1. 1 Motivation We wish to test different trajectories on the Stanford Test Track in order to gain insight into the effects of different trajectory parameters on climbing effectiveness, such as: –Foot velocity at impact –Detachment strategies –Velocity & acceleration during pull stroke A tool is needed for trajectory generation, allowing for fast, simple iteration and effective control of trajectory. Stanford Test Track

2. 2 Requirements Provide a mechanism for user to specify a trajectory in an intuitive way. Provide visual feedback of actual 3-D trajectory. Using inverse kinematics, generate the necessary outputs to run this trajectory on hardware. –Stanford Test Track (motors controlling crank and wing angle) –RiSE platform (motors feeding into differential)

3. 3 Overall Procedure Initial Trajectory Inputs Possible Input Methods: 1.Beta Based Input 2.Time Based Input Matlab Preprocessor Output to Test Track or RiSE Visual Feedback of Actual 3D Trajectory

4. 4 Test Track 3D Trajectory Crank Angle Wing Angle Toe Position Touching wall Lifted from wall  =0  – Arc length along 2-D trajectory  - Wing Angle  – Crank Angle Climbing direction 

5. 5  (Crank Angle) Vs  (arc length on Foot trajectory)  (0 ~ 1)   t t . .   Moving forward Foot trajectory Mapping between  and 

6. 6 Defining phases based on  * * * * Stroke Disengagement Swing   ~0.85  ~0.4 Engagement Climbing direction stroke engagementdisengagement swing .  

7. 7 Input Method 1 (Beta Based) User specified  d  dt) vs  and  vs  Current system we are using Specify desired number and location of input points Approximate functions using Fourier Series Advantage: Intuitive way of specifying point velocity (  ) and wing angle (  ) at a specific toe position (  ) Disadvantage: Difficult to define input values at a specific time (t)  – Arc length along 2-D trajectory  - Wing Angle  – Crank Angle.. Foot Contact:  Foot Detachment:  Foot Contact Foot Detachment

8. 8 Input Method 2 (Time Based) User specified  vs t and  vs t 4 phases - quintic splines (matched end conditions) Advantages: Exact Trajectory with explicit constraints on maximum  and  Control over accelerations in task coordinates Disadvantage: Difficult to define parameters at a specific toe position (  )...  – Arc length along 2-D trajectory  - Wing Angle  – Crank Angle

9. 9 Mapping Procedure of Current System ( library of Matlab functions )  – Arc length along 2-D trajectory  - Wing Angle  – Crank Angle Initial Inputs Test Track OutputRiSE Output Configuration File User Inputs Link lengths Gear ratios of differential

10. 10 Summary Matlab preprocessor –Allows for testing different leg trajectories to find better trajectory for climbing Input:  d  dt) vs  and  vs  Mapping Method –Fourier Curve Fit –Inverse Kinematics –Interpolation Output –Test Track input:  vs t and  vs t –RiSE input:  1 vs t and  2 vs t  – Arc length along 2-D trajectory  – Wing Angle  – Crank Angle   – Rotation angle of Motor 1  2 – Rotation angle of Motor 2.