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L2 Gain And Passivity Techniques In Nonlinear Control

This paper focuses on time-optimal path tracking, a subproblem in time-optimal motion planning of robot systems. Through a nonlinear change of variables, the time-optimal path tracking problem is transformed here into a convex optimal control problem with a single state. Various convexity-preserving extension are introduced, resulting in a versatile approach for optimal path tracking. A direct transcription method is presented that reduces finding the globally optimal trajectory to solving a second-order cone program using robust numerical algorithms that are freely available. Validation against known examples and application to a more complex example illustrate the versatility and practicality of the new method.

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Time-Optimal Path Tracking for Robots: A Convex Optimization Approach

An online method for obtaining smooth, jerk-bounded trajectories has been developed and implemented. Jerk limitation is important in industrial robot applications, since it results in improved path tracking and reduced wear on the robot. The method described herein uses a concatenation of fifth-order polynomials to provide a smooth trajectory between two way points. The trajectory approximates a linear segment with parabolic blends trajectory. A sine wave template is used to calculate the end conditions (control points) for ramps from zero acceleration to nonzero acceleration. Joining these control points with quintic polynomials results in a controlled quintic trajectory that does not oscillate, and is near time optimal for the jerk and acceleration limits specified. The method requires only the computation of the quintic control points, up to a maximum of eight points per trajectory way point. This provides hard bounds for online motion algorithm computation time. A method for blending these straight-line trajectories over a series of way points is also discussed. Simulations and experimental results on an industrial robot are presented.

Jerk-bounded manipulator trajectory planning: design for real-time applications

A new method for smooth trajectory planning of robot manipulators

This article presents a method for determining smooth and time-optimal path constrained trajectories for robotic manipulators and investigates the performance of these trajectories both through simulations and experiments. The desired smoothness of the trajectory is imposed through limits on the torque rates. The third derivative of the path parameter with respect to time, the pseudo-jerk, is the controlled input. The limits on the actuator torques translate into state-dependent limits on the pseudo-acceleration. The time-optimal control objective is cast as an optimization problem by using cubic splines to parametrize the state space trajectory. The optimization problem is solved using the flexible tolerance method. The experimental results presented show that the planned smooth trajectories provide superior feasible time-optimal motion. © 2000 John Wiley & Sons, Inc.

Smooth and time-optimal trajectory planning for industrial manipulators along specified paths

A new simulation approach is proposed to improve the stability and the perceived rigidity of contacts during haptic interaction with multirigid body virtual environments. The approach computes impulsive forces upon contact and penalty and friction forces during contact. The impulsive forces are derived using a new multiple collision resolution method that never increases the kinetic energy of the system. When new contacts arise, the impulsive forces generate large hand accelerations without requiring increased contact stiffness and damping. Virtual objects and linkages are regarded as points in the configuration space, and no distinction is made between them in the proposed approach.

/pdf/haptic-rendering-of-rigid-contacts-using-impulsive-and-1zc3rhio19.pdf

Haptic rendering of rigid contacts using impulsive and penalty forces

Distributed model predictive control of constrained weakly coupled nonlinear systems

A graphical technique for determining the existence of limit cycles, their amplitude, frequency, and stability when they exist, and the stability of a single-loop feedback system with n - 1 memoryless nonlinear elements and one nonlinear element with memory is considered. The approach here is to assume an input to a nonlinear element and then apply the Nyquist stability condition to the linear system resulting after the nonlinear elements have been approximated by their describing functions. The method requires no trial and error procedure, is noniterative in nature, and is especially easy to apply. The method is subject to the usual errors and restrictions of the describing function method. An extension of the method to include n non-linear elements with memory and n nonlinear elements in parallel is also included. Three numerical examples are included to illustrate the method.

http://ieeexplore.ieee.org/iel5/9/24117/01099625.pdf

Daniela Constantinescu

Papers

Smooth and time-optimal trajectory planning for industrial manipulators along specified paths

Smooth and time-optimal trajectory planning for industrial manipulators along specified paths

Haptic rendering of rigid contacts using impulsive and penalty forces

Distributed model predictive control of constrained weakly coupled nonlinear systems

A describing function technique for multiple nonlinearities in a single-loop feedback system