Even though we try to generate a COM trajectory which keeps the ZMP within the support polygon the ZMP can still exit the support polygon due to differences between the actual robot and the LIPM model which we use to generate our trajectory as well as unexpected disturbances.
Therefore to prevent the robot’s feet from tipping over and the robot from falling, ZMP stabilization is required. What this means is that the feet torques will be modified to prevent the ZMP from leaving the support polygon.
One naive way to do this is to use a simple PD (Proportional Derivative) controller to make the ZMP follow a predefined path. However the performance of this method depends on the gains of the PD controller, too high and the robot will not be able to follow its given COM trajectory when a large disturbance(such as a push) is applied, too low and the feet can still tip over. In fact in my ICM2011 paper I have shown that this method leads to reduced COM tracking performance, reduced force rejection ability, increased complexity because two trajectories (COM and ZMP) are needed instead of one and lastly it cant prevent sliding or twisting of the foot, only tipping can be prevented.
A better way to perform ZMP stabilization is to use a sort of magnitude filter for the joint torques[1,2] which limits the joint torques to such a value that the ZMP can move close to the edge of the support region but not beyond it. I will try to explain more about this topic in the future. Please check the page about my masters research and my masters thesis for more details.
Here is a block diagram of the torque filter with a position controller.
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- Kirill Van Heerden and Atsuo Kawamura, “Maintaining floor-foot contact of a biped robot by force constrained position control”, Mechatronics, ICM . Proceedings of the IEEE International Conference on, Istanbul, Turkey, 2011
- Kirill Van Heerden and Atsuo Kawamura, “An investigation on robust biped walking using compliant force control and a online walking pattern generator.” Industrial Electronics, IECON . Proceedings of the IEEE International Conference on, page 1453-1458, Phoenix, USA, 2010.