Joint Torques and Velocities in a 3-mass Linear Inverted Pendulum Model of Bipedal Gait

Recovery of a Humanoid Robot from a Destabilising Impact

“…The second challenge that needs to be overcome is the lateral motion of the robot required to lift the leg. Bugmann's [2] paper on the 3-MLIPM describes the lateral motion during a walking gait, where the lateral motion is at maximum velocity when both feet are on the ground, and acceleration is minimal. However, in the case of a robot suddenly reacting to an external impact the opposite is true, the robot has no velocity, and needs maximum acceleration to account for this.…”

“…Bugmann [2] expanded upon the LIPM to create a 3-Mass Linear Inverted Pendulum Model (3-MLIPM). By looking at torques created by gravity and how they relate to propulsion torques, the following formula can be found for a system of n number of joints and masses:…”

“…m3 is located at (0,0) and does not affect the dynamics of the system. [2] Using these torque equations to work out accelerations, it is possible to work out the upper-body (m 1 ) motion for a walking gait. The swinging foot (m 2 ) is assumed to have a sinusoidal motion where T is the time to complete one whole cycle of the gait:…”

“…To calculate this, the motion needs to be re-calculated considering the fact that the robot now has a swinging foot with a non-zero mass. It is assumed that the swinging foot has a sinusoidal motion, similar to equation (2). However, unlike the previous equation the new position of x 2 is not a fixed distance ahead of the previous pivot point but needs to be determined based on the impact.…”