Trajectory
Week 8
Learning Outcomes
• By the end of week 8 session, students
will trajectory of industrial robots.
Course Outline
• Trajectory.
• Initial, via and final points.
• Interpretation of trajectory.
Trajectory
• Refers to a time history of position,
velocity, and acceleration for each degree
of freedom, i.e. how do we move joints
with respect to time (joint coordinates).
• As cartesian coordinate (x,y,z) is a more
desirable information from user’s
perspective, inverse kinematics process is
required prior to developing trajectories.
Robot Motion
θ3
Z
tf
t0
θ2
tf
Y
t
Joint coordinates
t0
X
Cartesian coordinates
t0
tf
t
tf
t
θ1
t0 = t initial
tf = t final
t0
Trajectory Planner
Path & Kinematics Constraints
Cartesian Path
Trajectory
Generator
Dynamics Constraint
q (t ), q (t ), q(t )
Trajectory
(joint coordinates)
Joint Coordinate Algorithm
t  t0
loop : increment of t by t (time interval)
t  t  t
find h(t ) ; joint position at time t
if t  t f , then stop
end of loop
where h(t )  trajector y function in joint space
Cartesian Coordinate
Algorithm
t  t0
loop : increment of t by t (time interval)
t  t  t
find H (t ) ; cartesian position at time t
h(t )  InvK H (t )  ; joint position
if t  t f , then stop
end of loop
where H(t )  trajector y function in Cartesian space.
Steps in Robot Motion
Tasks
Task Plan
Action Plan
Path Plan
Trajectory
Plan
Controller
Robot
• Path planning
• Cartesian path
• Issues: obstacle avoidance, shortest
path
• Trajectory planning,
• “interpolate” or “approximate” the
desired path by a class of
polynomial functions and generates
a sequence of time-based “control
set points” for the control of
manipulator from the initial
configuration to its destination.
Sensor
Ref. City College of New York.