|A Lamprey-Based Undulatory Robot|
The swimming behavior of fishes ranges in organization from anguilliform ( relying on lateral axial undulations) to carangiform (relying on a flapping tail and/or fins). Anguilliform locomotion is common in eels and lamprey. We have developed a multi-media analytical system for reverse kinematic analysis of lamprey swimming (Ayers and Fletcher, 1990; Ayers, 1992). Anguilliform swimming results from propagation of flexion waves from the anterior region of the body to more caudal regions (see below). During anguilliform locomotion, the propagation time of the waves from nose to tail is equal to the period of the undulations so that the body axis typically exhibits an "S" shape.
Head on view of swim initiation
Top view of swim initiation
Propagating flexion waves alternate on the two sides to generate undulations. The amplitude and timing of the axial undulations are controlled independently (Ayers, 1989). Swimming behavior is controlled on a flexion wave by flexion wave basis. Turning and other maneuvering actions are mediated by modulation of the amplitude individual flexion waves .
|Generation of swimming thrust. The upper panel undicates a reverse animation of a sequence of undulation. The middle panel indicates the position of lateral flexions in successive frames of the video of lamprey swimming behavior. The lower panel indicates the instantaneous thrust in grams monitored with a strain gauge tethered at 25% of body length.|
The thrust generated during anguilliform swimming is pulsatile. Peaks of thrust are generated as flexion waves propagate to ~65% of body length and are correlated with maximal unbending of the body axis. Our working hypothesis is that the magnitude of thrust is regulated by modulation of axial stiffness by coactivation of musculature on the two sides of the body. Control of axial stiffness is necessary to adapt the speed of locomotion from low search speeds to more rapid persuit behavior Our robot concept includes this capability.
|Overall organization of undulation controller. Segmental oscillators are connected by contralateral and ipsilateral coordinating elements. The oscillators in turn activate linear actuators which flex different regions of the body axis.|
Numerous physiological studies have demonstrated that undulatory locomotion is generated by segmental central pattern generators (Grillner and Wallen, 1984) which are coordinated by contralateral and ipsilateral coordinating systems (Fig. 4). The central pattern generators in turn activate motor neurons which are recruited in order of size to grade the intensity of contractions and the resultant lateral flexions (Grillner and Kashin, 1976).
|Activation patterns of segmental actuators during slow and rapid swimming. Each trace in the two panels indicates the activity status of different quartile actuator wires|
The necessary control signals are easily generated with a finite-state machine organized into command system, coordinating system, central pattern generator components (Ayers and Crisman, 1992). In this architecture, oscillator and recruiter components modulate the timing and amplitude respectively of the actuator control signals. We have implemented such a controller for both ambulatory robot (Ayers, Crisman and Massa, 1993).
We employ shape memory metal wires as linear actuators to mediate axial undulations. Nitinol wires of diameters as small as 50Á can generate tensions of up to 30 grams. Arrays of such wires are activated by a neuronal network-based controller to generate undulatory movement by sequentially activating flexions over different body regions.
Development of this robot is an ambitious undertaking and we need to start with experiments on a laboratory model and proceed to more refined implementations. The final robot will consist of a rubber body form molded on a flexible polyurethane strip. An anterior compartment will contain sensors, the processor, batteries and signal control logic. The controller is implemented by a sequential processor which sets and clears digital output signals based on the state of the controller.
The actual control signals may strobed through a serial line to a set of shift registers, each bit of which gates a transistors which controls current to the actuators. Thus the actuator control signals are regularly reset at the time of state changes in the controlling program.
The body of the robot is composed of a flexible polyurethane strip which has an array of Nitinol¬ wires affixed on each side. The wire arrays are staggered along the body axis so that the most anterior and posterior wires do not overlap. This allows the body to flex at any point and for flexion waves to propagate. The rod and Nitinol¬ array are encased in a molded rubber form. During preliminary testing we have determined that the cooling by a surrounding water or oil bath is adequate to permit rapid wire relaxation and undulations at up to 4 hz.
The undulation controller generates patterns of activation of elements of the nitinol wire arrays which feature a rostro-caudal phase lag and contralateral alternation. These patterns of activation are achieved with the finite state machine. Each element of the Nitinol array is controlled by a separate oscillator and recruiter component. Regulation of thrust can be achieved, in principle by modulation of the spatial range of contraction mediated by the Nitinol¬ actuators. Modulation of the spatial range can be achieved by providing current at different distances along the wire relative to a grounded end.
The robot is designed to be neutrally buoyant. The system is constructed so that the center of gravity in the roll plane is quite ventral and the axis is slightly positively buoyant toward the nose. Given these characteristics, increases in thrust will propel the robot toward the surface.
We are continuing studies in collaboration with Dr. William Vorus which combine the above motor systems analysis, hydrodynamics analysis and robotics to synthesize an undulatory robotic system which relies on biologically-based controllers to mediate efficient wakeless propulsion. We have used hydrodynamic analysis to demonstrate that such undulatory propulsion is wakeless and of high efficiency when compared tail flapping locomotion and are comparing this analysis with experimental findings in lamprey. As described above, this mode of propulsion can be readily realized in a simple undulatory actuator which relies on shape memory alloys to generate axial contractions.
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