task. How to translate a task to motion or a series of movements is a non-trivial problem. The complexity of the task, the structure of the robot, and the desired performance determine the sequence of movements, the path, and the course of motion as a function of time, namely the trajectory. As we discuss in this thesis, a trajectory can be acquired from a human demonstration or generated by carefully designing an objective function. In the first approach, we examine a number of robotic setups which are suitable for human demonstration. More notably, admittance control as a new dimension to the robot-assisted teleoperation is investigated. We also describe a free-floating behavior which makes robust lead-through programming possible. As a way to utilize these setups, we present some ideas for developing a high-level language for an event-based programming common to assembly tasks.<br/><br>
<br/><br>
Since immediate reaction to variations in the target state and/or robot state is desirable, we reformulate the trajectory generation problem as a controller design problem. Using the Hamilton-Jacobi-Bellman equation, we derive a closed-loop solution to the fixed-time trajectory-generation problem with a minimum-jerk cost functional. We show that the resulting trajectory coincides with a fifth-order polynomial function of time that instantaneously updates due to changes in the reference signal and/or the robot states. <br/><br>
<br/><br>
A short comparison is made between kinematic and dynamic models for generating optimal trajectories. The conclusion is that given conservative kinematic constraints, both models behave in a similar way. Having this in mind, we derive an analytic solution to the problem of fixed-time trajectory generation with a quadratic cost function under velocity and acceleration constraints. The advantage of the analytic solution compared to an on-line optimization approach lies in the efficiency of the computation. <br/><br>
<br/><br>
To extend the idea of closed-loop trajectory generation, we adapt the Model Predictive Control (MPC) framework. MPC is traditionally applied to tracking problems, i.e., when there is an explicit reference signal. Thus, it is a common practice to have a separate layer that generates the reference signal. We propose an integrated approach by introducing a final state constraint in the formulation. Additionally, we give the interpretation that the difference between tracking and point-to-point trajectory-planning problems is in the density of the specified desired reference signal. We utilize a strategy to reduce the discretization time successively. This way, we respect the real-time constraints for computation time while the accuracy of the solution is gradually improved as the deadline approaches. We have verified our proposed MPC approach to trajectory generation in a ball-catching experiment.},
  author       = {Ghazaei, Mahdi},
  language     = {eng},
  note         = {Licentiate Thesis},
  pages        = {120},
  publisher    = {Department of Automatic Control, Lund Institute of Technology, Lund University},
  title        = {Topics in Trajectory Generation for Robots},
  year         = {2015},
}