Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Manipulation fundamentally requires the manipulator to be mechanically coupled to the object being manipulated; the manipulator may not be treated as an isolated system. This three-part paper presents an approach to the control of dynamic interaction between a manipulator and its environment. In Part I this approach is developed by considering the mechanics of interaction between physical systems. Control of position or force alone is inadequate; control of dynamic behavior is also required. It is shown that as manipulation is a fundamentally nonlinear problem, the distinction between impedance and admittance is essential, and given the environment contains inertial objects, the manipulator must be an impedance. A generalization of a Norton equivalent network is defined for a broad class of nonlinear manipulators which separates the control of motion from the control of impedance while preserving the superposition properties of the Norton network. It is shown that components of the manipulator impedance may be combined by superposition even when they are nonlinear.

A new conceptually simple approach to controlling compliant motions of a robot manipulator is presented. The “hybrid” technique described combines force and torque information with positional data to satisfy simultaneous position and force trajectory constraints specified in a convenient task related coordinate system. Analysis, simulation, and experiments are used to evaluate the controller’s ability to execute trajectories using feedback from a force sensing wrist and from position sensors found in the manipulator joints. The results show that the method achieves stable, accurate control of force and position trajectories for a variety of test conditions.

Industrial robots are mechanical manipulators whose dynamic characteristics are highly nonlinear. To control a manipulator which carries a variable or unknown load and moves along a planned path, it is required to compute the forces and torques needed to drive all its joints accurately and frequently at an adequate sampling frequency (no less than 60 Hz for the arm considered). This paper presents a new approach of computation based on the method of Newton-Euler formulation which is independent of the type of manipulator-configuration. This method involves the successive transformation of velocities and accelerations from the base of the manipulator out to the gripper, link by link, using the relationships of moving coordinate systems. Forces are then transformed back from the gripper to the base to obtain the joint torques. Theoretically the mathematical model is “exact”. A program has been written in floating point assembly language which has an average execution time of 4.5 milliseconds on a PDP 11/45 computer for a Stanford manipulator. This allows an on-line computation within control systems with a sampling frequency no lower than 60 Hz. A further advantage of using this method is that the amount of computation increases linearly with the number of links whereas the conventional method based on Lagrangian formulation increases as the quartic of the number of links.

Trong bài báo này, chúng tôi nghiên cứu mô hình hóa và điều khiển các robot manipulators có khớp nún. Đầu tiên, chúng tôi suy diễn một mô hình đơn giản để mô tả động lực học của các manipulators có khớp nún. Mô hình được suy diễn dưới hai giả định về sự kết nối động lực giữa các bộ truyền động và các thanh nối, và mô hình này hữu ích trong các trường hợp mà độ đàn hồi trong các khớp quan trọng hơn so với sự tương tác quán tính giữa các động cơ và các thanh nối. Khi độ cứng của khớp tiến đến vô cùng, mô hình của chúng tôi sẽ giảm thành mô hình cứng thông thường được tìm thấy trong tài liệu, cho thấy tính hợp lý của các giả định mô hình của chúng tôi. Chúng tôi chỉ ra rằng mô hình của chúng tôi có tính khả thi cao hơn đáng kể trong việc thiết kế bộ điều khiển hơn so với các mô hình phi tuyến trước đó đã được sử dụng để mô hình hóa các robot manipulators có khớp nún. Cụ thể, các phương trình chuyển động phi tuyến mà chúng tôi suy diễn được chứng minh là có thể tuyến tính hóa toàn cầu thông qua biến đổi tọa độ khả vi và phản hồi tĩnh phi tuyến, một kết quả không áp dụng được cho các mô hình đã được suy diễn trước đó của các robot manipulators có khớp nún. Chúng tôi cũng chi tiết một phương pháp thay thế để điều khiển phi tuyến dựa trên một hình thức rối số của các phương trình chuyển động và khái niệm về đa tạp tích phân. Chúng tôi chỉ ra rằng bằng cách sử dụng phản hồi phi tuyến thích hợp, đa tạp trong không gian trạng thái mà mô tả động lực học của robot manipulators cứng, tức là robot không có độ đàn hồi của khớp, có thể được làm bất biến dưới các nghiệm của hệ thống khớp nún. Các hệ quả của kết quả này đối với việc điều khiển các robot có khớp nún được thảo luận.

A digital feedforward control algorithm for tracking desired time varying signals is presented. The feedforward controller cancels all the closed-loop poles and cancellable closed-loop zeros. For uncancellable zeros, which include zeros outside the unit circle, the feedforward controller cancels the phase shift induced by them. The phase cancellation assures that the frequency response between the desired output and actual output exhibits zero phase shift for all the frequencies. The algorithm is particularly suited to the general motion control problems including robotic arms and positioning tables. A typical motion control problem is used to show the effectiveness of the proposed feedforward controller.

Stick-slip friction is present to some degree in almost all actuators and mechanisms and is often responsible for performance limitations. Simulation of stick-slip friction is difficult because of strongly nonlinear behavior in the vicinity of zero velocity. A straightforward method for representing and simulating friction effects is presented. True zero velocity sticking is represented without equation reformulation or the introduction of numerical stiffness problems.

The singularity problem is an inherent problem in controlling robot manipulators with articulated configuration. In this paper, we propose to determine the joint motion for the requested motion of the endeffector by evaluating the feasibility of the joint motion. The determined joint motion is called an inverse kinematic solution with singularity robustness, because it denotes feasible solution even at or in the neighborhood of singular points. The singularity robust inverse (SR-inverse) is introduced as an alternative to the pseudoinverse of the Jacobian matrix. The SR-inverse of the Jacobian matrix provides us with an approximating motion close to the desired Cartesian trajectory of the endeffector, even when the inverse kinematic solution by the inverse or the pseudoinverse of the Jacobian matrix is not feasible at or in the neighborhood of singular points. The properties of the SR-inverse are clarified by comparing it with the inverse and the pseudoinverse. The computational complexity of the SR-inverse is considered to discuss its implementability. Several simulation results are also shown to illustrate the singularity problem and the effectiveness of the inverse kinematic solution with singularity robustness.

This paper presents a survey of recent research in cooperative control of multivehicle systems, using a common mathematical framework to allow different methods to be described in a unified way. The survey has three primary parts: an overview of current applications of cooperative control, a summary of some of the key technical approaches that have been explored, and a description of some possible future directions for research. Specific technical areas that are discussed include formation control, cooperative tasking, spatiotemporal planning, and consensus.

Biaxial control systems for generating predetermined paths under load disturbances, such as encountered in NC and CNC systems for machine tools, are conventionally designed such that the control of each axis is independent of the other. The present paper is concerned with providing cross-couplings for biaxial control systems, whereby an error in either axis affects the control loops of both axes. An algorithm for a cross-coupled control system is presented, and the performance of the cross-coupled system is mathematically analyzed and compared with the conventional CNC system having individual axis control. It is shown that cross-coupling between axes improves the contour accuracy while the velocity response of each axis is only slightly reduced. Although the proposed cross-coupled system requires additional hardware for implementation with an NC system, operation with a CNC-based system requires only software modifications to the system control program.

This paper reviews stochastic system identification methods that have been used to estimate the modal parameters of vibrating structures in operational conditions. It is found that many classical input-output methods have an output-only counterpart. For instance, the Complex Mode Indication Function (CMIF) can be applied both to Frequency Response Functions and output power and cross spectra. The Polyreference Time Domain (PTD) method applied to impulse responses is similar to the Instrumental Variable (IV) method applied to output covariances. The Eigensystem Realization Algorithm (ERA) is equivalent to stochastic subspace identification.