This paper considers interaction of the human arm with "virtual" objects simulated mechanically by a planar robot. Haptic perception of spatial properties of objects is distorted. It is reasonable to expect that it may be distorted in a geometrically consistent way. Three experiments were performed to quantify perceptual distortion of length, angle and orientation. We found that spatial perception is geometrically inconsistent across these perceptual tasks. Given that spatial perception is distorted, it is plausible that motor behavior may be distorted in a way consistent with perceptual distortion. In a fourth experiment, subjects were asked to draw circles. The results were geometrically inconsistent with those of the length perception experiment. Interestingly, although the results were inconsistent (statistically different), this difference was not strong (the relative distortion between the observed distributions was small). Some computational implications of this research for haptic perception and motor planning are discussed.

Abstract-Mechanical impedance is the dynamic generalization of stiffness, and determines interactive behavior by definition. Although the argument for explicitly controlling impedance is strong, impedance control has had only a modest impact on robotic manipulator control practice. This is due in part to the fact that it is difficult to select suitable impedances given tasks. A spatial impedance controller is presented that simplifies impedance selection. Impedance is characterized using "spatially affine" families of compliance and damping, which are characterized by nonspatial and spatial parameters. Nonspatial parameters are selected independently of configuration of the object with which the robot must interact. Spatial parameters depend on object configurations, but transform in an intuitive, well-defined way. Control laws corresponding to these compliance and damping families are derived assuming a commonly used robot model. While the compliance control law was implemented in simulation and on a real robot, this paper emphasizes the underlying theory.

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Notch hinges are flexural hinges used to make complex, precise mechanisms. They are typically modeled as single degree-of-freedom hinges with an associated joint stiffness. This is not adequate for all purposes. This paper computes the six degree-of-freedom stiffness properties of notch hinges using finite element methods. The results are parameterized in terms of meaningful design parameters.

Interactive control schemes, such as stiffness control and impedance control, are widely accepted as a means to actively accommodate environmental forces, but have not been widely applied. This is in part because well-known controllers are parametrized in a mathematically convenient, but nonintuitive way. “Spatial compliance control” is a Euclidean-geometrical version of compliance control that is parametrized in an intuitive way. A family of compliances is introduced with spatial transformation properties that simplify spatial reasoning aspects of compliance parameter selection. A control law is derived assuming that the robot consists of a serial linkage of rigid links actuated by variable-effort actuators.

This paper looks at spatio-geometric modeling of elastically coupled rigid bodies. Desirable properties of compliance families are defined (sufficient diversity, parsimony, frame-indifference, and port-indifference). A novel compliance family with the desired properties is defined using geometric potential energy functions. The configuration-dependent wrenches corresponding to these potential functions are derived in a form suitable for automatic computation.

This paper presents a rigorous, analytical framework for interactive control methods such as sti ness and impedance control. This paper does not present a novel synthesis method for robot control design. Rather, it presents a proper framework to analyse controllers for robots whose purpose is to interact energetically with the environment.First geometrical tools are introduced that are used in kinematic and dynamic analysis of the spatio-mechanical systems common in robotics.`Port behaviour' and`behavioural deviation' are then de®ned both intuitively and rigorously. The utility of this framework is demonstrated by a non-trivial example. Concepts of the behavioural approach are used. NomenclatureQ con®guration space X work space A actuator con®guration space U actuator signal input space M measurable variable space E euclidian Space T¤ X tangent bundle of X T ¤ X cotangent bundle of X T r;s X tensor bundle of type … r; s † T¤ X p tangent space of X at p 2 X T ¤ X p cotangent space of X at p 2 X T r;s X p tensor space of type … r; s † at p 2 X C a ne connection on X k C parallel w.r.t. connection C F free¯ow space E free e ort space pr … n † nth prolongatioñ W W port outcome space W extended port outcome space U universe of port outcomes B port behaviour T £W W

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