Dan Reznik

A flat rigid plate is a universal planar manipulator

We consider the problem of parallel part manipulation, i.e., the simultaneous position and orientation control of one or more parts in a bounded region of the plane. We propose a novel, minimalist device, based on a single horizontally-vibrating flat plate. We show that a closed rigid motion of the plate, involving its 3 DOF, can be computed which produces desired average forces at a finite number of points, e.g., parts locations. This implies that one or more parts can follow independent trajectories simultaneously, as they interact with a single vibrating plate. This is in sharp contrast with more complex designs such as massively-parallel actuator arrays and/or prehensile manipulation. Dynamic simulation is used to test the current method in two parallel part manipulation examples. A prototype of the device has been built with inexpensive parts; physical implementation of the proposed method is currently underway.

Building a Universal Planar Manipulator

Distributed manipulation devices make use of a large number of actuators, organized in array fashion, to manipulate a small number of parts. Inspired by minimalism we look at a complementary question: can a device with few degrees of actuation freedom be used to flexibly manipulate a large number of parts? In previous publications we have shown that a single horizontally-vibrating plate is just such a device. This suggests that actuator count can be traded for control complexity. In this paper we review our theory of minimalist manipulation and describe implementation solutions towards a working prototype.

Dynamic simulation and virtual control of a deformable fingertip

An efficient computational model for the dynamics of a deformable robot fingertip is presented. The dynamic model is based on a discretization of the fingertips volume into a lattice of masses locally interconnected by damped springs. The lattices parameters are adjusted in correspondence with bulk properties of the fingertips deformable material (rubber). In the task studied, the fingertip moves toward a rigid flat surface, contacts it, and presses against it. This motion is commanded by an external feedback controller which communicates with the dynamic model through a virtual control interface: The controller applies forces and torques to the dynamic model and the dynamic model responds in real-time with position/velocity/force feedback information. In this fashion, the controller interacts with the fingertips model in the same way it would interact with the actual physical system. This type of paradigm is envisioned as a prototyping/testing tool in the design of control systems for deformable objects as well as for applications involving the haptic (i.e., sensorially realistic) interaction between a human and a virtual (deformable) object. Graphical snapshots of a real time simulation of the task under study are presented which reveal the physical and computational plausibility of the model.

Motion Planning With Uncertainty For Highly Redundant Kinematic Structures I. "Free Snake" Motion

A strategy is described for on-line motion ]planning with incomplete information for a special type of highly redundant planar robot kinematics, called a snake. The snake consists of many simple serially connected links and has on-line sensing which provides information about its immediate surroundings. The task is to move the snake head point from its starting position to a known target position while generating collision-free motion for the rest of the snake body, in an environment filled with unknown obstacles of arbitrary shape. Computationally, the procedure is linear in the number of the snake Links; it is highly efficient and can be easily realized in real time. The procedure makes use of a unit motion far a single link based on the tractriz curve. This choice results in automatically achieving a “natural” motion distributed continulously and asymmetrically along the snake body - the joint displacements tend to ‘“die out” in the direction from the head to the tail. The generated path possessies an optimality property - the instantaneous total displacement of all the links/joints is minimum.