Trajectory Generation

Question 1

What is the purpose of tragectory generation?

Answer 1

computing the required path of the tool frame into a set of joint motions.
Cartesian trajectory generation

Question 2

What are 2 types of spatial constraints?

Answer 2

Via points:
used to define intermediate points between the inital and final pose
Path points:
set of all via points, inital and final point

Question 3

How is a smooth function defined?

Answer 3

A desirable motion that is a continuous function with a continuous first derivative

Question 4

Define a joint-space scheme

Answer 4

Define joint variables as functions of time
-all path points converted to joint angles
-a smooth function
-time required for each segment must be the same

Question 5

How do we make a smooth motion?

Answer 5

There are at least 4 constraints on ø(t)
constraints on intital and final values
ø(0) = ø0
ø(tf) = øf
constraints on velocity being continuous
ø_dot (0) = 0
ø_dot(tf) = 0

Question 6

How are trajectory constraints satisfied?

Answer 6

If we have 4 constraints, a cubic polynomial with four coeffcients is used

Question 7

What are the difference in constraints between a path with via points and a trajectory path without?

Answer 7

With via points, the velocity constraints between the two points are non-zero
ø_dot(0) = ø_dot_initial
ø_dot(tf) = ø_dot_final

without via points, the velocity constraints are 0 at initial and final

Question 8

How can via points be specified?

Answer 8

1. The user specifies the desired velocity at each via point
2. System automatically chooses by using a heuristic
3. The system automatically chooses the velocities so that acceleration at the via points is continuous

Question 9

How does a simple heuristic work?

Answer 9

Define the connections between via points as straight lines
If the slope of the lines change sign, choose zero velocity for that point
If the slope does not change sign, choose average between the 2 slopes