For redundant robot kinematics with a degree of redundancy 1 a self-motion vector field is examined whose equilibrium points lie at singular configurations of the kinematics, and whose orbits determine the self-motion manifolds. It is proved that the self-motion vector field is divergence-free. Locally, around singular configurations of corank 1, the self-motion vector field defines a 2-dimensional Hamiltonian dynamical system. An analysis of the phase portrait of this system in a neighbourhood of a singular configuration solves completely the question of avoidability or unavoidability of this configuration. Complementarily, sufficient conditions for avoidability and unavoidability are proposed in an analytic form involving the self-motion Hamilton function. The approach is illustrated with examples. A connection with normal forms of kinematics is established.

This paper describes an efficient and fast algorithm for finding the minimum distance between two convex polyhedrons in a three dimensional space. To obtain the minimal distance, the proposed computational scheme is based on a direct approach to minimizing the distance function which produces a succession of optimal search directions along object boundaries. This algorithm combines the gradient projection method'; and an additional optimal search direction when the gradient projection method leads to a zigzagging phenomenon. In this case, the additional optimal search direction accelerates significantly the convergence of the process. Extensive numerical experiments with convex polyhedra show the performance of this algorithm when compared with that of previous approaches. The proposed algorithm may be very helpful in solving the computation of minimal distance between a pair of convex sets, the collision detection problem or to track the closest points of moving convex objects.

We have designed a robotic arm based on a double parallel four bar linkage to act as an assistant in minimally invasive surgical procedures. The remote center of motion (RCM) geometry of the robot arm kinematically constraints the robot motion such that minimal translation of an instrument held by the robot takes place at the entry portal into the patientApos;s body. In addition to the two rotational degrees of freedom comprising the RCM arm, distal translation and rotation are provided to manoeuver the instrument within the patient's body about an axis coincident with the RCM. An XYZ translation stage located proximal to the RCM arm provides positioning capability to establish the RCM location relative to the patients anatomy. An electronics set capable of controlling the system, as well as performing a series of safety checks to verify correct system operation, has also been designed and constructed. The robot is capable of precise positional motion. Repeatability in the ±10 micron range is demonstrated. The complete robotic system consists of the robot hardware and an IBM PC-AT based servo controller connected via a custom shared memory link to a host IBM PS/2. For laparoscopic applications, the PS/2 includes an image capture board to capture and process video camera images. A camera rotation stage has also been designed for this application. We have successfully demonstrated this system as an assistant in a laparoscopic cholecystectomy. Further applications for this system involving active tissue manipulation are under development.

We consider the problem of sensor-based motion planning for a three-dimensional robot arm manipulator operating among unknown obstacles. When every point of the robot body is subject to potential collision. The corresponding planning system must include these four basic components: sensor hardware; real-time signal/sensory data processing hardware/software; a local step planning subsystem that works at the basic sample rate of the arm; and finally, a subsystem for global planning. The arm sensor system developed at Yale University presents a proximity sensitive skin that covers the whole body of the arm and consists of an array of discrete active infrared sensors that detect obstacles by processing reflected light. The sensor data then undergoes low level processing via a step planning procedure, which converts sensor information into local normals at the contact points in the configuration space of the robot. This paper presents preliminary results on the fourth component, a real-time algorithm that realizes the upper, global level of planning. Based on the current collection of local normals, the algorithm generates preferable directions of motion around obstacles, so as to guarantee reaching the target position if it is reachable. Experimental results from testing the developed system are also discussed.

A method has been developed for accurately determining the differential movement of known objects from multiple camera views. The method has been applied to a robot System to find the repeatability and accuracy of the robot in both rotational and translational terms and also for tracking an object using visual feedback.

A SCARA type direct-drive robot which can be used in the assembly operation of printed circuit boards was designed and manufactured with graphite fiber epoxy composite material. The optimum stacking angle of the graphite fiber which gives the minimum deflection of the composite robot arm was calculated by the energy method and the manufacturing method of the box-type cross section of the robot arm with composite materials was developed.

In order to compare the dynamic characteristics of the composite material robot arm with a conventional material robot arm, an aluminum robot arm which has the same dimensions and thickness of the composite robot arm was manufactured.

The static and dynamic characteristics of the composite material robot arm such as static deflection, natural frequency and damping as well as weight saving were considerably improved compared to those of the aluminum robot arm.

Part 1 of the paper* was concerned with the Jacobian of serial robot-arms and its matrix of cofactors; part 2 emphasizes the end-effector's velocity characteristics as affected at special configurations. The displacement about a ‘fixture-point’ is extended dually to a ‘fixture-plane’, and then to a ‘fixture-line’. These fixture-elements serve to highlight the prolixity of special configurations. Reciprocal screws lead to a complete survey of how the end-effector can ‘twist’ when one freedom is lost; extension to loss of more freedoms is explained. Then the fixture-elements are given elementary displacements that allow common requirements to be studied with the minimum of complications. Further investigation is thought to have promise for robot-control.

This paper proposes a fast tracking error control method for a mobile robot with two differentially driven wheels. The tracking error between reference state and current state is transformed to the required displacement changes of each drive wheel by a wheel Jacobian. The major objective of this paper is to propose a control method for eliminating the tracking error quickly by controlling two independent driving wheels at the same time. To avoid long computational requirements of a Cartesian-based control, a kinematic model of the vehicle and co-ordinate system are introduced. Several simulation results are presented using this method. The fast tracking error control method proposed is mainly hardware-independent and Hence can be applied to various kinds of mobile robots which have two differentially driven wheels. The method was implemented on an experimental vehicle, WCVS, The experimentation shows a performance suitable for practical applications.