Trajectory Pattern Method Research Articles

Low-harmonic trajectory synthesis using trajectory pattern method (TPM) for high-speed and high-precision machinery

Abstract. In high-speed and high-precision machinery, trajectories with high-frequency harmonic content are one of the main sources of reduction of operational precision. Trajectories with high-frequency harmonic content generally demand even higher-harmonic actuating forces/torques due to the nonlinear dynamics of such systems, which may excite natural modes of vibration of the system and/or be beyond the dynamic response limitation of the actuation devices. In this paper, a global interpolation algorithm that uses the trajectory pattern method (TPM) for synthesizing low-harmonic trajectories is presented. The trajectory synthesis with the TPM is performed with a prescribed fundamental frequency and continuous jounce boundary condition, which would minimize the number of high-harmonic components in the required actuation forces/torques and avoid excitation of the system modes of vibration. The minimal curvature variation energy method, Lagrange multiplier method, and contour error control are used to obtain smooth kinematic profiles and satisfy the trajectory accuracy requirements. As an example, trajectory patterns that consist of a fundamental frequency sinusoidal time function and its first three harmonics are used to synthesize the desired trajectories for a selected dynamic system. The synthesized trajectories are shown to cause minimal system vibration during its operation. A comparison with a commonly used trajectory synthesis method clearly shows the superiority of the developed TPM-based approach in reducing vibration and demand on the actuator dynamic response, thereby allowing the system to operate at higher speeds and precision.

A corner smoothing algorithm using Trajectory Pattern Method (TPM) for high-speed and high-quality machining

In micro-line segments machining, transition curves with high harmonic components are more prone to causing vibration issues in the feed drive system, which affects machining efficiency and quality severely. To construct low harmonic trajectories, this paper proposes a corner smoothing algorithm that uses the Trajectory Pattern Method (TPM). The transition curve construction and axial motion scheduling are performed with a specified fundamental frequency in one step, which reduces the smoothing process time and avoids excitation of natural modes of vibration of the system. The synthesized trajectories and axial kinematic profiles are all smooth and only contain the selected fundamental frequency and its first two odd harmonics, which minimizes the number of high harmonic components in the required actuation forces/torques and avoids excitation of the system modes of vibration. Linear programming is used to synthesize the trajectories. The proposed algorithm is shown to achieve near time-optimal trajectories. The provided experimental analysis and comparisons demonstrate that the proposed algorithm achieves smooth axial kinematic profiles with low harmonic contents, which would improve machining efficiency and quality.

On the inherent characteristics of the dynamics of rigid link robot manipulators

A method to determine the inherent characteristics of the nonlinear dynamics of open-loop chain robot manipulators with rigid links is developed using the trajectory pattern method. The method is based on the selection of a basic trajectory pattern and examining the corresponding inverse dynamics model. The trajectory pattern employed in the present study is synthesized with a fundamental sinusoidal time function and its second harmonic. This basic trajectory is appropriate since it corresponds to one of the most basic robot manipulator motions. The inherent characteristics of the dynamics of a manipulator is studied by examining the harmonic content of the actuating torques necessary for open-loop tracking of the selected trajectory pattern, and the relative significance of each harmonic. The harmonic content and the relative contribution of each harmonic are shown to be functions of the length of the path of motion in the joint coordinate space, path positioning, and the fundamental frequency of the trajectory, but independent of the number of degrees-of-freedom of the manipulator. The study provides the basis for the development of systematic approaches to path and trajectory planning from the vibration and control points of view, and design of manipulators with superior dynamic performance. As an example, the characteristics of the dynamics of a spatial 3R manipulator is investigated.

Task-specific optimal simultaneous kinematic, dynamic, and control design of high-performance robotic systems

A task-specific optimal simultaneous kinematic, dynamic and control design approach is proposed for high-performance computer-controlled machines, such as robots. This mechatronics design approach is based on the trajectory pattern method and a fundamentally new design philosophy that such machines, in general, and ultrahigh-performance machines, in particular, must only be designed to perform a class or classes of motions effectively. In the proposed approach, given the structure of the manipulator, its kinematic, dynamic, and control parameters are optimized simultaneously with the parameters that describe a selected trajectory pattern with which the desired class(es) of task(s) can best be performed. In one example, a weighted sum of the norms of the higher harmonics appearing in the actuating torques and the integral of the position and velocity tracking errors are used to form the optimality criterion. The selected optimality criterion should yield a system that is optimally designed to accurately follow the specified trajectory at high speed. Other objective functions can be readily formulated to synthesize systems for optimal performance. Based on the developed design methodology, a two-degrees-of-freedom robot manipulator with a closed-loop chain is optimally designed and constructed for point-to-point motions. The preliminary results of experiments indicate that the robot can, in fact, execute point-to-point motions rapidly and with minimal residual vibration. The potentials of the developed method and its implementation for generally defined motion patterns are discussed.

Natural Heuristic Dynamic Programming for Dynamic Systems Control

Heuristic Dynamic Programming (HDP) is the simplest kind of Adaptive Critic (Werbos, 1992). It can be used to maximize or minimize any utility function, such as total energy or trajectory error, of a system over time in a noisy environment. This article proposes a new version of HDP, called NHDP (Natural Heuristic Dynamic Programming). This new version incorporates basic HDP algorithm with the following features:(i) use of Trajectory Pattern Method to guarantee smoothness of trajectory and control signals; (ii) use multiple critic networks to localize effect of each parameter mimicking the natural biological model of human brain; and (iii) allow the controller to learn from slow to fast motion, analogous to the natural learning behavior of humans. A simple dynamic system is used to illustrate NHDP.

A new model-based tracking controller for robot manipulators using trajectory pattern inverse dynamics

A novel inverse-dynamic model-based tracking controller is presented. The inverse dynamics models are derived using the trajectory pattern method. The path of motion is divided into a number of relatively large segments, along which the motion is described by a selected trajectory pattern. The resulting inverse dynamics models are in the form of a summation of a fundamental sinusoidal time function and a number of its harmonics with constant coefficients. The coefficients are computed offline using analytical expressions that are derived for the selected trajectory pattern. The controller permits ultra-high-speed generation of the desired trajectory and feedforward signals. The online computations are minimal and can all be performed in parallel. The inverse-dynamic model of a spatial 3R manipulator is derived for a specified trajectory pattern. The controller structure and simulation results indicating its effectiveness are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>