Foot CoM reach specified x_translation in minimum time
Posted: Wed Mar 21, 2018 7:42 am
Dear Professors Umberger and Lee,
Thanks for creating this Project, it has enabled me to further develop my understanding of optimal control theory and the programming requirements necessary for solving an optimal control problem.
I have currently managed to adapt the example Matlab scripts for use with the LowerLimb.osim model (e.g. specified equality constraints for the final time, 0.75 s, of the three q's (hip, knee and ankle angles)). My next objective is to determine the optimal states (x) and controls (u, excitations) required for the foot CoM to reach a specified x_translation in the minimum time possible.
All the examples I have currently been following use a fixed final time (0.75 s in the example problem), with the states and controls discretized at 25 nodes (0.03125 s intervals). However, in the next problem that I am trying to solve (reach specified x_translation in the minimum time possible) the final time is able to change, and according to my reading the final time should be added to the controls vector. This latter part is what I am having difficulties with, and I am struggling to get my head around it. I was therefore wondering whether you had any suggestions/reading materials that I could possibly turn too for assistance? I am certain that it will involve discretizing the states and controls to 25 nodes, but the time interval between each of these nodes will be dependent on the optimal final time.
Kind regards,
Nicos Haralabidis
PhD Student
University of Bath
Thanks for creating this Project, it has enabled me to further develop my understanding of optimal control theory and the programming requirements necessary for solving an optimal control problem.
I have currently managed to adapt the example Matlab scripts for use with the LowerLimb.osim model (e.g. specified equality constraints for the final time, 0.75 s, of the three q's (hip, knee and ankle angles)). My next objective is to determine the optimal states (x) and controls (u, excitations) required for the foot CoM to reach a specified x_translation in the minimum time possible.
All the examples I have currently been following use a fixed final time (0.75 s in the example problem), with the states and controls discretized at 25 nodes (0.03125 s intervals). However, in the next problem that I am trying to solve (reach specified x_translation in the minimum time possible) the final time is able to change, and according to my reading the final time should be added to the controls vector. This latter part is what I am having difficulties with, and I am struggling to get my head around it. I was therefore wondering whether you had any suggestions/reading materials that I could possibly turn too for assistance? I am certain that it will involve discretizing the states and controls to 25 nodes, but the time interval between each of these nodes will be dependent on the optimal final time.
Kind regards,
Nicos Haralabidis
PhD Student
University of Bath