Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

An introduction to the Kalman filter

In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.

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An Introduction to the Kalman Filter

An image guided catheter navigation system for navigating a region of a patient includes an imaging device, a tracking device, a controller, and a display. The imaging device generates images of the region of the patient. The tracking device tracks the location of the catheter in the region of the patient. The controller superimposes an icon representing the catheter onto the images generated from the imaging device based upon the location of the catheter. The display displays the image of the region with the catheter superimposed onto the image at the current location of the catheter.

Navigation system for cardiac therapies

A Three Dimensional Structure (3DS) Memory (100) allows for physical separation of the memory circuits (103) and the control logic circuit (101) onto different layers (103) such that each layer may be separately optimized. One control logic circuit (101) suffices for several memory circuits (103), reducing cost. Fabrication of 3DS memory (100) involves thinning of the memory circuit (103) to less than 50 microns in thickness and bonding the circuit to a circuit stack while still in wafer substrate form. Fine-grain high density inter-layer vertical bus connections (105) are used. The 3DS memory (100) manufacturing method enables several performance and physical size efficiencies, and is implemented with established semiconductor processing techniques.

Three dimensional structure memory

Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the 19th century - a feat he celebrated by carving the founding equations into a stone bridge - mathematicians and engineers have been fascinated by these mathematical objects. They are used in applications as various as describing the geometry of space-time, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J.B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations.

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Quaternions and rotation sequences : a primer with applications to orbits, aerospace, and virtual reality

A field (e.g., a magnetic field) which nutates about a pointing vector is used to both track or locate an object in addition to determining the relative orientation of this object. Apparatus for generating such a field includes mutually orthogonal coils and circuitry for supplying an unmodulated carrier, hereafter called DC signal, to one coil and an AC modulated carrier signal, hereafter called AC signal, to at least one (usually two) other coil, such that the maximum intensity vector of a magnetic field produced by the currents in the coils nutates about a mean axis called the pointing vector direction of the field. The generated field is sensed in at least two orthogonal directions at the object to be tracked and whose orientation is to be determined. The sensed signals provide an indication of the direction and orientation of the object relative to the coordinates of the generating means.

Object tracking and orientation determination means, system and process

An electromagnetic field which nutates about a pointing vector is used to both track or locate a remote object in addition to determining the relative orientation of the object. Apparatus for generating such a field includes mutually orthogonal dipole radiators, defining a reference coordinate frame, and circuitry for supplying excitations, such that the maximum intensity vector of a vector field produced by these excitations in the radiators nutates about a mean axis or axis of nutation which is called the pointing vector direction of the field. A pointing coordinate frame has the x-axis coincident with the pointing vector and the y-axis in the x-y plane of the reference frame. Mutually orthogonal sensors at the object sense the field and establish a sense coordinate frame, which can be coincident with the coordinate frame of the remote body. Coordinate transformer means, system and process are used in connection with determining the pointing and angular position of the sense frame with respect to the reference frame. A first error signal relating the sense frame to the pointing frame is transformed into a second error signal relating the sense frame to the reference frame. This second error signal is used to generate the three Euler angles defining the orientation of the sense frame relative to the reference frame and to generate the pointing angles defining the translation of the sense frame from the reference frame. Means, system and process are described, thus, capable of continuously measuring five independent angles through the use of one field generating means, one field sensing means at the remote object, and signal processing means. Two of the angles specify the direction to, or location of, the remote object and the remaining three angles define the angular orientation of the remote object, the angles defining the sense frame with respect to the fixed reference coordinate frame of the field generating means.

Tracking and determining orientation of object using coordinate transformation means, system and process

A method and apparatus is provided for determining remote object orientation and position with an electromagnetic coupling. A plurality of radiating antennas are provided for radiating electromagnetic energy. Each of the radiating antennas have independent components for defining a source reference coordinate frame. A transmitter is provided for applying electrical signals to the radiating antennas for generating a plurality of electromagnetic fields. The signals are multiplexed so that the fields are distinguishable from one another. A plurality of receiving antennas are disposed on a remote object for receiving the transmitted electromagnetic fields. The receiving antennas have a plurality of independent components for detecting the transmitted electromagnetic fields and defining a sensor reference coordinate frame. An analyzer is provided for receiving the output of the receiving antennas and converting the components of the transmitted electromagnetic fields into remote object position and orientation relative to the source reference coordinate frame. The analyzing means includes means for processing the components of the electromagnetic fields in an uncoupled manner into remote object position and remote object orientation. The processing technique provides an uncoupled, noniterative, closed form solution for both position and orientation which is fast and includes no discontinuities. The processing speed is enhanced with a parallel processing technique which provides for simultaneous determination of the position and orientation parameters. The speed of the processing technique is further enhanced by provision of quaternion solutions for position and orientation. A new virtual real-time binocular computer graphics application is provided which is particularly adapted for generating the cockpit view of an aircraft pilot in a flight simulator.

Method and apparatus for determining remote object orientation and position

A field (e.g., a magnetic field) which nutates about a pointing vector is used to both track or locate an object in addition to determining the relative orientation of this object. Apparatus for generating such a field includes mutually orthogonal coils and circuitry for supplying an unmodulated carrier, hereafter called DC signal, to one coil and an AC modulated carrier signal, hereafter called AC signal, to at least one (usually two) other coil, such that the maximum intensity vector of a magnetic field produced by the currents in the coils nutates about a mean axis called the pointing vector direction of the field.

Jack Kuipers

Papers

Quaternions and rotation sequences : a primer with applications to orbits, aerospace, and virtual reality

Object tracking and orientation determination means, system and process

Tracking and determining orientation of object using coordinate transformation means, system and process

Method and apparatus for determining remote object orientation and position

Apparatus for generating a nutating electromagnetic field