Motions With Minimal Joint Torques for Redundant Manipulators

1993 ◽  
Vol 115 (3) ◽  
pp. 599-603 ◽  
Author(s):  
Lee Heow Pueh
Keyword(s):  
Present Method ◽  
Optimization Criterion ◽  
Redundant Manipulators ◽  
Global Level ◽  
Joint Torques ◽  
Optimization Criteria ◽  
Singular Configurations ◽  
Large Joint ◽  
Mechanical Manipulators

The article presents a method for obtaining motions with minimal joint torques for redundant mechanical manipulators. The existing methods based on the local resolution of redundancy do not guarantee that singular configurations, which lead to large joint torques and joint accelerations, will also be avoided while optimizing joint torques. For the present method, the degrees of redundancy are resolved at the global level. It is observed that motions with optimal joint torques are usually associated with large joint speeds and joint accelerations, compared with the joint speeds and joint accelerations for motions with minimal joint speeds or joint accelerations. To overcome this problem, the optimization criterion for minimal joint torques is modified by combining it separately with the optimization criteria for both minimal joint speeds and minimal joint accelerations. The resulting optimal motions, with smaller joint speeds and joint accelerations, are achieved at the expense of having larger joint torques.

Applications of Damped Least-Squares Methods to Resolved-Rate and Resolved-Acceleration Control of Manipulators

1988 ◽  
Vol 110 (1) ◽  
pp. 31-38 ◽  
Author(s):  
C. W. Wampler ◽  
L. J. Leifer
Keyword(s):  
Least Squares ◽  
Rate Of Convergence ◽  
Sensory Feedback ◽  
Inverse Kinematic ◽  
Redundant Manipulators ◽  
Approximate Inverse ◽  
Singular Configurations ◽  
Large Joint ◽  
Resolved Acceleration Control ◽  
Damped Least Squares

Resolved-rate and resolved-acceleration controllers have been proposed for manipulators whose trajectories are determined by real-time sensory feedback. For redundant manipulators, these controllers have been generalized using the pseudoinverse of the manipulator Jacobian. However, near singular configurations, these controllers fail in that they require infeasibly large joint speeds. A damped least-squares reformation of the problem gives approximate inverse kinematic solutions that are free of singularities. Away from singularities the new controllers closely approximate their conventional counterparts; near singular configurations the new controllers remain well-behaved, although the rate of convergence decreases. This paper defines the new controllers and proves their stability. Some aspects of the behavior of the new resolved-rate controller are illustrated in simulations.

scholarly journals The Effect of Cost Function on Optimum Technique of the Undersomersault on Parallel Bars

2012 ◽  
Vol 28 (1) ◽  
pp. 10-19 ◽  
Author(s):  
Michael J. Hiley ◽  
Maurice R. Yeadon
Keyword(s):  
Motion Capture ◽  
Swing Phase ◽  
Optimization Criterion ◽  
Limiting Factor ◽  
Computer Simulation Model ◽  
Joint Torques ◽  
Optimization Criteria ◽  
The Third ◽  
Optimum Technique ◽  
To Receive

The undersomersault, or felge, to handstand on parallel bars has become an important skill in Men’s Artistic Gymnastics as it forms the basis of many complex variations. To receive no deductions from the judges, the undersomersault must be performed without demonstrating the use of strength to achieve the final handstand position. Two male gymnasts each performed nine undersomersaults from handstand to handstand while data were recorded using an automatic motion capture system. The highest and lowest scoring trials of each gymnast, as determined by four international judges, were chosen for further analysis. Three optimization criteria were used to generate undersomersault technique during the swing phase of the skill using a computer simulation model: minimization of peak joint torques, minimization of horizontal velocity before release, and maximization of angular momentum. The techniques used by both gymnasts could be explained using the second optimization criterion which facilitated further skill development. The first optimization criterion generated a technique advocated for beginners where strength might be expected to be a limiting factor. The third optimization criterion resulted in a different type of undersomersault movement of greater difficulty according to the FIG Code of Points.

scholarly journals Joint torque and velocity optimization for a redundant leg of quadruped robot

2017 ◽  
Vol 14 (5) ◽  
pp. 172988141773189 ◽  
Author(s):  
Taihui Zhang ◽  
Honglei An ◽  
Hongxu Ma
Keyword(s):  
Angular Velocity ◽  
Sagittal Plane ◽  
Load Capacity ◽  
Optimization Criterion ◽  
Quadruped Robot ◽  
Joint Torque ◽  
Quadratic Program ◽  
Hydraulic Actuator ◽  
Joint Torques ◽  
Physical Limitations

Hydraulic actuated quadruped robot similar to BigDog has two primary performance requirements, load capacity and walking speed, so that it is necessary to balance joint torque and joint velocity when designing the dimension of single leg and controlling its motion. On the one hand, because there are three joints per leg on sagittal plane, it is necessary to firstly optimize the distribution of torque and angular velocity of every joint on the basis of their different requirements. On the other hand, because the performance of hydraulic actuator is limited, it is significant to keep the joint torque and angular velocity in actuator physical limitations. Therefore, it is essential to balance the joint torque and angular velocity which have negative correlation under the condition of constant power of the hydraulic actuator. The main purpose of this article is to optimize the distribution of joint torques and velocity of a redundant single leg with joint physical limitations. Firstly, a modified optimization criterion combining joint torques with angular velocity that takes both support phase and flight phase into account is proposed, and then the modified optimization criterion is converted into a normal quadratic programming problem. A kind of recurrent neural network is used to solve the quadratic program problem. This method avoids tremendous matrix inversion and fits for time-varying system. The achieved optimized distribution of joint torques and velocity is useful for aiding mechanical design and the following motion control. Simulation results presented in this article confirm the efficiency of this optimization algorithm.

Comparison of Damped Velocity and Acceleration Control for Non-Redundant Manipulators

2000 ◽  
Author(s):  
Yu-Che Chen ◽  
Kevin A. O’Neil
Keyword(s):  
Path Tracking ◽  
Least Square ◽  
Dynamics Simulation ◽  
Control Algorithms ◽  
Redundant Manipulators ◽  
Velocity Control ◽  
Redundant Manipulator ◽  
Singular Configurations ◽  
On Line ◽  
Simulation Results

Abstract Damped Least Square (DLS) method has been widely used as an on-line algorithm for manipulator path tracking near and at singular configurations. Wampler (1986) formulated the framework of DLS method applied to velocity control and addressed the applicability of DLS method to acceleration control. The purpose of this paper is to demonstrate the differences in the joint paths generated by damped velocity and damped acceleration control algorithms in non-redundant manipulators. We examine these joint paths, find the cause of the differences, and demonstrate the features of damped acceleration control in non-redundant manipulator dynamics. Simulation results on a planar 2R and a spatial 6R manipulator moving through and near singular configurations verify the phenomena analyzed.

Resolved Motion Adaptive Control for Mechanical Manipulators

1984 ◽  
Vol 106 (2) ◽  
pp. 134-142 ◽  
Author(s):  
C. S. G. Lee ◽  
B. H. Lee
Keyword(s):  
Adaptive Control ◽  
Low Cost ◽  
Equations Of Motion ◽  
Least Square ◽  
Hand Position ◽  
Recursive Least Square ◽  
Joint Torques ◽  
Hand Trajectory ◽  
Self Tuning ◽  
Mechanical Manipulators

This paper presents the development of a resolved motion adaptive control which adopts the ideas of “resolved motion rate control” [8] and “resolved motion acceleration control” [10] to control a manipulator in Cartesian coordinates for various loading conditions. The proposed adaptive control is performed at the hand level and is based on the linearized perturbation system along a desired hand trajectory. The controlled system is characterized by feedforward and feedback components which can be computed separately and simultaneously. The feedforward component resolves the specified positions, velocities, and accelerations of the hand into a set of values of joint positions, velocities, and accelerations from which the nominal joint torques are computed using the Newton-Euler equations of motion to compensate all the interaction forces among the various joints. The feedback component consisting of recursive least square identification scheme and an optimal adaptive self-tuning controller for the linearized system computes the perturbation torques which reduce the manipulator hand position and velocity errors along the nominal hand trajectory. The feasibility of implementing the proposed adaptive control using present day low-cost microprocessors is explored.

A Comparison of Continuum and Lumped-Mass Models for Hyper-Redundant Manipulator Mechanics

1993 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Continuum Model ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Lumped Mass ◽  
Mass Model ◽  
Joint Torques ◽  
Lumped Mass Model ◽  
The Continuum

Abstract The most efficient methods for representing dynamics in the literature require serial computations which are proportional to the number of manipulator degrees-of-freedom. Furthermore, these methods are not fully parallelizable. For ‘hyper-redundant’ manipulators, which may have tens, hundreds, or thousands of actuators, these formulations preclude real time implementation. This paper therefore looks at the mechanics of hyper-redundant manipulators from the point of view of an approximation to an ‘infinite degree-of-freedom’ (or continuum) problem. The dynamics for this infinite dimensional case is developed. The approximate dynamics of actual hyper-redundant manipulators is then reduced to a problem which is O(1) in the number of serial computations, i.e., the algorithm is O(n) in the total number of computations, but these computations are completely parallelizable. This is achieved by ‘projecting’ the dynamics of the continuum model onto the actual robotic structure. The results are compared with a lumped mass model of a particular hyper-redundant manipulator. It is found that the continuum model can be used to generate joint torques to within ten percent of values computed from the lumped mass model.

Stabilized minimum infinity-norm torque solution for redundant manipulators

Robotica ◽  
1998 ◽  
Vol 16 (2) ◽  
pp. 193-205 ◽  
Author(s):  
Ick-Chan Shim ◽  
Yong-San Yoon
Keyword(s):  
Dynamic Control ◽  
Inequality Constraint ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
End Effector ◽  
Joint Torques ◽  
Infinity Norm ◽  
Instability Problem ◽  
Geometrical Relation ◽  
Feasibility Constraint

The minimization of the joint torques based on the ∞-norm is proposed for the dynamic control of a kinematically redundant manipulator. The ∞-norm is preferred to the 2-norm in the minimization of the joint torques since the maximum torques of the actuators are limited. To obtain the minimum ∞-norm torque solution, we devised a new algorithm that uses the acceleration polyhedron representing the end-effector's acceleration capability. Usually the minimization of the joint torques has an instability problem for the long trajectories of the end-effector. To suppress this instability problem, an inequality constraint, named the feasibility constraint, is developed from the geometrical relation between the required end-effector acceleration and the acceleration polyhedron. The minimization of the °-norm of the joint torques subject to the feasibility constraint is shown to improve the performances through the simulations of a 3-link planar redundant manipulator.

A new dynamic manipulability ellipsoid for redundant manipulators

Robotica ◽  
2000 ◽  
Vol 18 (4) ◽  
pp. 381-387 ◽  
Author(s):  
Pasquale Chiacchio
Keyword(s):  
Case Studies ◽  
Robotic Manipulators ◽  
Redundant Manipulators ◽  
Task Space ◽  
End Effector ◽  
Space Analysis ◽  
Singular Configurations ◽  
Definition Of

Manipulability ellipsoids are effective tools to perform task space analysis of robotic manipulators in terms of velocities, accelerations and forces at the end effector. In this paper a new definition of a dynamic manipulability ellipsoid for redundant manipulators is proposed which leads to more correct results in evaluating manipulator capabilities in terms of task-space accelerations. The case of manipulators in singular configurations is also analyzed. Two case studies are presented to illustrate the correctness of the proposed approach.

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