Trajectory Planning

1. Trajectory Planning

TRAJECTORY PLANNING
Lecture 10
Irob 2305 Introduction to Robotics

2. Introduction

INTRODUCTION
• Path and trajectory planning means the way that a robot is moved from one
location to another in a controlled manner.
• The sequence of movements for a controlled movement between the motion
segment, in straight-line motion or in sequential motions.
• It requires the use of both kinematics and dynamics of robots.
Sequential robot movements: path and trajectory

3. Problem Formulation

PROBLEM FORMULATION
The problem of motion planning can be stated
as follows. Given:
A start pose of the robot
A desired goal pose
A geometric description of the robot
A geometric description of the world
Find a path that moves the robot gradually from
start to goal while never touching any obstacle

4. Problem Formulation

PROBLEM FORMULATION

5. Path and Trajectory

PATH AND TRAJECTORY
Trajectory
Path
• It’s a way of getting from A to B
• A set of points that links A to B
• Says nothing about the speed at which we
progress along the path
There is no notion of time
• A path and a schedule for getting from A
to B
there is a notion of a time or speed

6. Path planning

PATH PLANNING
The main path planning tasks for a robot are as follows:
• grasping and releasing objects
• moving from place to place
• following previously specified paths
• following moving objects
• working with other manipulators
• exerting forces (i.e. pushing, pulling and holding)
• exerting torques
• collecting data
• using tools

7. Path planning

PATH PLANNING
o The process of computing a sequence of position, velocities and accelerations
o A trajectory is a description of the robot motion through space
o Trajectory planning is the task of associating time with the path
o The path positions may be described in several ways, for example joint
coordinates
o A trajectory planner is highly specific to the path plan
o Once time has been associated with positions, the velocities and accelerations
may be found

8. Motion planning: Path and Trajectory

MOTION PLANNING: PATH AND TRAJECTORY
Tasks
Path
A set of points that links a start and a goal
(pose only).
Task Planning
Path Planning
Trajectory Planning
Control
Trajectory
Scheduled motion to follow, including time
information (pose, speed, and acceleration)

9. Trajectory classification

TRAJECTORY CLASSIFIC ATION

10.

Trajectory planning
Cartesian (task space) scheme
- The motion between the two points is
known at all times and controllable.
- It is easy to visualize the trajectory, but
is is difficult to ensure that singularity
Joint-space scheme
- The description of the motion to be
made by the robot by its joint values.
- The motion between the two points is
unpredictable.

11. Joint space and task space trajectory

JOINT SPACE AND TASK SPACE TRAJECTORY
Task space
Trajectory interpolated in task space
Inverse kinematics solved every time step
Joint space
Inverse kinematics solved only at waypoints
Joint positions interpolated in between

12. Joint space and task space trajectory

JOINT SPACE AND TASK SPACE TRAJECTORY
Task Space
Joint Space
Pros.
• Motion is predictable
(interpolation in the task space)
• Better handling of obstacles and
collisions
• Faster execution (IK at waypoints
only)
• Actuator motion is smooth and
easier to validate
Cons.
• Slower execution (IK every time
step)
• Actuator motion is not necessarily
smooth and more difficult to
validate
• Intermediate points not guaranteed
to respect joints limits or be
collision-free

13. JOINT-SPACE VS. CARTESIAN-SPACE DESCRIPTIONS

JOINT-SPACE VS. C ARTESIAN-SPACE
DESCRIPTIONS

14. Trajectory Planning

TRAJECTORY PLANNING

15. Some typical trajectories

SOME TYPIC AL TRAJECTORIES
Point to point
straight lines
Interpolation
curves

16. Video segment

VIDEO SEGMENT
https://www.youtube.com/watch?v=popvnHUu3uU