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Robot Kinematics and Joint Space Trajectory Planning

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Damian T. Gordon
Damian T. Gordon
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The Robot System Control System Sensors Kinematics Dynamics Task Planning Software Hardware Mechanical Design Actuators
Robot Kinematics. ,[object Object],[object Object],[object Object],[object Object]
Co-ordinate Frames z y x Right-handed Co-ordinate frame x Base Frame x Tool Frame x Goal Frame x Link Frame x Camera Frame
Kinematic Relationship ,[object Object],[object Object],z y x z y x
Homogeneous Transformations  x  y 3  1 Translation  z 1 Global Scale r1 r2 r3 r4 r5 r6 r7 r8 r9 3  3 Rotational Matrix 0 0 0 1  3 Perspective
Kinematic Considerations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Inverse Kinematics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Multiple Solutions Goal ,[object Object],[object Object],[object Object]
Non Existence of Solution ,[object Object],[object Object],[object Object],Goal
Kinematics  Control ,[object Object],Cartesian Space Joint Space Actuator Space Kinematics Dynamics Control z y x
Joint Space Trajectories ,[object Object],[object Object],[object Object]
Joint Space Trajectory Planning Consider a robot with only one link. A B (  0 , t 0 ) (  f , t f ) ,[object Object],[object Object],[object Object]
Joint Space Schemes. ,[object Object],angle  f time 0 t f  0 Lots of choices for continuous functions Cubic Polynomial Splines
Cubic Polynomials ,[object Object],A starts at rest and at angle   B finishes at rest and at angle  f A cubic polynomial has four co-efficients which satisfy the four constraints:
An Exercise for you: ,[object Object]
An exercise for us ,[object Object]
Making A Spline. ,[object Object],angle time A B Via points t via1 t via2
More Joint Space Schemes ,[object Object],[object Object],[object Object],[object Object]
Kinematics  Control ,[object Object],Cartesian Space Joint Space Actuator Space Kinematics Dynamics Control z y x

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Robot Kinematics and Joint Space Trajectory Planning

  • 1. The Robot System Control System Sensors Kinematics Dynamics Task Planning Software Hardware Mechanical Design Actuators
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  • 5. Homogeneous Transformations  x  y 3  1 Translation  z 1 Global Scale r1 r2 r3 r4 r5 r6 r7 r8 r9 3  3 Rotational Matrix 0 0 0 1  3 Perspective
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