Design and Control of Human Powered Swimming Machines

    Principal Investigator:  Perry Y. Li

    Mechatronics and Intelligent Control Laboratory

    Swimming machineAbstract

    This  project is concerned with the design and control of a ``human powered swimming machine". The requirements of the machine is to utilize human power optimally, by taking into account the biomechanical features of the human, in order to generate aquatic locomotion. Swimming is achieved by mimicking piscine swimming - i.e. by the heaving and pitching of a tail fin so as to generate configuration of vortices that give rise to efficient propulsion. To be effective, the machine must be capable interacting with the human and with the surrounding water appropriately. For instance, it may be required to store energy from the water and from the human from one instance and release it at opportune moments. The broader context of this research is to elucidate the fundamental principles in the design and control of machines that must cooperate and interact with their environment in dynamic and energy efficient manners. Other applications that fall into this category include the design of prosthesis for amputees.
     

    Overview and background

    The proposed project will investigate the issues in the design and control of a ``human powered swimming machine". The broader context of this research is to elucidate the fundamental principles in the design and control of machines that must cooperate and interact with their environments in dynamic and energy efficient manners. The objectives for the proposed swimming machine are that it should utilize human power efficiently to generate aquatic locomotion and that it should be highly maneuverable. Such a machine has to  interact simultaneously with two environments: the human who serves as the energy source on the one hand, and the surrounding water with which the machine has to exchange momentum for propulsion on the other. The interaction between the machine and the human should enable the human to generate the maximum power at minimal effort. This requires that the machine be aware of, and can take advantage of, the biomechanical characteristics of the human.  The machine's interaction with the surrounding water     must create the necessary momentum for propulsion and maneuvering by consuming as little energy as possible. Since the surrounding water may also carry energy, the machine should, whenever possible, capture and utilize this energy to its advantage. This suggests that the operation of the swimming machine should take into account the dynamics of the aquatic environment, and be able to sense and react to the hydrodynamics appropriately. An example of other practical machines that must utilize human power efficiently and dynamically interact with its environment is the passive artificial prosthesis, for example, for above knee lower extremity amputees. These systems rely exclusively on the power generated by the intact musclulatures of the amputee for terrestial locomotion. Beside having to generate  the swing / stance gait sequence, the prosthesis must be capable of storing energy during stance and releasing it at toe-off. Any improvement in the utilization of the human power in this case increases the mobility of the patient and thus impact positively on the patient's quality of life.

    Biomechanical Efficiency

    The biomechanical characteristic most relevant to our research is the force-velocity relation \cite{McMahon} or the Hill relation in honor of its discover A.V. Hill \cite{Hill}, of the muscular-skeletal system. The force-velocity relation states that for a particular level of
    neurological activation of a muscle, i.e. the effort level, the force of contraction decreases monotonically as the speed of shortening of the muscle increases. Since the total mechanical power generated by the muscle is the product between the contraction force and the shortening speed,  the mechanical power generated by the muscle will be maximized for a given effort level, if the muscle is made to contract at the specific ``optimal speed". The readers will recognize that the use of gears on bicycles is aimed towards using the muscles at approximately this optimal speed to increase the biomechanical efficiency. Although the concept of operating at the ``optimal speed for maximum power" can be extended to multiply jointed motions that involve many muscles, such as cycling, it must be noted, however, that the optimal velocity depends strongly both on the joint configurations, and the specific subject. Therefore, a highly subject dependent relationship between the force, velocity, and configuration (Hill surface for short) is needed to determine the ``optimal velocity profile", which is the optimal velocity  at each configuration. Recently, this ``optimal velocity profile" concept was applied to the design of a novel class of exercise machines that are more efficient for the users. In that research \cite{LiHorMech97,LiHorMech97b}, we developed on-line adaptive control algorithms that are capable of identifying the Hill surface of the subject, determining the ``optimal velocity profile" for the subject, and controlling the exercise resistance in real time, so that the user always exercises at his/her ``optimal velocity profile". Using the patented concept and algorithms, each individual user can thus accomplish a set amount of exercise in the shortest amount of time!! An extensive clinical study \cite{SHACC97} has conclusively proven this result.  The study in \cite{SHACC97} also showed that subjects who exercise at the ``optimal velocity profile" do not fatigue faster than otherwise. These results conclude that by following the  ``optimal velocity profile" concept, human subjects can generate more work by maximizing their power output over long duration.

    Our success in designing exercise machines that can effectively  extract power and work from {\em individual users} leads us to believe that the same concept should and can be applied to the design of human powered machines - i.e. machines that utilize human power for useful work, for example, for aquatic locomotion as in the present project. Abstractly speaking, an efficient human powered machine must present to the human a nonlinear mechanical impedance that matches the biomechanical impedance of the human.

    Hydrodynamic efficiency

    An energetically efficient means of interaction between a mechanism and its surrounding water to generate locomotion is suggested by the way aquatic animals swim. Extensive studies of the how aquatic animals swim began with Gray's pioneering work in 1935 on the energetics of dolphins swimming \cite{gr:hfs_uce}. In this study, the force required to propell a  dolphin shaped body at typical swimming speeds, is compared to the muscle strength of the animal. Surprising, it was shown that the force required is seven fold that of what is available from the muscles of the dolphin.  This result, known as the Gray paradox, sparked much research activities amongst zoologists, scientists, mathematicians and engineers alike. The key findings of these research reveal that aquatic animals can reduce their effect drag by manipulating the vortices shed behind them. By controlling the heaving and pitching movements of their tail fins, configurations of the vortices advantageous for propulsion are created \cite{tf:sci_mit}. The observed configuration behind a fish or dolphin is similar to that of a Karman Street seen behind a bluff  body, except that the polarity of the vortices are reversed. Unlike a Karman Street behind a bluff body, which generates a high speed jet in the direction of the body relative to the rest of the stream (and hence a drag force), the reverse Karman Street forms a jet in the posterior direction. This high speed jet generates a powerful propulsive thrust that propel the animal forward. The thrust afforded by this propulsion mechanism has been correlated to the Strouhal number
    (St) which is a function of the frequency of oscillation $(Hz)$  and the width of wake \cite{ba:ocfh_mit,go:avc_mit,tf:otd_mit}. Experimental findings show that efficiency is maximized when $St \approx 0.25$. This result correlates well with $St$ observed in aquatic animals \cite{go:avc_mit}. Research that utilize heaving and oscillating foil for propulsion has mainly focused on actuating the foil in an {\em openloop} fashion, so that the heaving and pitching movements are periodic and the Strouhal number $St \approx 0.25$.

    When one computes the power necessary to actuate the foil periodically as suggested by piscine locomotion,  it is found that  the actuator does not perform positive work throughout the period. Instead, the foil spends a good portion of the period in a deccelerative mode: i.e. the actuators on the foil must absorb the braking energy during this portion. Indeed, Harper et al. \cite{ha:mdsd_bost} showed, using a model developed using the Lighthill's linear aerofoil theory \cite{lh:nof_rae,lh:aap_uc_e}, showed that overall energy efficiency can be improved by placing a mechanical springs in parallel with the actuators of the foil, it is possible to capture and store the braking energy to be released when the foil is in the positive work cycle. However, they also showed that if the springs are not well chosen, unstable dynamic coupling between the surrounding water and the flapping foil can result.

    Research in efficient propulsion mechanism using flapping foil has been significantly lacking in several aspects. First, although the Strouhal number is a good guide to how the foil should be actuated, it only provides information on the actuation frequency.  A model based computational method for an optimal periodic profile of the movement has not been established. Secondly, it is known that some fish can use very little energy to swim upstream. The conjecture is that the fish can capture and utilize the energy in the stream. Specifically, if the stream has some vorticity (generated behind bluff bodies),  the fish may be able to generate opposing vortices so as to generate thrust inducing water jets, or other hydrodynamic forces to execute turns or other maneuvers. This intriging possibility
    has not been investigated in artificial propulsion system. To realize this possibility,  closed loop control,  in the sense of measuring (or estimating) the vorticity in the water and then moving the foil accordingly must be utilized. This aspect of work, and indeed the estimation of vorticity as far as we know  has not  been attempted.

    Click here for more pictures of the UMn-Human powered swumming machine.

    Graduate student(s) working on this project:

    • Saroj Saimek
    • Brad Augustine

    Publications to date:

    • S. Saimek and P. Y. Li, "Motion Planning and Control of a Swimming Machine", Proceedings of the 2001 American Control Conference, Arlington VA, June 2001.
    • P. Y. Li and S. Saimek, "Modeling and Estimation of Hydrodynamic Potentials", 38th IEEE Conference on Decision and Control, Dec. 1999

    Sponsor:
       
      University of Minnesota Grant-in-Aid Program