Topics in Trajectory Generation for Robots
(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 nontrivial 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 robotassisted teleoperation is investigated. We also describe a freefloating... (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 nontrivial 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 robotassisted teleoperation is investigated. We also describe a freefloating behavior which makes robust leadthrough programming possible. As a way to utilize these setups, we present some ideas for developing a highlevel language for an eventbased 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 HamiltonJacobiBellman equation, we derive a closedloop solution to the fixedtime trajectorygeneration problem with a minimumjerk cost functional. We show that the resulting trajectory coincides with a fifthorder 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 fixedtime trajectory generation with a quadratic cost function under velocity and acceleration constraints. The advantage of the analytic solution compared to an online optimization approach lies in the efficiency of the computation.
To extend the idea of closedloop 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 pointtopoint trajectoryplanning 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 realtime 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 ballcatching experiment. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/5148838
 author
 Ghazaei, Mahdi ^{LU}
 supervisor

 Rolf Johansson ^{LU}
 Anders Robertsson ^{LU}
 Jacek Malec ^{LU}
 organization
 publishing date
 2015
 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
 34df53b3d9494a76b23d786a98d05052 (old id 5148838)
 date added to LUP
 20150306 09:32:09
 date last changed
 20180302 09:43:27
@misc{34df53b3d9494a76b23d786a98d05052, 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 nontrivial 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 robotassisted teleoperation is investigated. We also describe a freefloating behavior which makes robust leadthrough programming possible. As a way to utilize these setups, we present some ideas for developing a highlevel language for an eventbased 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 HamiltonJacobiBellman equation, we derive a closedloop solution to the fixedtime trajectorygeneration problem with a minimumjerk cost functional. We show that the resulting trajectory coincides with a fifthorder 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 fixedtime trajectory generation with a quadratic cost function under velocity and acceleration constraints. The advantage of the analytic solution compared to an online optimization approach lies in the efficiency of the computation. <br/><br> <br/><br> To extend the idea of closedloop 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 pointtopoint trajectoryplanning 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 realtime 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 ballcatching 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}, }