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

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

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

Test Track 3D Trajectory

Crank Angle

Wing Angle

Toe Position

Touchingwall

Lifted from wall

=0

– Arc length along 2-D trajectory - Wing Angle – Crank Angle

Climbing direction

5

(Crank Angle) Vs (arc length on Foot trajectory)

(0 ~ 1)

t t

.

.

Moving forward

Foot trajectory

Mapping between and

6

Defining phases based on

**

**

Stroke

Disengagement

Swing

~0.85

~0.4

Engagement

Climbing direction

stroke

engagement disengagement

swing

.

7

Input Method 1 (Beta Based)User specified ddt) 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

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

Mapping Procedure of Current System(library of Matlab functions)

– Arc length along 2-D trajectory - Wing Angle – Crank Angle

Initial Inputs Test Track Output RiSE Output

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

10

Summary

• Matlab preprocessor– Allows for testing different leg trajectories to find better trajectory

for climbing

• Input: ddt) 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

.