# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Time-Optimal Control by Iterating Forward and Backward in Time

(2014)
Department of Automatic Control
Abstract
When costumers look for a robot for their factory two things are important. The robot should be as efficient as possible, but still be cheap. In order to make the robot efficient the robot-controller has to know the dynamics of the robot and its limits. Based on these it can then generate a time-optimal plan (trajectory) for each movement. The standard way of generating a time-optimal trajectory with the exact dynamics and limits is very computationally heavy. Today most approaches do the planning based on the hardest limits on each axis of the robot. These values are then used even though the current limits might allow the robot to move faster. This means that the full capacity of the robot will not be utilized and because of this the... (More)
When costumers look for a robot for their factory two things are important. The robot should be as efficient as possible, but still be cheap. In order to make the robot efficient the robot-controller has to know the dynamics of the robot and its limits. Based on these it can then generate a time-optimal plan (trajectory) for each movement. The standard way of generating a time-optimal trajectory with the exact dynamics and limits is very computationally heavy. Today most approaches do the planning based on the hardest limits on each axis of the robot. These values are then used even though the current limits might allow the robot to move faster. This means that the full capacity of the robot will not be utilized and because of this the efficiency is lowered.

In this thesis a different method for generating time-optimal trajectories is tested. The approach is based on iterating forward and backward in time and finding the point where the two paths meet. This approach has the advantage of that it is based on simulating the system. Therefore more complex dynamics can be included in the planning by just calculating a value instead of complicating the optimization problem. Another benefit is that robot manufacturers usually create simulation models of new robots already. This means that very little extra effort would be needed to create the trajectory generator using this approach and this reduces development costs.

Four different approaches for patching together the forward and backward paths are discussed in the thesis. The different techniques are tested on a simplified model of one servo axis of a robot and compared against a known time optimal solution for the simplified model. One of the techniques shows very good results and generates trajectories that are time-optimal. (Less)
author
supervisor
organization
year
type
H3 - Professional qualifications (4 Years - )
subject
other publication id
ISRN LUTFD2/TFRT--5944--SE
language
English
month=nov
id
4778579
2014-11-17 09:49:46
date last changed
2014-12-05 09:55:27
```@misc{4778579,
abstract     = {When costumers look for a robot for their factory two things are important. The robot should be as efficient as possible, but still be cheap. In order to make the robot efficient the robot-controller has to know the dynamics of the robot and its limits. Based on these it can then generate a time-optimal plan (trajectory) for each movement. The standard way of generating a time-optimal trajectory with the exact dynamics and limits is very computationally heavy. Today most approaches do the planning based on the hardest limits on each axis of the robot. These values are then used even though the current limits might allow the robot to move faster. This means that the full capacity of the robot will not be utilized and because of this the efficiency is lowered.

In this thesis a different method for generating time-optimal trajectories is tested. The approach is based on iterating forward and backward in time and finding the point where the two paths meet. This approach has the advantage of that it is based on simulating the system. Therefore more complex dynamics can be included in the planning by just calculating a value instead of complicating the optimization problem. Another benefit is that robot manufacturers usually create simulation models of new robots already. This means that very little extra effort would be needed to create the trajectory generator using this approach and this reduces development costs.

Four different approaches for patching together the forward and backward paths are discussed in the thesis. The different techniques are tested on a simplified model of one servo axis of a robot and compared against a known time optimal solution for the simplified model. One of the techniques shows very good results and generates trajectories that are time-optimal.},