When the yaw angle exceeds 90° the robot cannot maintain balance states in Simscape

I used simscape to simulate，modeling and control of a wheeled biped robot. I used LQR to calculate the torque for the robot to maintain balance states. I used a lot of balls to simulate the contact between the tire and the ground. Everything is ok when the yaw angle of the robot is less than 90 degree.

• here is yaw 0 dgree

• here is yaw 60 dgree

when the yaw angle is greater than 90 degree, can't maintain balance.

• here is yaw 90 dgree

• here is yaw 180 dgree

when I change the positive and negative sign of the both hub torque at 180 degree yaw angle , everything return to normal as the same as the 0 degree.

• here is yaw 180 dgree but change the positive and negative sign of the both hub torque

What's happaning? Is it because of the spatial contact force？

[Aquatris]

it might be there is a transformation error in your control logic. If you manually change the torque signs at 180 degree, everything works, indicating there might be a missing yaw rate transformation in your logic.

[Tan Shuwen is pig]

no,I don't think so. The robot is symmetry,the states of the robot at 0 and 180 degree should be same.

[Sam Chak]

Aquatris deduced what happened based on your description, and cannot rule out that instability issue is caused by human error in the coding of rotation matrix or transformation between Euler angle and quaternion in the LQR based computed torque.

[Sam Chak]

Hi @Tan Shuwen

One aspect that intrigues me is why the two-wheeled robot tumbled violently when there was no external torque acting on it other than the balancing torques from the wheels. One possible explanation is that an incorrect rotation sequence was used, causing the robot to experience a singularity at a yaw angle of 90° and a large torque output.

Note: Admin may regard your username of choice as a potentially disrespectful remark.

Answer 1

[Tan Shuwen is pig]

@Sam Chak @Aquatris Hi, thanks for your response. Yes, all of it is caused by singlarity at a yaw angle of 90°. I just use a stupid way to fix it,

if(yaw<-90 | yaw>90)

T = -T % T is the hub torque

end

Although there may be some instability and oscillation when yaw angle passing through 90 °, balance can be maintained.