A Nonlinear Optimization Technique Applied to PWM Signals

2012 ◽  
Author(s):  
Vinicius Novicki Obadowski ◽  
Andre Arthur Perleberg Lerm ◽  
Wagner de_Freitas Ciarelli
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Technique

Approximate Motion Synthesis of Spherical Kinematic Chains

2007 ◽  
Author(s):  
Venkatesh Venkataramanujam ◽  
Pierre Larochelle
Keyword(s):  
Finite Number ◽  
Nonlinear Optimization ◽  
Optimization Technique ◽  
Analytic Representation ◽  
Dimensional Synthesis ◽  
Motion Synthesis ◽  
Kinematic Chains ◽  
Synthesis Technique

In this paper we present a novel dimensional synthesis technique for approximate motion synthesis of spherical kinematic chains. The methodology uses an analytic representation of the spherical RR dyad’s workspace that is parameterized by its dimensional synthesis variables. A two loop nonlinear optimization technique is then employed to minimize the distance from the dyad’s workspace to a finite number of desired orientations of the workpiece. The result is an approximate motion dimensional synthesis technique that is applicable to spherical open and closed kinematic chains. Here, we specifically address the spherical RR open and 4R closed chains however the methodology is applicable to all spherical kinematic chains. Finally, we present two examples that demonstrate the utility of the synthesis technique.

Optimization of Polynomial Trajectories for Robotic Manipulators

1991 ◽  
Author(s):  
Yüksel Yildirim ◽  
Chinyere Onwubiko ◽  
Eugene F. Fichter
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Technique ◽  
Search Method ◽  
Pattern Search ◽  
Minimum Time ◽  
Planning Problem ◽  
End Effector ◽  
Pattern Search Method ◽  
Spline Curves ◽  
Robot Tasks

Abstract This paper utilizes the modified pattern search method to solve the nonlinear optimization problem of design of minimum-time robot trajectories between given end states in a workspace containing obstacles. This method is applied to a collision-free path of a two-degree-of-freedom elbow manipulator. Bezier curves, B-spline curves, and parabolic blend curves are used to simplify end-effector path planning. Motion of the manipulator, represented by a sequence of Cartesian knots along the end-effector path, is first transformed into sets of joints displacements. Piecewise cubic spline functions are then fit to the sequence of joint displacements. The minimum-time trajectory planning problem is formulated as the problem of minimizing the total traveling time, taken as objective function, subject to constraints on joint positions, velocities, accelerations, jerks, motor torques, and end-effector acceleration. The computer program, ROBOPATH, has been developed to implement this algorithm for generating end-effector paths and joint trajectories for a manipulator with two links. The results show the modified pattern search method to be a very effective nonlinear optimization technique in design of minimum-time robot trajectories. Also, ROBOPATH can be a useful tool in the design of manipulators, robot tasks and workcells.

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