# SIMple BIpedal CONtroller

Body Positions

Body Torque Gains

Feedback Gain

Swing Time

Gaits
Controls

# Details

SIMBICON is a framework for producing bipedal gaits. The biped follows a finite state machine so that it tries to arrive at the proposed orientations for each state through Proportional Derivative Controllers. Above, State 0 is where the agent starts from. States 1-4 can be modified to produce different style gaits. Proportional Derivative Controllers produce torques on bodies in order to reach a desired orientation. Torques are computed as:

$\tau = k_p (\theta_d - \theta) - k_d \dot \theta$

$\theta_d$ is the desired orientation of the body. $\theta$ is the current orientation, and $\dot \theta$ is the angular velocity of the body. $k_d$ is just $k_p/10$ which is controlled by the torque gain sliders for each body segment. You can control $k_p$ Through the use of the gain sliders. The last component is the feedback component. This modifies the swing hip angle depending on the distance from the hip to the stance ankle as well as the linear velocity of the hip. The stance ankle is shown with a light blue circle. The hip is shown in a pink circle. The relationship is as follows:

$\theta_d = \theta_{d0} + c_d d + c_v v$

where $\theta_d$ is the new target angle, $\theta_{d0}$ is the old angle, $d$ is the distance between the stance and the hip, and $v$ is the linear velocity of the hip. The gain $c_v$ is just $c_d$ which is controlled by the feedback slider. Since there are 2 symmetric cycles (right and left), it is possible to have different gain values for each cycle.

The swing time is the time allowed for the swing hip to arrive during States 1 and 3. After that time is reached, the swing foot tries to make contact with the ground by swinging backwards in States 2 and 4. Once it has made contact, the biped moves on to the next state. After state 4, the biped cycles through the states again until it falls.

The physics simulation is stepping at 1700 Hz.