Parallelism in Manipulator Dynamics

This paper addresses the problem of efficiently computing the motor torques required to drive a lower-pair kinematic chain (e.g., a typical manipulator arm in free motion, or a mechanical leg in the swing phase) given the desired trajectory; i.e., the Inverse Dynamics problem. It investigates the high degree of parallelism inherent in the computations, and presents two "mathematically exact" formulations especially suited to high-speed, highly parallel implementations using special-purpose hardware or VLSI devices. In principle, the formulations should permit the calculations to run at a speed bounded only by I/O. The first presented is a parallel version of the recent linear Newton-Euler recursive algorithm. The time cost is also linear in the number of joints, but the real-time coefficients are reduced by almost two orders of magnitude. The second formulation reports a new parallel algorithm which shows that it is possible to improve upon the linear time dependency. The real time required to perform the calculations increases only as the [log2] of the number of joints. Either formulation is susceptible to a systolic pipelined architecture in which complete sets of joint torques emerge at successive intervals of four floating-point operations. Hardware requirements necessary to support the algorithm are considered and found not to be excessive, and a VLSI implementation architecture is suggested. We indicate possible applications to incorporating dynamical considerations into trajectory planning, e.g. it may be possible to build an on-line trajectory optimizer.

TEMPEST: A Template Editor for Structured Text

TEMPEST is a full-screen text editor that incorporates a structural paradigm in addition to the more traditional textual paradigm provided by most editors. While the textual paradigm treats the text as a sequence of characters, the structural paradigm treats it as a collection of named blocks which the user can define, group, and manipulate. Blocks can be defined to correspond to the structural features of he text, thereby providing more meaningful objects to operate on than characters of lines. The structural representation of the text is kept in the background, giving TEMPEST the appearance of a typical text editor. The structural and textual interfaces coexist equally, however, so one can always operate on the text from wither point of view. TEMPEST's representation scheme provides no semantic understanding of structure. This approach sacrifices depth, but affords a broad range of applicability and requires very little computational overhead. A prototype has been implemented to illustrate the feasibility and potential areas of application of the central ideas. It was developed and runs on an IBM Personal Computer.