Fascinating work! My senior thesis was about least-energy path planning for serial manipulators using direct collocation with nonlinear programming(DCNLP). Glad to watch your tutorials, it’s illuminating.
Thank you very much for your work and for spreading it. I learned a lot from him, and I will try to apply what I learned in my master's degree. Thank you very much.
It took me a few views to fully understand what's going on here. This is neat stuff. I suppose since the solver generates several possible gaits, a cost function could be used as a "selector" for which one to use depending on if we want to optimize speed, battery usage, etc. I suppose the only drawback to this method is that the number of steps to take must be specified at the beginning even though that could be tricky to guess in real-time
very inspiring! By the way, i have a question about dynamic modelling of quadruped robot using lagrangian. In my case, i consider it as a multi rigid body. Here is my question: while computing the legs dynamic model, specially the mass matrix of inertia, should i express the jacobian of the leg with respect to the global frame or with respect to its own reference frame (used for DH parameters)? thanks for answering
Hi, great work I had a question about the continuous phase durations The part I am confused about is how did you pass the phase duration as a parameter to be optimized during the program cause according to the dynamics the step time should not be directly related. If you could explain a bit more about the phase duration part it would be great!!
Where do you solve this optimization problem? Is there a computer on the robot or do you send the data to some other super computer. I was curious because optimization problems require significant amount of computational power and decision here needs to be as quick as possible.
For Gait Optimization, how is the number of swing and stance phase for each leg selected? The length of each phase is continuous but it seems that the number of phases must be selected
Yes, absolutely, that number is fixed in advanced. It can for instance be based on the total duration of the trajectory. A higher number of steps allows more gaits to be generated, but also introduces more variables, thereby making the solving slower. So it's a trade-off.
Thanks! There are different splines for foot position, foot force and base position. How many polynomials you use for each of these per phase is variable, but 1-3 is often enough.
![[Tutorial] Optimization, Optimal Control, Trajectory Optimization, and Splines](/img/1.gif)
Fascinating work! My senior thesis was about least-energy path planning for serial manipulators using direct collocation with nonlinear programming(DCNLP). Glad to watch your tutorials, it’s illuminating.
Excellent Work, first ROS package I've had that just works out of the box
That is how we roll!😎
Great work! It is very helpful for me to understand these optimization based trajectory planning approaches for legged robots.
Really high quality video - great stuff!
fulfills all constraints*
Good and brilliant presentation.
Thank you very much for your work and for spreading it.
I learned a lot from him, and I will try to apply what I learned in my master's degree.
Thank you very much.
This is such a great video, Thanks so much for making this! :)
It took me a few views to fully understand what's going on here. This is neat stuff. I suppose since the solver generates several possible gaits, a cost function could be used as a "selector" for which one to use depending on if we want to optimize speed, battery usage, etc. I suppose the only drawback to this method is that the number of steps to take must be specified at the beginning even though that could be tricky to guess in real-time
Great work!
An excelent work!!! :D
Impressive!!
excellent!!!
very inspiring! By the way, i have a question about dynamic modelling of quadruped robot using lagrangian. In my case, i consider it as a multi rigid body. Here is my question: while computing the legs dynamic model, specially the mass matrix of inertia, should i express the jacobian of the leg with respect to the global frame or with respect to its own reference frame (used for DH parameters)? thanks for answering
Hi, great work
I had a question about the continuous phase durations
The part I am confused about is how did you pass the phase duration as a parameter to be optimized during the program cause according to the dynamics the step time should not be directly related. If you could explain a bit more about the phase duration part it would be great!!
Where do you solve this optimization problem? Is there a computer on the robot or do you send the data to some other super computer. I was curious because optimization problems require significant amount of computational power and decision here needs to be as quick as possible.
For Gait Optimization, how is the number of swing and stance phase for each leg selected? The length of each phase is continuous but it seems that the number of phases must be selected
Yes, absolutely, that number is fixed in advanced. It can for instance be based on the total duration of the trajectory. A higher number of steps allows more gaits to be generated, but also introduces more variables, thereby making the solving slower. So it's a trade-off.
Hi, great work :)
I wanted to ask something in your Trajectory optimization formulation.
Is the number of knot points per phase constant or variable?
Thanks! There are different splines for foot position, foot force and base position. How many polynomials you use for each of these per phase is variable, but 1-3 is often enough.
@@alexanderwinkler6821 Thank you very much 🙏
I wish I saw this before I build my 2 legged robots. You can check it out on my channel if you are interested. Let me know what you think thanks.