Tutorial: Gait and Trajectory Optimization for Legged Robots

Paper, video, open-source code, slides and more:
www.awinkler.me
Intro:
00:29 - Why Legged Robots?
01:15 - Context of Robot Motion Planning
05:09 - Integrated Motion Planning
Main:
09:15 - Optimization Variables (Base, Feet, Forces)
09:54 - Dynamic Constraint (Single Rigid Body Dynamics)
11:41 - Kinematic Constraint (Range-of-Motion Box)
13:05 - Gait Optimization without Integer Programming
16:37 - Phase-based End-Effector Parameterization
19:56 - Terrain Constraints
Results:
32:01 - Video of generated Motions ( • Gait and Trajectory Op... )
26:14 - Summary
27:57 - Open-source Software (github.com/awinkler)
Publication:
"Gait and Trajectory Optimization for Legged Systems
through Phase-based End-Effector Parameterization",
Alexander. W. Winkler, Dario Bellicoso, Marco Hutter, Jonas Buchli,
Robotics and Automation Letters (RA-L), 2018.
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This research has been funded by the Swiss National Center of Competence in Research Robotics (NCCR Robotics) and is also part of ANYmal Research, a community to advance legged robotics.
Icons from: www.behance.net/gallery/22478...

[@haodongzheng7045]

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.

[@chaubyzou8143]

Great work! It is very helpful for me to understand these optimization based trajectory planning approaches for legged robots.

[@TheRaspberryPiGuy]

Really high quality video - great stuff!

[@sashu1998]

Excellent Work, first ROS package I've had that just works out of the box

[@alexanderwinkler6821]

That is how we roll!😎

[@brycenarcisomercines5036]

This is such a great video, Thanks so much for making this! :)

[@397522042]

Great work!

[@MonteLogic]

fulfills all constraints* Good and brilliant presentation.

[@gabrielduarte4152]

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.

[@MdelaRE1]

An excelent work!!! :D

[@jamesnayak5391]

excellent!!!

[@omarsilva924]

Impressive!!

[@samuelclay9663]

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

[@prakrutkotecha5868]

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!!

[@hobycedric6279]

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

[@noorahamedgadamphalli8197]

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.

[@hubble-02]

Hi, great work :) I wanted to ask something in your Trajectory optimization formulation. Is the number of knot points per phase constant or variable?

[@alexanderwinkler6821]

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.

[@hubble-02]

@@alexanderwinkler6821 Thank you very much 🙏

[@jstm]

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

[@alexanderwinkler6821]

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.

[@Build_the_Future]

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.