Last week, with the help of the Optragen/SNOPT optimization framework, we designed a joint trajectory to accomplish a single phase of a quasi-static walking gait. With one foot serving as our reference/stance frame (ie. we assumed this stance foot laid flush with the ground and remained static w.r.t. the world), we defined a trajectory for the other foot frame to rise off the ground, swing forward and step back down onto the ground. Simultaneously, the CoM of the biped was restricted to remain within its support polygon. Now, you will implement and demo this gait on your actual biped robots.

1. Implement the trajectory defining the single-leg phase of your gait on the biped robot.

Submit a demonstration (either live or via video recording) of your biped robot executing this phase of your gait.

Note(s):

1. While the trajectory is being executed, you may have to pin the stance foot of the robot to the ground/table using your hand. Try to pin the stance foot such that it can tip forward/backward but NOT laterally (ie. side-to-side). Remember that your models of the biped are planar; CoM constraints guard against forward-backward tipping only and that is what you want to verify. In the near future, you will demo your full gaits on a circular, planar boom that will constrain against laterally motion for you.

2. When defining your optimization problem (Optragen/SNOPT), most of you left the time horizon normalized, 'hl = 1.0'. This is perfectly fine. However, when you transition this to the actual biped, you may not want it to complete in only 1 second (if we take the units of 'hl' to be seconds). In this case, you will just have to scale your trajectory over a longer time period. If your trajectory is 100 points long, instead of each waypoint-to-waypoint duration being $\frac{1}{100} = 10$ ms long, you can multiply this by, for example, 3, so that your entire trajectory is now 3 seconds long. In other words, just stretch your generated trajectory over a longer period of time.

3. Something else you may want to keep in mind is that the Dynamixel AX-12A motor max. speed is 59 rpm. However, if your gaits take on the order of multiple seconds to execute, it's highly unlikely you'll hit velocity saturation.