Robotics has been supplemented by the growing body of techniques associated with formal languages. One remaining challenge for bottom-up formal methods is to provide effective abstractions to their top-down counterparts in order to achieve a seamless integration. This paper describes our efforts to tackle this challenge in the domain of spatial behavior. Our general goal is to understand principles involved in the formation of hierarchic representations that can greatly simplify the control and planning tasks. We propose that this hierarchy be built from the bottom-up according to formal language principles, while incorporating principles from dynamical systems theory. The general idea is that relevant interactions between the agent's dynamics, task and environment are manifested as patterns. Compared to other approaches these patterns are not based on abstract, high-level constructs but convey a form of meaning that inherently ties the system's dynamics, environment and task characteristics. Understanding the natural principles underlying hierarchic organization of behavior is a fundamental step toward developing formal languages dealing with dynamical systems. It can be applied to help understand spatial intelligence and eventually help design more versatile and adaptive agents.

A number of haptic devices have recently become available on the commercial market, and these devices are becoming common not only in research but in consumer use as well. In this paper, a new parallel mechanism, referred to herein as DELTA-R (meaning DELTA-Redundant, formerly referred to as DELTA-4) is proposed for a new haptic device having high-quality force display capability and operability. DELTA-R allows three-degree-of-freedom (DOF) translational motions. The key features of DELTA-R, as compared with conventional parallel mechanisms, are redundant actuation, a smaller footprint, a larger working area, and improved access to the end effector. The prototype is equipped with a 3-DOF rotation mechanism, the center of motion of which is located on the wrist position of the operator. An evaluation test of the force display was conducted using a prototype of the proposed mechanism. This paper describes the kinematic design, kinematic modeling, kinematic analysis, prototype implementation, and evaluations.