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====== ZMP based Cycloid walking algorithm for Darwin-OP ======

This Tutorial assumes you have some background in ZMP walking algorithms. 

**A quick recap of what is ZMP:**
  * ZMP or Zero Moment Point is the point on the humanoid robot's foot where the moment due to the forces and moments acting on the robot is neutralized. 
  * This ZMP(the zero moment POINT) must always lie within the in the robots's support polygon for the robot to keep balance. 

The concept of cycloid walking was used to impliment ZMP walking.

**Cycloid Walking:** 
  * This concept basically says that the robot can be modeled as an inverted pendulum with the length of the pendulum being the height of the COM of the robot from the ground. If the natural frequency of this pendulum is used as the frequency of the robot walk the robot will maintin stablity. 
 
  * For the Darwin-OP in sitting position the COM is at a height of 208.12mm from the ground. 
  * The natural frequency of the robot was found out to be 1.092Hz. 
  * Thus the time period of the robot's steps are .9156sec.

The next step in making the Darwin-Op walk is to generate trajectories for the motion of the COM and the ankle. To generate this Matlab was used. 

**Walking Specs Used:**

  * Full Step Length : 25 mm
  * Step Height : 35mm
  * Step Time : 0.9156 sec (time for two steps,i.e. the period of walk)
  * Single support time period : 75% of Time period.
  * Double support time period : 25% of Time period.

**A plot of these trajectories is shown in the pic below.**

{{dylanw:Darwin_OP_walking_Trajectories.jpg}}\\ 

These trajectories are then used to generate the trajectory points for each leg joint that will make the robot walk. This was done using Inverse kinematics for the Darwin-OP. This plot is shown in the pic below.

**Joint angle trajectory for each leg separately**

{{dylanw:Darwin_OP_left_joit_Positions.jpg}}\\ 



{{dylanw:Darwin_OP_right_joit_Positions.jpg}}\\ 


===== Other Pages =====

  * [[drexel_darwin_sim|Darwin-OP Simulation on Webots and DRC-Sim(Gazebo)]]

  * [[drexel_darwin_walking_webots|Darwin-OP Walking Simulation on Webots]]

  * [[drexel_darwin_walking_gazebo|Darwin-OP Walking Simulation on DRC-Sim(Gazebo)]]