Guideline for Trajectory Planning

[Sibsoon]

Hi I am very uncertain how exactly the trajectory planning should behave. Since there is no exact description but I expect to be graded by some sorts of test I would appreciate some clarification.

I read in another thread that if there are no velocities but only a turning speed the robodog should turn in place. I assume that when a forward velocity and a turning speed is defined the robodog should walk a circle, yet I am not entirely sure if this is right. This brings up the question why we have a sideways velocity? Is our robot able to move sideways then? If only a sideways velocity and a turning speed is defined, is the robodog supposed to walk a sideways circle or does he "slides"(or walks) sidewas while turning (doing a pirouette).

The assignment slides and the recording unfortunately don't clarify this either. thx

[eastskykang]

Hi,

We want the robot base(body)'s center of mass follows the velocity command. Here the velocity command is a vector [v_f, v_s, w] where v_f is forward speed of base (in m/s), v_s is sideways speed of base (in m/s), and finally w (in rad/s) is turning rate of the base.

Note that v_f, v_s are horizontal velocity of the robot in its local frame. If the robot's heading toward certain direction, the forward speed is the speed of the base toward that direction

A trajectory according 0.7 m/s forward speed when the robot's heading angle is non-zero.

Of course, our dogbot can move sideways too (the system is holonomic!). In fact, it can move toward any horizontal direction unlike a car where of the motion is constrained to its heading.

Finally, the turning rate is yaw rate of the robot. It is a entity defined in global frame. Thus, for the velocity command [0, 0, w], the center of the mass of the base should stay in the same position while the heading angle of the base changes over time.

The motion according to 0.4 rad/s turning rate

Here are reference trajectory for [v_f=0.2, v_s=0, w=-0.3] and [v_f=0, v_s=0.2, w=-0.3] for your info.

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Here're some hints for trajectory planning.

Let's compute the global position and heading angle of the robot at timestep i+1 given the position and heading angle at i. This will be i+1th knot of a reference trajectory. i = 0 is the current timestep.

Let's start from the heading angle. The heading angle of the robot at timestep i+1 can be expressed as the following:

θⁱ⁺¹ = θⁱ + wh

where h is a size of timestep. So from i=0, you can start numerical integration for computing θ for every timestep over the trajectory's time-horizon.

For global position of the base, don't forget to consider the heading of the robot. You have to convert v_f, v_s into global frame entities. Then, you can integrate it for global position as we did for the heading angle. I hope this helps.

[Sibsoon]

thank you very much.

[kaikai23]

Hi Dongho, thank you for the test cases!

My robot bahaves correctly in your above settings, but when the forward speed gets higher (e.g., 2m/s), the dog's legs become unrealistic, as shown in the picture.

Should I fix this problem or is it fine to just have it like this?

[eastskykang]

@kaikai23 could you create a separated issue thread?