Harmonic drives can exhibit very nonlinear dynamic behavior. In order to capture this behavior, not only must dynamic models include accurate representations of transmission friction, compliance, and kinematic error, but also important features of harmonic-drive gear-tooth geometry and interaction must be understood. In this investigation, experimental observations were used to guide the development of a model to describe harmonic-drive operation. Unlike less detailed representations, this model was able to replicate many of the features observed in actual harmonic-drive dynamic response. Unfortunately, since model parameters can only be derived from careful analysis of experimental dynamic response, it seems unlikely that any comparably sufficient representation can be constructed with parameter values obtained from catalogs or simple experimental observations.

This paper examines the effects of errors in applied force on robot force-controlled task performance. Two configuration-dependent effects of force errors are identified. Kinematic stability errors occur when the robot configuration is such that small inaccuracies in joint torque create relatively large robot link displacements. This sensitivity to torque errors can seriously inhibit task performance in certain configurations. Task performance can also be affected by errors in the endpoint force angle which can be significant for even small changes in joint torque. Performance maps are developed as tools to identify robot configurations sensitive to these errors. The effects of force errors are demonstrated in the performance of a planar peg and hole task by a three link manipulator under joint torque control.>

The authors present an extension to the impulse shaping technique for commanding machines to move with reduced residual vibration. The extension, called frequency sampling, is a method for generating constraints that are used to obtain shaping sequences which minimize residual vibration in systems such as robots whose resonant frequencies change during motion. The authors present a review of impulse shaping methods, a development of the proposed extension, and a comparison of results of tests conducted on a simple model of the Space Shuttle robot arm. Frequency shaping provides a method for minimizing the impulse sequence duration required to give the desired insensitivity.>

Three dynamic characteristics of robot systems are discussed: rigid-body bandwidth, dynamically noncolocated flexible modes, and dynamically colocated flexible modes. All of these combine to limit the closed-loop bandwidth achievable in the individual joint control loops of the robot. They play a particularly important role in establishing performance limits for robots under force control.>

Spacecraft, space-borne robotic systems, and manufacturing equipment often utilize lightweight materials and configurations that give rise to vibration problems. Prior research has led to the development of input command preshapers that can significantly reduce residual vibration. These shapers exhibit marked insensitivity to errors in natural frequency estimates and can be combined to minimize vibration at more than one frequency. A method for the development of multiple mode input shapers which are simpler to implement than previous designs and produce smaller system response delays is presented. The new technique involves the solution of a group of simultaneous nonlinear impulse constraint equations. The resulting shapers were tested on a model of MACE, an MIT/NASA experimental flexible structure.>

A primary source of difficulty in automated assembly is the uncertainty in the relative position of the parts being assembled. This study focuses on a machine learning approach for solving the problem. Force sensor information, responses to recent moves and results from previous assemblies are used to generate a set of production rules. These rules govern the motion of the robot during the assembly process.>

A flexible three-degree-of-freedom robot is described, and its behavior is compared with a simple model of a vibrating system. The robot has three rotary joints and two flexible steel links, causing it to exhibit many complicated modes of vibration. A nondimensional analysis of the model showing how it responds to ramp commands and acceleration commands is presented, and the results are compared with those for the actual robot. Using the model, one can select input commands that minimize the vibration of the robot.>

A method is described for limiting vibration in flexible systems by shaping the system inputs. Unlike most previous attempts at input shaping, this method does not require an extensive system model or lengthy numerical computation; only knowledge of the system's natural frequency and damping ratio is required. The effectiveness of this method when there are errors in the system model is explored and quantified. An algorithm is presented which, given an upper bound on acceptable residual vibration amplitude, determines a shaping strategy that is insensitive to errors in the estimated natural frequency.>

The authors illustrate the need for planning in assembly and describe a set of modeling and planning techniques developed to generate robust force-control strategies for a certain class of assemblies. Specifically, they develop strategies for the chamferless insertion of a planar peg into a hole and the insertion of a three-dimensional rectangular peg into a rectangular hole. The complexity of applying these techniques in three dimensions is also discussed. It is seen from the analysis of the insertion of a planar peg into a chamferless hole that there are cases where an assembly may not be reliably carried out if the contact configurations between parts are not constrained. In such cases it is necessary to a priori specify the configurations through which the assembly must pass, and guarantee that only those configurations are encountered. From the analysis for the insertion of a three-dimensional rectangular peg into a chamferless hole, it is seen that for moderately complex assemblies involving may possible configurations, the specification of a set of configurations through which parts must pass is considerably more difficult than for the planar case. However, by considering only a subset of the possible configurations chosen on the basis of a set of heuristics, successful assembly strategies can be generated.>

The problems of designing a robot with joint and link flexibility are discussed. The relationship between the deflection of the robot under gravity is correlated with the fundamental frequency of vibration. Different types of link geometry are considered, evaluating the flexibility potential of different materials. Some general conclusions and guidelines for constructing a flexible robot are given. It is found that, for maximum flexibility with minimum stiffness, the best material choice for the links is titanium. Some aluminium alloys may be inexpensive alternatives, but the fatigue characteristics of aluminium are unacceptable in most applications. Coiled springs give very little stiffness in comparison to their strength, but their weight makes them unusable in all but planar applications.>

Three dynamic problems which arise in robot systems are discussed: rigid-body bandwidth; dynamically noncolocated flexible modes; and dynamically colocated flexible modes. These effects combine to set the closed-loop bandwidth achievable in the individual joint control loops. Simple models of robot systems are presented to illustrate these three dynamic effects. Some laboratory data are then presented and analyzed in these terms. Finally, the implications for robot system design is discussed in the hope that these issues will be considered in the development of the next generation of robot systems and machine tools.>

The authors evaluate a signal generation technique for commanding high-performance machines to move without exciting residual vibration. This time-domain input-shaping technique works like a filter that is designed to eliminate decaying sinusoidal resonance responses. It is compared to a variety of filtering techniques and is shown to perform more effectively than any of them. In particular, frequency-domain filter design techniques are less effective for shaping vibration-reducing inputs to systems. The three-impulse shaping sequence offers significant performance advantages in that moves require less time and result in little or no residual vibration. In addition, the response is not sensitive to variations in the system parameters.>

Dynamic models have been developed in an attempt to match the response of a robot arm. The experimental data show rigid-body and five resonant modes. The frequency response and pole-zero arrays for various models of structural flexibility are compared with the data to evaluate the characteristics of the models, and to provide insight into the nature of the flexibility in the robot. Certain models are better able to depict transmission flexibility white others describe types of structural flexibility.>

To avoid vibration of robot arms when they are moved very rapidly, a set of shaped force profiles have been developed to minimize the excitation energy at the system's first natural frequency during motion. The system is assumed to be velocity-limited. The force profiles are constructed from a versine (one-cosine) function and its harmonics, with coefficients chosen to minimize the spectral magnitude near the system natural frequency. The profiles can be tuned to the closed-loop natural frequency of a closed-loop system with motor position and velocity feedback. When integrated twice, the force profile becomes a reference trajectory which serves to bring the system to peak velocity with minimum excitation at the first natural frequency. Using a suitable dwell time between acceleration and deceleration, a specified position can be reached quickly with minimum residual vibration and within while never exceeding the velocity limit.>

A method for generating shaped command inputs which reduce endpoint vibration is presented. The technique applies to both open- and closed-loop systems. The Draper Laboratory's Space Shuttle remote manipulator system nonlinear simulator is used to verify the substantial reduction of residual vibration. In addition, the shaped inputs have been designed to closely approximate the time-optimal input, therefore only a small move time penalty is incurred.>

This paper provides an analytical overview of the dynamics involved in force control. Models are developed which demonstrate, for the one-axis explicit force control case, the effects on system closed-loop bandwidth of a) robot system dynamics that are not usually considered in the controller design; b) drive-train and task nonlinearities; and c) actuator and controller dynamics. The merits and limitations of conventional solutions are weighed, and some new solutions are proposed. Conclusions are drawn which give insights into the relative importance of the effects discussed.

A light-stripe vision system which quickly and accurately locates polyhedral part features is presented. An image of three line segments generated by the intersection of a plane of light and a polyhedral feature is used to localize the feature. Sufficient conditions for six degree-of-freedom positional constraint are discussed and the solution for determining the rigid transformation of a general polyhedral feature is presented. The accuracy of a prototype sensing system in locating a right corner feature is 0.1 degrees (1.5 milliradians) per standard deviation in rotation and 0.002 inches (0.055 mm) per standard deviation in translation. The time required for the measurements is 2.5 to 3 seconds. Much shorter times are also realizable.

Robots which perform rapid motions tend to excite system resonant frequencies. In order to perform a sequence of tasks more quickly, both move time and vibration settling time must be reduced. In addition, this must be accomplished in the presence of time-varying resonant frequencies. In this paper, functions are derived which accomplish open-loop moves rapidly with greatly reduced residual vibration amplitude, as resonant frequencies are allowed to vary by ±10%. First, a direct relationship is established between the frequency spectrum of the input functions and the resulting residual acceleration amplitude. This establishes a specification on spectral magnitude at resonance which must be satisfied in order to bring residual vibration within acceptable bounds. Then functions are derived as a series expansion of ramped sinusoid functions with coefficients chosen so as to minimize spectral magnitude in a frequency band surrounding resonance. Finally, some simulations are performed to indicate that these functions can reduce residual vibration considerably even when the resonant frequency changes by 10%.

Part orientation errors can potentially be corrected by making the proper responses to the forces generated during parts mating. Preliminary experiments performed on a 5 degree of freedom peg-in-hole insertion machine indicate that parts mating can generate clear, repeatable force/position histories. This paper discusses the preliminary development of algorithms that transform this raw position and force data into automated assembly routines.

A series of lumped-parameter models is developed in an effort to predict the dynamics of simple force-controlled robot systems. The models include some effects of robot structural dynamics, sensor compliance, and workpiece dynamics. A qualitative analysis suggests that the robot dynamics contribute to force-controlled instability.

The accuracy with which objects that generate images of line segments may be located in the presence of quantization noise is investigated. Expressions for the standard deviation of errors in orientation and translation are derived. The accuracy of these expressions is substantiated by a number of Monte Carlo simulations and experimental tests.

Quality of the dynamic response of a robotic manipulator is dependent upon a variety of factors. In this paper, we will discuss the effects on dynamic performance of robot system design and of structural resonant characteristics. A model of the actuator and controller system for a cartesian robot will be presented and its simulated performmance evaluated. Comparison will be made between performance of the model and that of the actual robot system. A model for system resonant characteristics will then be developed and predictions compared with experimental data.