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PR 502: Robot Dynamics & Control
Action Plan Path Plan Trajectory Plan Controller Robot Sensor
Trajectory Planning
Motion Planning: Path planning Geometric path Issues: obstacle avoidance, shortest path Trajectory planning, interpolate or approximate interpolate approximate the desired path by a class of polynomial functions and generates a sequence of timetimebased control set points for the points control of manipulator from the initial configuration to its destination.
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Tasks Task Plan
Robot Trajectory Planning
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Trajectory Planning
Kinematics and Dynamics :
Where the end effector is going to be What are the joint variables must be What is the velocity of the motion What are the forces at the joints
Trajectory Planning
Goals
Coordinate the trajectories of two robot manipulators so as to avoid collisions and deadlock. deadlock. Minimize total execution time
Trajectory Planning
The way the robot is moved from one location to another in controlled manner
Definitions
Path Curve in Coordinate space Trajectory Time history of positions along a path
Sequence of movements that must be made create a controlled motion
Note : Trajectory planning needs both Kinematics and Kinetics
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Joint v. Cartesian Space
Joint space description
Description of motion to be made by the robot by its joint variables The motion between the two point is unpredictable
Trajectory Planning
Trajectory planning of a 2 DOF robot arm
(x , y)
Cartesian space description
A description of sequence of movements that a robot makes Advantages : Easy to visualize
Disadvantages : Computationally extensive, require fast processing processing
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Cartesian Space Trajectory Planning
Possibility 1 : Straight line path between the point A and B Method : Draw a line and divide into segments Solve for the angles for each segment Cartesian space representation Interpolation between the point A and B However, joint angles are not uniformly changed.
Cartesian Space Trajectory Planning
More segments High accuracy Problem : Actuators should be strong enough to provide large forces necessary to accelerate and decelerate the joint as needed. Solution : Smaller segments at the beginning and in the end.
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Cartesian Space Trajectory Planning
Possibility 2 : Not a straight line but a different curve
Ex : a quadratic equation
Joint space trajectory planning
Possibility 1: both joints are at maximum speed Result : segments of the movement are not similar to each other
Path is irregular Need to solve inverse kinematics equations
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Joint space trajectory planning
Possibility 2 : Normalized joint motion
Normalized by a common factor such that the joint with smaller motion will move proportionally slower and both joints will start and stop their motion simultaneously
Joint space trajectory planning
Possibility 3: motion planning with controlled characteristics.
Polynomials of different orders Linear functions Parabolic blends
Characteristics
Both joints are at different speeds Move continuously together
Result : segments of the movement are similar to each other
Path is still irregular Need to solve Inverse Kinematics equations Joint space representation
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Polynomial trajectory planning
Known : initial location : Orientation of the robot Solve Inverse Kinematics equations and calculate the final joint angles
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Joint space trajectory planning
Joint space trajectory planning
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Joint space trajectory planning
Joint space trajectory planning
Problem : Acceleration cannot be defined with a 3rd order polynomial Solution : Use a 5th order polynomial.
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Joint space trajectory planning
Joint space trajectory planning
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Joint space trajectory planning
Linear segments with parabolic blends Objective :
Joint space trajectory planning
Problem : At the beginning and the in the end acceleration must be infinite in order to maintain a constant velocity. Solution : Linear segments are blended with parabolic sections.
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To run the joint at constant speed between two points Linear function :
Velocity is constant Acceleration is zero
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Joint space trajectory planning
Joint space trajectory planning
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Joint space trajectory planning
Joint space trajectory planning
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Joint space trajectory planning
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Joint space trajectory planning
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