What is Optimal Preview Control:

• Optimal preview control is yet another methodology that can be used for generating walking trajectories for humanoid walking.

• In this method we predetermine the ZMP trajectories that we want the robot follow, which will in-turn determine the walking gait, and these set of trajectories is used as an input to a system that is modeled to give out the COM trajectories.

• We then determine the rest of the joint trajectories based of the COM trajectories.

Why we need Optimal Preview Control:

The cycloid based walking algorithm seemed to work very well but then why need yet another type.

• In the cycloid based walking algorithm there was a big constraint, the step frequency must always be equal to the natural frequency of the Robot(the pendulum model of the Robot).

• This means when ever we need to take a step we need it to do so at only that particularly rate, if the rate of step changes then the robot goes to instability.

• And obviously a robot in its daily routine will need to step at different frequencies, this is where the optimal preview controller helps.

• The ZMP trajectories that we define is what is determining the step frequency and the complete walking gait.

• By defining a ZMP trajectory that ensures robot's stability, the joint trajectories can be easily generated.

How the Optimal Preview Controller Works:

• The Humanoid robot is modeled as a cart on a table model, where the height of the table is the height of the COM from the ground.

• The movement of the Cart defines the movement of the COM . Such a model is defined for movement of the COM along the sagittal and coronal planes.

• As the Cart moves along the table the resultant ZMP moves along the foot of the table, If the ZMP goes outside the foot of the table cart is gonna trip over.

• This setup is modeled as a system such that given a set of ZMP trajectories it calculates the COM trajectories.

• When determining the COM trajectories it previews the future inputs, which allows it to respond to step changes in the trajectories.

Different plots of trajectories was generated for the Darwin-OP is shown below:

The COM Trajectories generated using the reference ZMP

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'Left Ankle and Hip trajectories generated for the generated COM trajectory'

Left Ankle and Hiptrajectories generated for the generated COM trajectory

Left Leg joint trajectories generated based of the COM trajectory

Right Leg joint trajectories generated based of the COM trajectory

The Optimal Preview paper that I used to understand Optimal Preview Controller