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On Generating Safe Controllers for Discrete-Time Linear Systems

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Towards a 3g Crawling Robot through the Integration of Microrobot Technologies* Ranjana Sahai, Srinath Avadhanula, Richard Groff, Erik Steltz, Robert Wood, and Ronald S. Fearing Electrical Engineering and Computer Science Department University of California, Berkeley Berkeley, CA 94720 USA [email protected] or [email protected] * This work has been supported by the following grants: NSF DMI-0423153 and NSF DMI-0115091. Abstract - This paper discusses the biomimetic design and assembly of a 3g self-contained crawling robot fabricated through the integrated use of various microrobot technologies. The hexapod structure is designed to move in an alternating tripod gait driven by two piezoelectric actuators connected by sliding plates to two sets of three legs. We present results of both the kinematic and static analyses of the driving mechanism that essentially consists of three slider cranks in series. This analysis confirmed the force differential needed to propel the device. We then review various other microrobot technologies that have been developed including actuator design and fabrication, power and control electronics design, programming via a finite state machine, and the development of bioinspired fiber arrays. These technologies were then successfully integrated into the device. The robot is now functioning and we have already fabricated three iterations of the proposed device. We hope with further design iterations to produce a fully operational model in the near future. Index Terms – biomimetics, crawling microrobots, design and fabrication I. INTRODUCTION Currently in robotics, biomimetics and miniaturization are two common trends. From minimally invasive surgery instruments that are inspired by tapeworms [1] to miniature aircraft inspired by flies [2], scientists continue their quest to make even smaller robotic devices and, while doing so, increasingly look to nature for guidance. Unfortunately, designing and manufacturing these tiny structures are often limited by processes that are expensive and not easily accessible. Thus, the motivation behind the work presented here is the need to have suitable methods for easily prototyping such devices. In our chosen area of concentration, the centimeter and sub-centimeter-sized scale, we are looking to develop and integrate technologies that would allow this easy prototyping. Our ultimate goal will be to reduce these processes into a kit of components from which a variety of such prototype structures can be made in a relatively low cost fashion. As a step in this direction, this paper looks at combining various structure fabrication processes, actuators, and power electronics developed particularly for structures of this size in our own chosen biomimetic robot design, a 3g crawling robot. We discuss the design and assembly of this device, provide brief descriptions of the various integrated technologies, and, finally, give our results and conclusions from following this process. II. ROBOT DESIGN A. Background The development of a robot with legs as opposed to wheels (nature’s solution for adapting to various types of terrain) has been investigated as far back as 1940. Reference [3] provides a review of some of these various designs over the years. Some other designs of particular note from the point of view of biomimetic structures and terrain adaptability include Stanford’s SpinybotII (uses lessons learned from insect spines to design a robot capable of climbing various rough surfaces [4]), University of Michigan’s RHex (takes advantage of compliant legs that make a full rotation to achieve high terrain adaptability with no sensing [5]), and the hybrid leg and wheel motion of Case Western’s Mini-Whegs [6]. In terms of size, however, the robot we are building here more closely resembles efforts such as in [7] and [8] although our structure is larger than both these cases. Table 1 summarizes the features of our design with other legged or wheeled mechanisms on this scale. TABLE I COMPARISON OF VARIOUS MICROROBOTS Robot Mass Velocity Size Tethered Motion Sandia’s 28g 8.5 mm/s 6.35 mm No Wheeled Hollar’s Solar Powered Ant 10.2 mg 1.3 mm/s (design) 8.6mm No Not yet Ebefors 83 mg 6 mm/s 15mm Yes Legged EPFL’s Inchy Not listed 30 cm/s 25 mm No Wheeled Our design 3.1g 10 mm/s (design) 35mm No Not yet We should also note that from the two basic types of robotic structures, serial or parallel, we are focusing on flexure-based parallel mechanisms. Serial mechanisms have an open kinematic structure and are simple to design. However, several of their joints have to be actuated either through joint based actuators or through cables operated by ground-based motors. This limits their performance,dynamics and positioning accuracy. Parallel mechanisms based on closed kinematic chains, on the other hand, are free from these limitations since they can be operated by using only ground-based actuators. Since all the joints except the ground ones are passive, it is relatively simple to incorporate flexure joints in parallel mechanisms. This is desirable from our standpoint since flexure joints are easier to manufacture on the centimeter-size scale. B. Basic Structure The basic structure chosen for our particular crawler is shown in Fig. 1. Each leg is the familiar slider crank where the crank is extended to form the leg as shown. Further details of the leg mechanism are provided in a later section. To simplify the structure and reduce the number of actuators required, the six legs are broken into two sets of three coupled motions through the use of two linear slides. This produces a tripod gate as will be discussed in a later section. Finally, there is another four-bar structure to transfer the actuator motion to each of the slides. The three mechanisms (the leg, the slide, and the connection to the actuator) are basically just a series of three slider crank mechanisms. The kinematics of slider cranks has been worked out in several sources, such as in [9], so we shall not repeat the derivation here. Fig. 2, however, presents the results of such a kinematic analysis applied to the combined structure. It shows the motion the various components go through and the arc subtended by the foot. Fig. 3 shows the displacements of the actuator, the slide, and the foot (horizontal component) during this simulated motion. One can clearly see the


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