© 2002 by The Society for Integrative and Comparative Biology
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Low Impedance Walking Robots1
1 Franklin W. Olin College of Engineering, 1735 Great Plain Avenue, Needham, Massachusetts, 02492-1245
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For both historical and technological reasons, most robots, including those meant to mimic animals or operate in natural environments,3 use actuators and control systems that have high (stiff) mechanical impedance. By contrast, most animals exhibit low (soft) impedance. While a robot's stiff joints may be programmed to closely imitate the recorded motion of an animal's soft joints, any unexpected position disturbances will generate reactive forces and torques much higher for the robot than for the animal. The dual of this is also true: while an animal will react to a force disturbance by significantly yielding position, a typical robot will greatly resist.
These differences cause three deleterious effects for high impedance robots. First, the higher forces may cause damage to the robot or to its environment (which is particularly important if that environment includes people). Second, the robot must acquire very precise information about its position relative to the environment so as to minimize its velocity upon impact. Third, many of the self-stabilizing effects of natural dynamics are "shorted out"4 by the robot's high impedance, so that stabilization requires more effort from the control system.
Over the past 5 yr, our laboratory has designed a series of walking robots based on "Series-Elastic Actuators" and "Virtual Model Control." Using these two techniques, we have been able to build low-impedance walking robots that are both safe and robust, that operate blindly without any model of upcoming terrain, and that add minimal control effort in parallel to their self-stabilizing passive dynamics. We have discovered that it is possible to achieve surprisingly effective ambulation from rather simple mechanisms and control systems. After describing the historical and technological motivations for our approach, this paper gives an overview of our methods and shows some of the results we have obtained.
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INTRODUCTION |
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Robots are starting to walk, moving beyond the factory floor and into natural environments.
Practical walking robots will probably first be used in the military, helping soldiers gather information, distract the enemy and avoid harm. Such robots will also be helpful in civil disaster relief and the scientific exploration of hazardous sites on earth, in space, and on other planets and moons. As costs come down, walking robots will find a place in our homes, improving the quality of our lives, particularly for those of us that are aged, infirm, or just tired of housekeeping.
Robots can also be a boon for biomechanics researchers. Because robots are much easier to instrument and modify than animals, they are wonderful models for verifying biomechanical theories and can occasionally even uncover biomechanical phenomena not previously discovered from animal observation or experiment. In our laboratory, for example, students have used robotic models to discover that the passive stiffness of a gymnast's extended arms during a layout somersault stabilizes, without any further control, rotation about the intermediate axis of inertia (Playter, 1994
; Playter and Raibert, 1994); that a curved foot and a little vertical damping is enough to stabilize hopping or running with only a fixed speed motor, crank, and spring (and no other control) (Ringrose, 1997); and that the limit to walking speed on earth is due not to the Froud number, as is commonly emphasized in biomechanics texts (McMahon, 1984), but rather to the limited velocity of leg swing due to the greatly increased power required to drive legs not connected to the ground at frequencies much higher than passive resonance (Pratt, 2000).
It all sounds wonderful, yet how a walking robot should be constructed and programmed to be as mobile as, say, a Seeing Eye dog, is still an open question. A number of walking robots have been built, including the most advanced walking bipedal robot by the Honda Corporation (Hirai et al., 1998). But despite the extraordinary engineering these robots represent and the impressive demonstrations they provide, their motions are mostly scripted and still look somewhat unnatural. They are generally not trusted to interact with people and poor handling of unexpected disturbances has limited them to well-known environments. Why is this so? Experiments in our laboratory and others (de Lasa and Buehler, 2001), have led us to believe that a significant handicap of current biomimetic robots is their typically high impedance actuators and control systems. The impedance we refer to is a measure of how unplanned variations to position, movement, or acceleration caused by the outside world are resisted (i.e., impeded) by a joint or set of joints intent on following a specific trajectory. Impedances may be simple (as in the case of a spring) or complex (as in the case of a mass or damper), but in all cases a high impedance joint greatly resists the influence of external forces, and is thus "stiff," while a low-impedance joint allows external forces to influence its movement easily, and is thus "soft."
The Honda robot, for example, uses a mode of control (Zero-Moment Point Control (Vukobratovic and Juricic, 1969)) that requires the robot to accurately obey precisely calculated trajectories, modified only by a few force sensors in the ankles (Hirai et al., 1998). This is a high impedance solution.
Evidence from the natural world, by contrast, shows that natural impedances in animals are quite low. For example, human arms trying to follow trajectories despite disturbances display an impedance on the order of 50 Nm/rad (Gomi and Kawato, 1997). This means that a sideways force on the order of 9.8 Newtons (1 kgf or 2.2 lbf) applied perpendicular to the wrist will deflect a human forearm (e.g., 0.3 m long) held close to the body by around 3 degrees, despite the best efforts of the subject to keep the position of the wrist fixed relative to the body. Vertical stiffness during running is on the order of 10 kN/m (Farley et al., 1993), e.g., if a runner is loaded with 98 Newtons (10 kgf or 22 lbf), they will sink down, on average, by about 1 cm. These impedances are remarkably low (i.e., soft), especially when compared to typical position-controlled robots, whose low frequency actuator impedance is nearly infinite due to the presence of integrative terms in feedback loops (or which use such high proportional feedback gain that the actuators do not perceptibly deflect even at maximum loads). The stiffness of such robots is dictated by their structural material, typically a very stiff metal or composite, and their structural geometry (typically circular or square in cross-section, for maximum stiffness). The Honda robot's joints do have some rubber series elements to prevent damage due to shock (Gomi et al., 1995), but these elements are much stiffer than measured impedances in animals.
Why have the designers of these robots chosen to make their impedances so high when examples from nature show otherwise? There are three reasons, one historical, the second due to the difference between physics and engineering, and the third a matter of control languages.
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THE HISTORY OF HIGH IMPEDANCE ROBOTS |
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The earliest "robots" were the fixed-base mechanical automatons of the 18th century (Liu, 2000
). As these automata (like the theme-park "animatronic" robots of today) always were connected to their base, the forces they encountered, as long as they were not large enough to cause damage, were irrelevant. Rather, it was the trajectory of positions and velocities that captured the eye and made the automatons, like today's humanoid robots, so evocative.
The invention, around 1860, of the hydraulic servomotor to move the rudders of large ships, and later the turrets of heavy guns (Lewis, 1992) was the next great advance in robotics. But again, for these tasks, holding accurate position in the face of force disturbances was paramount and the force necessary to accomplish the task was irrelevant.
Numerically controlled machine tools were developed after World War II, programmed to shape metal to an accuracy of less than a thousandth of an inch (Reintjes, 1991). The force between the work piece and the cutting tool was highly unpredictable and feedback of actual vs. desired shape was not immediately available. Thus, the machine tool was built to have the highest possible passive impedance.
Following numerically controlled tools, the multi-purpose UNIMATE robot appeared in a GM factory in 1961 and ushered in the age of factory robots. Such robots eventually took over the tasks of part transport, painting, and welding (Engelberger, 1980). But like former robotic tasks, these tasks were position-controlled in nature, and the robots were designed with high output impedance.
Two needs in manufacturing remained unmet by robots: grinding and assembly. Both operations were inherently low-impedance tasks. In grinding, two very stiff materials (usually some very hard metal and an even harder rotating grinding wheel) were brought in contact, and the rate of material removed was most accurately controlled by modulating the contact force, not the part's position. Low impedance was also necessary for assembly, where two typically tightly toleranced metal parts were mated. As when people assembled such components, gentle assembly was best (Craig, 1989).
These tasks generated a great deal of research into low-impedance force controlled robots at Universities (Whitney, 1987), as well as some practical systems, but they were by far the exception, not the rule, for robot applications. The situation continues to this day, and much assembly is still done by hand even in the most automated factories.
Thus, despite a large body of research into low-impedance robots, most designers of today's walking robots (particularly those in industry) come from a background rich in the history of high impedance mechanisms and control.
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PHYSICS VS. ENGINEERING |
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In addition to history, there is another important reason why high-impedance design is popular in robotics: the difference between physics and engineering.
The simplest laws of physics provide us with equations that govern the relationship between the forces and motions of rigid bodies. But these equations say nothing about the difficulty of actually measuring or generating the variables in question.
In reality, despite the apparent parity of force and position in equations, position is both much more practical to measure and to generate than force.
Position can be measured very accurately with effectively zero contaminating impedance using optical or other non-contact methods, and even simple potentiometers do not have much friction. But to measure force one usually employs some type of mechanical force to position transducer, typically a high impedance elastic element (like a bar of metal), in parallel with a highly sensitive position sensor, like a strain gauge.
On the generation side, things are little different. Electro-Magnetic motors generate torque in proportion to current, but they have low torque density and specific torque, and thus need to be geared down to generate adequate torque for most robotic applications (Hunter et al., 1991). This gearing raises the apparent inertia of the motor by the square of the gear ratio, and the high back-drive friction of the gears makes the impedance even higher. Gears also lead to other impairments, including poor shock tolerance and poor regeneration efficiency.
Hydraulic cylinders are little better. While capable of generating very large forces without gears (and roughly in proportion to input pressure), hydraulics generally require tight fitting seals with high break-away friction, and the viscosity of the fluid going through the control valve raises output impedance significantly (Robinson, 2000). Most hydraulic systems are also very inefficient, and incapable of recovering regenerative power.
Piezoelectric actuators do generate high forces in proportion to applied voltage, but the motions are too small for most walking robotic applications. Elecro-active polymers and other artificial muscles show promise, but their practical deployment is still years away. Pneumatic actuators, both traditional and novel (Chou and Hannaford, 1996), suffer from high energy storage, which limits bandwidth and can pose a safety hazard.
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CONTROL |
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There is yet a third reason for the popularity of high impedance position control. Proper control of a robot has historically meant the robot's accurate tracking of several commanded variables through time, typically the desired joint positions. Where afferent sensors have been employed, sensor values have usually been compared to fixed thresholds to control the state transitions of a discrete state machine. For example, most industrial robots utilize "guarded moves" when executing trajectories, so that if output force (or motor current) is excessive, the robot is stopped. But more sophisticated afferent/efferent relationships have in general not been employed. Stiffness control (Salisbury, 1980
), Hybrid Position-Force Control (Raibert and Craig, 1981), Impedance control (Hogan, 1985), and Potential Fields (Khatib, 1986, 1987) are some exceptions that have arisen from University research. But all of these methods describe relatively simple relationships between input and output. Thus, the difficulty of robot designers to find a language to describe the behavior of low impedance robots has inhibited their design. In summary, the history of robotic applications, the realities of engineering technology, and the simple nature of present control languages favor high impedance actuation and control. This makes the prevailing design philosophy understandable, but like the misguided person looking for their lost keys under the light post even though they dropped them in the dark, it is possible, despite today's examples, that walking robots are not under the light post of traditional high-impedance design. It may be in the dark, low-impedance, areas that one may have to look for effective methods of design.
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METHODS |
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Series-elastic actuators
Over the past 20 yr, several researchers (Asada et al., 1981
; Salisbury et al., 1989; Holmberg et al., 1992) have put a low impedance actuator at each joint of a robot instead of just a force feedback sensor at the tip. Such robots unfortunately require exotic transmissions or have, in the case of direct drive, motors too heavy to be practical in a walking robot. Our laboratory has addressed this problem by developing Series-Elastic Actuators (Pratt and Williamson, 1995a, b; Williamson, 1995; Robinson et al., 1999). The schematic in Figure 1 shows how series-elastic actuators are constructed.
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In Figure 1, a desired force Fdesired commands the actuator as a whole. This command, along with the measured load motion Xload is processed by a feed-forward function FF to estimate the necessary force to be applied to the motor. Fdesired is also compared to the measured load force Fload (deduced from the spring's deformation) and the error is processed by the feed-back element FB. The feedback and feed-forward outputs are summed, and command the motor force Fmotor. The system thus acts to deform the spring according to the commanded force, resulting in the application of the desired force to the output. The inertia of the motor and the friction of the gears are attenuated greatly by the feed-forward and feed-back loops (Robinson, 2000
) resulting in very low impedance. Additionally, the gears are protected from shock loads in excess of the control bandwidth, and the elasticity can efficiently store and release energy, much as some animal tendons do (Alexander, 1988). Most importantly, this all happens without explicit control. By establishing a relationship between Xmesasured and Fdesired, the higher level control system can command any impedance desired, not just that of the series elasticity. If the commanded impedance happens to match the series elasticity, then the motor will stand still and the spring will do all the work (at very high bandwidth). In other cases, the relationship between these two variables may be set so as to generate other spring-like, damping, inertial, or any other impedance or non-linear relationship, limited only by the saturation of the motor. Beyond saturation, the actuator acts like a passive spring and remains stable (Pratt and Williamson, 1995b). While low-motion force bandwidth is lowered by the elasticity, for impedances typically used in walking, we have found that the bandwidth of elastic actuators is more than satisfactory. Shown below are a series of photographs of different series-elastic actuators we have constructed over the years.
Figure 2 shows early series-elastic actuators, which use springs in series with tendons driving each joint. This design was inspired by animal tendons, but had too much distal mass as well as calibration problems due to pulley eccentricity.
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Figures 3 and 4 show revolute actuators, Figure 3 using an X shaped cross section metal torsion spring while Figure 4 used rubber balls held between alternating teeth. The metal torsion spring's deflection was measured with a strain gauge mounted on one of the spring's flats and operating at very high strain, while the rubber ball design used light transmission through crossed polarized disks, thus providing for multi-turn non-contact sensing of spring deflection. The metal torsion rod design is currently used in the arm joints of the MIT AI Lab's robot COG, which have allowed it to safely perform a number of low-impedance and high shock tasks, such as turning cranks, writing on hard surfaces with a pencil, playing drums, and even hammering nails (Williamson, 1998
, 1999).
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Our most recent actuators are shown in Figures 5 and 6. Figure 5 shows our electric actuator, while Figure 6 shows our hydraulic unit (Robinson, 2000
). The electric actuator weighs 2.5 lbs., can generate ±300 lbs with a stroke of 3 inches and a force control bandwidth of 30 Hz, and has a dynamic range of 300:1. The hydraulic unit weighs 2 lbs., can output ±500 lbs. with a stroke of 3 inches and a force control bandwidth of 50 Hz, and has a dynamic range of 500:1.
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Virtual model control
Virtual model control is a language we have developed for describing interactive force behaviors (Pratt, 1994
, 1995; Pratt et al., 1996, 1997). It uses simulations of virtual mechanical components to generate real actuator torques (or forces). The torques create the same effect that the virtual components would have created, had they existed, thereby creating the illusion that the simulated components are connected to the real robot. Such components can include simple springs, dampers, dashpots, masses, latches, bearings, non-linear potential and dissipative fields, or any other imaginable component. Virtual components can even contain adaptive and learning elements. Virtual Model Control's real-time simulation is effected in the robot's computer by transducing positions and velocities from the real world robot onto a stick-figure representation of the robot in the simulated world, and transducing forces generated by virtual components upon that stick figure in the simulated world onto the robot's actuators in the real world. In this fashion, we calculate in real time the appropriate joint torques to make the robot behave, to whatever extent possible, as if the virtual parts were really there. Of course, some virtual components, like a sky hook for the achievement of levitation, are impossible to translate in this fashion, but many others are doable, making Virtual Model Control a useful and highly intuitive language for expressing desired environment-interactive behavior.
We have successfully made bipeds walk by attaching to them three virtual components: a wheeled "granny walker" that maintains body height and pitch, a reciprocating gate orthosis that maintains leg anti-symmetry and swing-leg lift, and a damper-attached "dog track bunny" that acts to maintain forward speed whenever 2 legs are on the ground (the idea being similar to a race dog accelerating to reduce the difference between a mechanical bunny's perceived speed and its own). Because of the high fidelity force control afforded to our robots by series-elastic actuators, we can just push the robot's body with a force proportional to the difference between desired and actual speed instead of using Raibert's previous method of using foot placement (Raibert, 1986) to modulate speed. Thus, our robots are freer to find good footholds, which is more critical for walking than running because a robot can fall over in the time of one step. Our robots also spend much more time with both legs on the ground then most, because they can smoothly share leg forces and the control system is insensitive to leg configuration.
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RESULTS |
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We have constructed a number of real and simulated low-impedance robots using series-elastic actuators and virtual model control. Our simulated blind hexapod can simultaneously negotiate rough terrain and balance a 2-D pendulum on its back while following a desired trajectory (Pratt et al., 1996
; Torres, 1996). More recently we have constructed a blind 2-D biped "Spring Flamingo" that can negotiate unexpected 15 degree hills (Chew et al., 1999; Pratt, 2000). Traces of its state variables are reproduced in Figure 7 from (Pratt, 2000). The Velocity graph shows forward velocity in meters/second. The state graph shows which of 5 discrete states the internal control is using. The estimated slope (in percent) comes from proprioception in the ankle—otherwise the robot is blind. The robot's height is given by the Z graph, whereas its forward tilt is indicated by the pitch graph. The total mechanical power output to the joints (e.g., their torque times their rotational velocity) is shown in the "mech power" graph.
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TRAVERSING A HILL |
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A series of photographs of the robot blindly traversing hills is shown in Figure 8:
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This robot's recovery from being pushed (also reproduced from (Pratt, 2000
)) is shown below. We have more recently constructed a human sized 3-D biped "M2" and a 3-D biped model of a Dinoasur Troodon named "Troody," shown in Figure 10.
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Movies of these robots (or in the case of M2, a simulation) may be found at http://leglab.robotics.olin.edu/mpeg.
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DISCUSSION |
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To get robots as mobile as animals, we believe one must adopt a design and control philosophy at odds with conventional wisdom in industrial robotics. We believe it is important to use low mechanical impedance, inspired by the relative softness with which animals (including humans) move their bodies. To build a robot according to this philosophy requires both a new type of actuator and a new type of programming language. For robots doing natural tasks (like walking) elasticity becomes a useful feature when purposefully incorporated into actuators and controlled in force feedback loops. Compared to traditional actuators, such Series-Elastic Actuators have lower minimum impedance, higher force fidelity, greater shock tolerance, guaranteed stability in transient contact with hard environments, energy storage for reactive tasks and economy of construction. Our Virtual Model Control language capitalizes on the low impedance these actuators provide by adding forces in parallel with the robot's natural dynamics that can almost get the robot to walk without any control (McGeer, 1990a, b,
1991). VMC also allows the robot's behavior to be described in a functionally transparent (i.e., physically meaningful) way, which is easy to program.
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ACKNOWLEDGMENTS |
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The work reported here could not have been done without the exemplary efforts and collaboration of many students, staff, and faculty members of the MIT Leg Laboratory over the past 5 yr, including: Andrew Allen, Barbara Barotti, Max Berniker, Mike Binnard, Juaquin Blaya, Olaf Bleck, Chee-Meng Chew, Courtney Clench, Bruce Deffenbaugh, Peter Dilworth, Lila French, Jeremy Gerstle, Andreas Hofmann, Hugh Herr, Jianjuen Hu, Greg Huang, Jonathan Hurst, Theresa Iozzulino, Jaganathan Kanniah, Ben Krupp, Matt Malchano, Steve Massaquoi, Ben Matteo, John Morrell, Chris Morse, Mike Palmer, Marc Raibert, Mike Whittig, Dave Robinson, Dan Paluska, Allen Parseghian, Rob Playter, Jerry Pratt, Rob Ringrose, Russ Tedrake, Anne Torres, Karsten Ulland, Mike Wessler, Ari Wilkenfeld, Matt Williamson, Anne Wright, and Amy Vandiver.
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1 From the Symposium Stability and Maneuverability presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 3–7 January 2001, at Chicago, Illinois.
2 Previous Address: MIT Leg Laboratory (part of the MIT AI Laboratory), Cambridge, MA.
E-mail: gill.pratt{at}olin.edu
3 By "Natural Environments" (as opposed to the factory floor) we mean environments where unpredictable collisions with breakable objects, including other animals (and people) commonly occur.
4 Electrical Engineers will wonder how a high impedance can "short out" natural dynamics. It must be remembered that the most common "DC motor transform" from mechanical variables to electrical ones associates velocity with voltage, and force with current, respectively. Thus, high mechanical impedance (low velocity for high force) transforms to low electrical impedance (low voltage for high current). In this transform, springs are inductors, masses are capacitors, and dampers are resistors.
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References |
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