Motivation

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

Stanford Test Track

• A tool is needed for trajectory generation,
  allowing for fast, simple iteration and effective
  control of trajectory.

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
Overall Procedure
Matlab Preprocessor

• Initial Trajectory Inputs
• Possible Input Methods
• Beta Based Input
• Time Based Input

Output to Test Track or RiSE
4
Test Track 3D Trajectory
b Arc length along 2-D trajectory f - Wing
Angle y Crank Angle
Climbing direction
Lifted from wall
Touching wall
Wing Angle
y
Crank Angle
b0
Toe Position
5
y (Crank Angle) Vs b (arc length on Foot
trajectory)
Foot trajectory
Moving forward
y (02p)
b (0 1)
Mapping between y and b
y
b
.
.
b
y
t
t
6
Defining phases based on b
Swing
engagement
disengagement
.
stroke
swing
b
f
Engagement
Disengagement
b 0.4
f
Stroke
b 0.85
Climbing direction
b
7
Input Method 1 (Beta Based)
b Arc length along 2-D trajectory f - Wing
Angle y Crank Angle
.

• User specified b(db/dt) vs b and f vs b
• 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 (b) and wing angle (f) at a
  specific toe position (b)
• Disadvantage Difficult to define input values at
  a specific time (t)

.
8
Input Method 2 (Time Based)
b Arc length along 2-D trajectory f - Wing
Angle y Crank Angle

• User specified b vs t and f vs t
• 4 phases - quintic splines (matched end
  conditions)
• Advantages
• Exact Trajectory with explicit constraints on
  maximum b and b
• Control over accelerations in task coordinates
• Disadvantage
• Difficult to define parameters at a specific toe
  position (b)

.
.
.
9
Mapping Procedure of Current System(library of
Matlab functions)
b Arc length along 2-D trajectory f - Wing
Angle y Crank Angle

• Configuration File
• User Inputs
• Link lengths
• Gear ratios of differential

Initial Inputs
Test Track Output
RiSE Output
10
Summary
b Arc length along 2-D trajectory f Wing
Angle y Crank Angle q1 Rotation angle of
Motor 1 q2 Rotation angle of Motor 2

• Matlab preprocessor
• Allows for testing different leg trajectories to
  find better trajectory for climbing
• Input b(db/dt) vs b and f vs b
• Mapping Method
• Fourier Curve Fit
• Inverse Kinematics
• Interpolation
• Output
• Test Track input y vs t and f vs t
• RiSE input q1 vs t and q2 vs t

.