Unique Joint Displacement Generation for Redundant Robotic Systems

1992 ◽  
Author(s):  
Y. S. Chung ◽  
M. Griffis ◽  
Joseph Duffy
Keyword(s):  
Potential Energy ◽  
Potential Energy Function ◽  
Joint Space ◽  
Torsional Stiffness ◽  
Inverse Kinematic Problem ◽  
End Effector ◽  
Serial Manipulators ◽  
Cyclic Type ◽  
Zero Potential ◽  
Joint Limits

Abstract This paper presents a novel, practical, and theoretically sound kinematic control strategy for redundant serial manipulators. This strategy yields repeatability in the joint space of a redundant serial manipulator whose end effector undergoes some general cyclic type motion. This is accomplish by defining a potential energy function that is based on springs being theoretically or conceptually located in the joints of the manipulator (torsional springs for revolute joints, translational springs for prismatic joints). Previous researchers have also minimized potential energy functions to solve the inverse kinematic problem for redundant serial manipulators. However, to the authors’ knowledge, the new strategy is the first to include the free angles of torsional springs and the free lengths of translational springs. This is important because it provides a meaningful reference for zero potential energy i.e. when all joints are at their free angles or free lengths. This reference for zero potential energy ensures the repeatability in the joint space of a redundant serial manipulator whose end effector undergoes a cyclic-type motion. Choices for the free angle and torsional stiffness of a joint (or the free length and translational stiffness) are made based upon the mechanical limits of the joint. For instance, the free angle of a joint is that angle which is midway between joint limits. Joint stiffnesses are chosen so that the most dexterous joint is the most pliable, and so that the least dexterous joint is the stiffest. This strategy ensures that joints of the manipulator are kept away from their respective joint limits.

Repeatable Joint Displacement Generation for Redundant Robotic Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 11-16 ◽  
Author(s):  
Y. S. Chung ◽  
M. Griffis ◽  
J. Duffy
Keyword(s):  
Joint Space ◽  
Inverse Kinematic ◽  
Torsional Stiffness ◽  
Numerical Verification ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Kinematic Equation ◽  
End Effector ◽  
Prismatic Joints ◽  
Cyclic Type

This paper presents a novel, practical, and theoretically sound kinematic control strategy for serial redundant manipulators. This strategy yields repeatability in the joint space of a serial redundant manipulator whose end effector undergoes some general cyclic type motion. This is accomplished by deriving a new inverse kinematic equation that is based on springs being theoretically or conceptually located in the joints of the manipulator (torsional springs for revolute joints, translational springs for prismatic joints). Previous researchers have also derived an inverse kinematic equation for serial redundant manipulators. However, to the authors’ knowledge, the new strategy is the first to include the free angles of torsional springs and the free lengths of translational springs. This is important because it ensures the repeatability in the joint space of a serial redundant manipulator whose end effector undergoes a cyclic type motion. Numerical verification for repeatability is done in terms of Lie bracket condition. Choices for the free angle and torsional stiffness of a joint (or the free length and translational stiffness) are made based upon the mechanical limits of the joint.

Operational Space Formulation Under Joint Constraints

2018 ◽  
Author(s):  
Juan D. Muñoz Osorio ◽  
Mario D. Fiore ◽  
Felix Allmendinger
Keyword(s):  
Joint Space ◽  
High Priority Task ◽  
Serial Manipulators ◽  
Operational Space ◽  
Hard Constraints ◽  
Novel Approach ◽  
Priority Task ◽  
On Line ◽  
Space Formulation ◽  
Joint Limits

In this paper, the problem of including hard constraints in the stack of tasks for torque-controlled serial manipulators is treated. The classic potential field approach is studied and a novel implementation of it is proposed. This implementation reduces the kinetic energy in the proximity of joint limits. Furthermore, a novel approach is proposed in order to include not only joint positions but also joint velocities and acceleration limits. This approach is called “Saturation in Joint Space” (SJS). The algorithm proceeds by creating a task with the highest priority in a stack of tasks scheme. This high priority task saturates the acceleration of the joints that would exceed their motion limits. The methods are tested and compared in simulation for the KUKA LBR iiwa. The SJS approach presents smoother behaviour near to the joint limits, while a Cartesian trajectory is traced. Experiments are performed to test the efficiency of this method in a real environment and under interaction with a human. The on-line saturation of the joint acceleration generates a friendly behaviour with the human even when he pushes the robot towards its limits.

PREDICTION OF THE TRANSPORT PROPERTIES OF SF6 WITH O2, CO2, CF4, N2 AND CH4 MIXTURES AT LOW DENSITY BY THE INVERSION METHOD (PART II)

2004 ◽  
Vol 03 (01) ◽  
pp. 69-90 ◽  
Author(s):  
BEHZAD HAGHIGHI ◽  
ALIREZA HASSANI DJAVANMARDI ◽  
MOHAMAD MEHDI PAPARI ◽  
MOHSEN NAJAFI
Keyword(s):  
Potential Energy ◽  
Diffusion Coefficients ◽  
Potential Energy Function ◽  
Model Potential ◽  
Inversion Method ◽  
Low Density ◽  
Initial Model ◽  
Lennard Jones ◽  
Inversion Procedure ◽  
And Diffusion

Viscosity and diffusion coefficients for five equimolar binary gas mixtures of SF 6 with O 2, CO 2, CF 4, N 2 and CH 4 gases are determined from the extended principle of corresponding states of viscosity by the inversion technique. The Lennard–Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The obtained interaction potential energies from the inversion procedure reproduce viscosity within 1% and diffusion coefficients within 5%.

Automatic Planning of Smooth Trajectories for Pick-and-Place Operations

1991 ◽  
Author(s):  
Clément M. Gosselin ◽  
Ammar Hadj-Messaoud
Keyword(s):  
Joint Space ◽  
Inverse Kinematic ◽  
Planning Problem ◽  
Inverse Kinematic Problem ◽  
Polynomial Solutions ◽  
Joint Coordinates ◽  
Pick And Place ◽  
Lift Off ◽  
The Relationship ◽  
Third Derivative

Abstract This paper proposes some new polynomial solutions to the trajectory planning problem encountered in pick-and-place operations. When a robotic manipulator is used for such operations, it is possible to plan the required trajectory in joint space, provided that the inverse kinematic problem has been solved for the initial and final configurations — and possibly for a lift-off and a set-down configuration — and that the workspace is free of obstacles. Polynomial solutions to this problem can be found in the literature. However, they usually provide continuity up to the second derivative only, leading to a discontinuous jerk. The solutions derived in this paper preserve the continuity of the third derivative of the joint coordinates, thereby ensuring smooth trajectories with smooth variations of the actuator currents. Moreover, whenever possible, unique polynomial expressions valid between the initial and final configurations are used in order to simplify the logic. Polynomial formulations without lift-off and set-down configurations are first presented. Then, these intermediate configurations are introduced, leading to a new set of solutions. A global algorithm is then discussed in order to clearly indicate the relationship between the different solutions. Finally, an example illustrating the application to a pick-and-place operation is solved.

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