The Effect of Transmission Design on Force-Controlled Manipulator Performance

Previous research in force control has focused on the choice of appropriate servo implementation without corresponding regard to the choice of mechanical hardware. This report analyzes the effect of mechanical properties such as contact compliance, actuator-to-joint compliance, torque ripple, and highly nonlinear dry friction in the transmission mechanisms of a manipulator. A set of requisites for high performance then guides the development of mechanical-design and servo strategies for improved performance. A single-degree-of-freedom transmission testbed was constructed that confirms the predicted effect of Coulomb friction on robustness; design and construction of a cable-driven, four-degree-of- freedom, "whole-arm" manipulator illustrates the recommended design strategies.

Control of Vibration in Mechanical Systems Using Shaped Reference Inputs

Dynamic systems which undergo rapid motion can excite natural frequencies that lead to residual vibration at the end of motion. This work presents a method to shape force profiles that reduce excitation energy at the natural frequencies in order to reduce residual vibration for fast moves. Such profiles are developed using a ramped sinusoid function and its harmonics, choosing coefficients to reduce spectral energy at the natural frequencies of the system. To improve robustness with respect to parameter uncertainty, spectral energy is reduced for a range of frequencies surrounding the nominal natural frequency. An additional set of versine profiles are also constructed to permit motion at constant speed for velocity-limited systems. These shaped force profiles are incorporated into a simple closed-loop system with position and velocity feedback. The force input is doubly integrated to generate a shaped position reference for the controller to follow. This control scheme is evaluated on the MIT Cartesian Robot. The shaped inputs generate motions with minimum residual vibration when actuator saturation is avoided. Feedback control compensates for the effect of friction Using only a knowledge of the natural frequencies of the system to shape the force inputs, vibration can also be attenuated in modes which vibrate in directions other than the motion direction. When moving several axes, the use of shaped inputs allows minimum residual vibration even when the natural frequencies are dynamically changing by a limited amount.

The Synthesis of Stable Force-Closure Grasps

This thesis addresses the problem of synthesizing grasps that are force-closure and stable. The synthesis of force-closure grasps constructs independent regions of contact for the fingertips, such that the motion of the grasped object is totally constrained. The synthesis of stable grasps constructs virtual springs at the contacts, such that the grasped object is stable, and has a desired stiffness matrix about its stable equilibrium. A grasp on an object is force-closure if and only if we can exert, through the set of contacts, arbitrary forces and moments on the object. So force-closure implies equilibrium exists because zero forces and moment is spanned. In the reverse direction, we prove that a non-marginal equilibrium grasp is also a force-closure grasp, if it has at least two point contacts with friction in 2D, or two soft-finger contacts or three hard-finger contacts in 3D. Next, we prove that all force-closure grasps can be made stable, by using either active or passive springs at the contacts. The thesis develops a simple relation between the stability and stiffness of the grasp and the spatial configuration of the virtual springs at the contacts. The stiffness of the grasp depends also on whether the points of contact stick, or slide without friction on straight or curved surfaces of the object. The thesis presents fast and simple algorithms for directly constructing stable fore-closure grasps based on the shape of the grasped object. The formal framework of force-closure and stable grasps provides a partial explanation to why we stably grasp objects to easily, and to why our fingers are better soft than hard.

Compliance and Force Control for Computer Controlled Manipulators

Compliant motion occurs when the manipulator position is constrained by the task geometry. Compliant motion may be produced either by a passive mechanical compliance built in to the manipulator, or by an active compliance implemented in the control servo loop. The second method, called force control, is the subject of this report. In particular, this report presents a theory of force control based on formal models of the manipulator, and the task geometry. The ideal effector is used to model the manipulator, and the task geometry is modeled by the ideal surface, which is the locus of all positions accessible to the ideal effector. Models are also defined for the goal trajectory, position control, and force control.

Modeling Robot Dynamic Performance for Endpoint Force Control

This research aims to understand the fundamental dynamic behavior of servo-controlled machinery in response to various types of sensory feedback. As an example of such a system, we study robot force control, a scheme which promises to greatly expand the capabilities of industrial robots by allowing manipulators to interact with uncertain and dynamic tasks. Dynamic models are developed which allow the effects of actuator dynamics, structural flexibility, and workpiece interaction to be explored in the frequency and time domains. The models are used first to explain the causes of robot force control instability, and then to find methods of improving this performance.

Parallel Coupled Micro-Macro Actuators

This thesis presents a new actuator system consisting of a micro-actuator and a macro-actuator coupled in parallel via a compliant transmission. The system is called the Parallel Coupled Micro-Macro Actuator, or PaCMMA. In this system, the micro-actuator is capable of high bandwidth force control due to its low mass and direct-drive connection to the output shaft. The compliant transmission of the macro-actuator reduces the impedance (stiffness) at the output shaft and increases the dynamic range of force. Performance improvement over single actuator systems was expected in force control, impedance control, force distortion and reduction of transient impact forces. A set of quantitative measures is proposed and the actuator system is evaluated against them: Force Control Bandwidth, Position Bandwidth, Dynamic Range, Impact Force, Impedance ("Backdriveability'"), Force Distortion and Force Performance Space. Several theoretical performance limits are derived from the saturation limits of the system. A control law is proposed and control system performance is compared to the theoretical limits. A prototype testbed was built using permanenent magnet motors and an experimental comparison was performed between this actuator concept and two single actuator systems. The following performance was observed: Force bandwidth of 56Hz, Torque Dynamic Range of 800:1, Peak Torque of 1040mNm, Minimum Torque of 1.3mNm. Peak Impact Force was reduced by an order of magnitude. Distortion at small amplitudes was reduced substantially. Backdriven impedance was reduced by 2-3 orders of magnitude. This actuator system shows promise for manipulator design as well as psychophysical tests of human performance.

Trajectory and Force Control of a Direct Drive Arm

Using the MIT Serial Link Direct Drive Arm as the main experimental device, various issues in trajectory and force control of manipulators were studied in this thesis. Since accurate modeling is important for any controller, issues of estimating the dynamic model of a manipulator and its load were addressed first. Practical and effective algorithms were developed fro the Newton-Euler equations to estimate the inertial parameters of manipulator rigid-body loads and links. Load estimation was implemented both on PUMA 600 robot and on the MIT Serial Link Direct Drive Arm. With the link estimation algorithm, the inertial parameters of the direct drive arm were obtained. For both load and link estimation results, the estimated parameters are good models of the actual system for control purposes since torques and forces can be predicted accurately from these estimated parameters. The estimated model of the direct drive arm was them used to evaluate trajectory following performance by feedforward and computed torque control algorithms. The experimental evaluations showed that the dynamic compensation can greatly improve trajectory following accuracy. Various stability issues of force control were studied next. It was determined that there are two types of instability in force control. Dynamic instability, present in all of the previous force control algorithms discussed in this thesis, is caused by the interaction of a manipulator with a stiff environment. Kinematics instability is present only in the hybrid control algorithm of Raibert and Craig, and is caused by the interaction of the inertia matrix with the Jacobian inverse coordinate transformation in the feedback path. Several methods were suggested and demonstrated experimentally to solve these stability problems. The result of the stability analyses were then incorporated in implementing a stable force/position controller on the direct drive arm by the modified resolved acceleration method using both joint torque and wrist force sensor feedbacks.

Numerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in octupolar cell traps

This work presents detailed numerical calculations of the dielectrophoretic force in octupolar traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using an indirect implementation of the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that the full MST calculation is only required in the study of non-spherical particles.