Performance comparison of specifications, linear motor, and hydraulic transmission system for vertical therapy robot module. Improvement in weight is highlighted.
Most haptic devices are intended primarily, if not exclusively, to exchange information with a human operator, and often replace or augment traditional computer displays with backdrivable, force-producing tactile interfaces. This includes popular commercial devices such as the PHANTOM (Massie & Salisbury, 1994) that are typically limited to at most several Newtons of endpoint force capacity, just enough to display simple virtual environments to the operator. Less conventional wearable haptic devices operate differently, but similarly have a low force capacity sufficient only to convey information (e.g. see devices described in (Biggs & Srinivasan, 2002)). By contrast, a class of applications that we refer to as
This definition is not intended to be rigid or comprehensive but to provide a framework to elucidate the challenges of developing devices with high force capacity and low mechanical endpoint impedance capable of rendering virtual environments. “Force” and “motion” are considered here to be generalized quantities that include force and position as well as their derivatives or integrals, which are often important. For instance, velocity is important to accommodate typical limb motion, and the rate of change of force is important to display impact-like experiences. This applies to controlled outputs from the devices as well as to backdriving. “Comparable to” means exceeding X% of (force and motion capabilities of relevant limbs), where X is as close to 100 as practical—often tens to hundreds of Newtons or more. “Much less than” means less than Y%, where Y << X; in fact the ratio X/Y is a key measure of high force haptic performance, and maximizing this ratio is the central challenge.
The application of robots to provide sensory-motor physiotherapy is a flagship application of high force haptics, and provides an instructive example of the engineering challenges unique to this emerging area. The ultimate goal is to promote, enhance and accelerate recovery after any injury that affects motor behavior. Common examples include stroke (cerebral vascular accident) (Volpe et al., 2009) and cerebral palsy (Krebs et al., 2009). Scientific and clinical evidence has shown that movement of the affected limbs is a key element of the recovery process. The compromised ability to move that immediately follows injury such as stroke may lead to permanent motor disability if left unaddressed, even though the peripheral neural, muscular and skeletal system is intact, a phenomenon that has been termed “learned non-use” (Taub and Uswatte, 2006; Wolf et al., 2006). In the case of cerebral palsy, unaddressed motor deficits also interfere with a child’s development, leading to severe, permanent motor disability. In contrast, studies (Nudo, 2007) have shown that activity-dependent neural plasticity can offset these degenerative trends and, in some cases, even reverse them.
The process of recovery resembles motor learning (Hogan et al., 2006) though there are notable differences, such as abnormal muscle tone or spasticity, that do not occur in motor learning. Providing a high “dosage” or “intensity” of movement experience (many repetitions) is one of the ways robotic tools may augment conventional physiotherapy. However, repetition alone is not enough: voluntary participation is essential (Volpe et al., 2004). To ensure voluntary participation, the machine must assist only as needed. Even more important, the machine must not suppress any productive movements a patient can make. It must “get out of the way” of appropriate movements while gently resisting inappropriate movements;
This may account for the contrasting results to date with upper-extremity and lower-extremity robotic therapy. Robotic treatment of upper-extremity stroke-related motor disorders has consistently succeeded, typically providing more than twice the benefit of conventional therapy alone (Kwakkel et al., 2007; Prange et al., 2006). It has even proven beneficial for stroke survivors in the “chronic phase”, many years after injury, when all recovery had apparently ceased. In contrast, clinical studies to date have shown that robotic treatment of lower-extremity motor disorders is about half as effective as conventional approaches (Hidler et al., 2009; Hornby et al., 2008). This may be due, in part, to the relatively smaller number of clinical studies but it may also be due to the fact that early lower-extremity therapy robots were designed to impose motion rather than provide guidance (Neckel et al., 2008; Israel et al., 2006). More recent designs for locomotor therapy have begun to address the formidable challenge of providing highly “back-drivable” (low impedance) interaction (Roy et al., 2009; Veneman et al., 2007) while supporting substantial fractions of body weight (Roberts, 2004).
Additional examples of high force haptic applications include human-assistive and exoskeletal devices (Guizzo & Goldstein, 2005, Kazerooni & Guo, 1993), physically cooperative man-machine systems (Peshkin et al., 2001) and similar applications. Like these other high force haptic devices, successful therapy robots must simultaneously embody a formidable set of capabilities, usually including all of the following:
1. The capacity to deliver large forces, sufficient to move human limbs actively against strong muscular effort by the subject (e.g. due to abnormal tone), and in some cases (e.g. balance & locomotion) to support substantial fractions of body weight
2. The ability to represent controlled, virtual environments (e.g. virtual walls or springs), in order to provide physical guidance, assistance (but only as needed), protection from force spikes, resistance (e.g. for strength training), and to communicate information
3. The ability to be backdriven, to avoid inhibiting a patient or operator’s attempts to move or observe the outcomes of these efforts
4. Large workspaces, up to a cubic meter or more, to accommodate the range of motion of human limbs
5. A number and arrangement of degrees of freedom compatible with large and small scale human movement
6. Guaranteed stability and safety while exchanging significant force and power with non-expert, impaired and unpredictable human subjects
In contrast, most existing haptic and robotic systems embody some subset of this list of features, but not all. More specifically, most existing robotic devices have either low force capacity with low mechanical impedance or high force capacity with high intrinsic impedance. Achieving this full set of features is a formidable engineering challenge that is limited by existing actuator and control technologies.
In this chapter we provide an overview of the tools available to address the high force haptic challenge by summarizing and critiquing available techniques, discussing several advanced approaches that show promise, and presenting a novel actuator architecture that may provide a superior solution for certain high force haptic applications. In the next section performance and stability considerations for high force haptic systems are summarized. Section 3 discusses the utility of available actuator and interaction control technologies for high force haptics. Section 4 introduces a novel hybrid actuator architecture that circumvents the fundamental limitations plaguing actuators for high force haptics. Analysis and experimental validation of a simple example are included. Concluding remarks are provided in Section 5. The prior and novel work presented here provides the foundation of a nascent toolkit of methods to design and build effective high force haptic machines.
2. Performance and Stability of High Force Haptic Systems
Haptic systems consist of a union between an engineered mechanical system (a haptic device) and a human operator. While haptic devices and robots both include actuators, sensors, control software, and mechanisms designed to achieve particular kinematics, haptics differ from most common robots because the physical coupling to an unknown and unpredictable human subject has a strong influence, by design, on the system’s behavior. From a control standpoint, this significantly influences how both performance and stability are understood. For a traditional motion-controlled robotic system, performance is measured by the system’s ability to track trajectories or move to locations in space. Stability is determined by the robot and its controller, possibly with consideration of static payloads.
For haptic devices, the considerations are quite different. Rather than control motion, haptic devices are intended to represent virtual objects, meaning that they must convincingly transition between apparent free motion and apparent contact with objects with specified physical properties. Performance is best understood as the quality of the virtual environment, or the “feel” presented to the operator by the haptic device. Furthermore, the operator is a dynamic system that is physically coupled to the haptic device. A critical distinction between typical robots and haptic devices is as follows: In robotic systems, performance and stability are both properties of the robot. In haptic systems, including high force haptic systems, performance is solely a property of the haptic device, while stability depends on
A proven method for analyzing physically coupled systems uses
The performance of the haptic device can be derived from its port impedance, which can be loosely thought of as dynamic stiffness, can be linear or nonlinear, and includes stiffness, inertia, friction and other dynamic behaviors, e.g. modes of vibration. Specifically, the intended feel at the interface can be represented by some virtual environment, which can be quantified by some impedance function, which may be linear or nonlinear and may vary in space and time. Performance can then be quantified by measuring the difference between the target impedance (or the target virtual environment) and that achieved in hardware. Phenomena that may detract from this performance can include unwanted inertia, compliance, or friction as well as unhelpful or distracting vibrations. This is consistent with the definitions of “fidelity” found in the haptics literature. A related performance metric, “transparency,” generally refers to only the quality of the haptic hardware and its ability to minimize or disguise parasitic dynamics that are not part of the software-generated virtual environment (Carignan & Cleary, 2000). Specific high force haptic applications may benefit from differing performance metrics based on the port impedance. For instance, when port impedance is linear or can be approximated as such, performance can be defined as a cost function
The weighting function
In contrast, the stability of an interactive system like that shown in figure 1 depends on the dynamic properties of both coupled ports. If both port functions are linear, the characteristic polynomial of the system in Fig. 1B is
The stability of the coupled system, termed
Because the dynamic properties of the operator cannot be controlled by the haptic system designer, guaranteeing coupled stability poses a challenge. One valuable concept for understanding coupled system stability is
Such a port function has phase between -90 and +90 for all frequencies. Colgate showed that when two passive port functions are coupled together as in Fig. 1, the total open-loop phase must be between -180 and +180 at all frequencies, and the Nyquist stability criterion cannot be violated, so the coupled pair is guaranteed to be stable (Colgate & Hogan, 1988). This is consistent with the energy properties of passive ports. If two passive ports are coupled, neither can generate energy indefinitely, and therefore stability is guaranteed. Because it is energy based, this extraordinarily powerful result works for linear and nonlinear systems (for nonlinear extensions, see e.g. (Wyatt et al., 1981)), and applies (perhaps with fine tuning) to all physical domains. To the extent that humans can be assumed to act as passive mechanical systems at their ports of interaction, passivity provides a powerful stability metric for high force haptics. While this has not been conclusively proven, given the complexities of the neuromuscular system, available empirical results and theory strongly suggest that this is indeed the case (Hogan, 1989). Unfortunately, making high force haptic systems passive can often limit performance. Certain simple control laws can preserve passivity, but given the limitations of available actuator hardware, these simple controllers often can not achieve adequate performance at the haptic system port. These challenges are reviewed in the next section.
3. Actuator and Control Technology for High Force Haptic Systems
Ideal high force haptic systems would achieve high forces while representing port impedance ranging from near zero to near infinite stiffness, friction and inertia, while guaranteeing passivity and coupled stability. Actuators for these idealized systems would require similar properties, plus some additional properties (e.g. low mass), depending on the system configuration. In this section we assess the value of various technologies in approaching this ideal, first by seeking a purely physical solution in the form of actuators effective at human scales (tens to hundreds of N, cm to m motions, frequencies less than 10 Hz), then by exploring the benefits of available advanced control methods.
3.1. Classical Actuator Technologies for High Force Haptics
Electromagnetic actuators can represent desired forces with extremely high fidelity when used in direct drive configurations. Friction can be extraordinarily low, especially at the low frequencies typical of interaction with humans (at higher frequencies eddy current or IR losses create drag). With the low intrinsic impedance of these actuators, simple and robust control algorithms, discussed below, may be used to provide a stiff interface and to preserve passivity. The main drawback is limited force density (Hollerbach et al., 1992), meaning that high forces lead to large, heavy actuators. Electromagnetic actuators are easy to use, and in many cases systems can be successfully designed to meet certain limited requirements in spite of force density limitations. An example is the MIT-MANUS robot for upper-limb physical therapy, which uses direct-drive rotary motors with a two-DOF (degree of freedom) planar closed-chain configuration that allows both actuators to remain stationary (Krebs et al., 2004). Other devices are effective due to very small translational workspaces (Berkelman et al., 1996). The force density limitation is far more difficult to overcome for open-chain serial systems. If the actuator for DOF #1 is carried by DOF #2, as is common for serial robot arms, then the mass of the actuator not only increases the force required for the DOF #2 actuator, but also adds to the endpoint inertia of that DOF. This problem emerges for most non-planar mechanisms, and is therefore very common. As forces increase, carrying the full weight of direct drive actuators rapidly becomes prohibitive. When rotary motors cannot be used, large motions pose an additional problem, as the high mass per unit force increases nearly linearly with range of motion.
An obvious way to improve the force density of electromagnetic or other actuators is to add gearing. This approach makes carrying actuators in a serial mechanism feasible and is used extensively in robots. Unfortunately a gear train compromises endpoint impedance, increasing the actuator’s apparent inertia and friction due to eddy current or IR losses, as observed at the endpoint, by the square of the gear ratio. Coulomb friction and stiction in the actuator are amplified linearly by the gear ratio. Furthermore, the gear train adds its own friction, inertia and backlash. As a result, even when transmissions are designed explicitly to minimize friction, high impedance is difficult to escape (Buerger et al., 2001). While some applications are amenable to modest gear ratios (typically less than about 5:1), larger gear ratios rapidly lead to unacceptable levels of reflected inertia and friction. The failure of gearing to solve the underlying force density problem in high force haptics distinguishes this problem from most robotics, where gearing is generally very successful.
The most significant problem with using direct-drive electromagnetic actuators for high force haptics is the need to carry their substantial mass when complex or serial mechanisms are used. Mechanical transmissions such as cables, belts, tapes and rods offer a potential opportunity to keep the actuators stationary or nearly stationary, in some robot configurations, while transmitting their force, motion and impedance properties to the interaction port. Cable transmissions, in particular, have been elegantly and cleverly designed to achieve reasonable force and impedance capabilities in high-DOF serial arms, e.g. the WAM arm (Townsend & Guertin, 1999). The complexity of the mechanisms that enable the WAM underscore the fact that routing of mechanical transmission members can be extremely challenging. When actuators for multiple DOFs of a serial mechanism are mounted at the base, the transmission elements for one or more DOFs must pass through or around other joint(s). This presents an extreme packaging challenge as the number of DOFs grows, and this challenge is compounded by the fact that fixed separation must generally be maintained between transmission nodes (e.g. between pulleys in a cable system). Cables, belts and transmission tapes must be held in tension, requiring tight, deterministic coupling between the actuators and the intermediate and terminal joints that they actuate, even as the intermediate joints are independently actuated. These flexible members also tend to introduce problematic dynamic resonances (a “guitar-string” effect) and can severely limit bandwidth. Transmission rods can be made more rigid, but present an even more difficult plumbing challenge, as the gears that mate adjacent rods must be kept in tightly controlled contact. In certain configurations, mechanical transmissions can offer an acceptable high force haptic solution, and thus represent an important tool. However, for other applications their limitations are insurmountable, and other options must be sought.
Appealingly, hydraulic actuators can achieve force densities at least an order of magnitude better than ungeared electromagnetic motors (Hollerbach et al., 1992). Because the working fluid is nominally incompressible, hydraulics can achieve very high stiffness relative to humans. Pressure sources and valves can be located remotely, with force and motion coupled to the interaction port through flexible tubing, which can be routed with greater flexibility than mechanical transmission elements. In spite of these apparent advantages hydraulics have been little-used for haptic interfaces (with some exceptions, e.g. see (Kazerooni & Guo, 1993, Lee & Ryu, 2008)). This is because the operation of conventional servovalves causes hydraulic actuators to have high intrinsic impedance, and in fact generally to be non-backdrivable. Hydraulic actuators rely on nonzero valve impedance to regulate output, placing a lower limit on the output impedance. The fundamental nature of this limit can be demonstrated by considering a typical pressure control valve design.
A servohydraulic system includes a high-pressure energy source, usually controlled to produce nominally constant pressure
This can be seen if the left half of the valve is modeled as a pair of fluid resistors, as shown below the schematic. The input orifice is modeled as the resistor
A pure pressure source would have
Pneumatic actuators are also capable of high force densities (Hollerbach et al., 1992) and provide behaviors unique among actuator technologies. While regulators that control gas pressure rely on flow restriction, much like hydraulic servovalves, low impedance is readily achieved due to the compressibility of the working fluid. Indeed gas compressibility presents one avenue to modulate the endpoint impedance, by directly manipulating the properties of the enclosed volume of gas in the actuator. However, representing high stiffness requires high pressure, and transitioning from low to high stiffness (e.g. to represent a virtual wall) requires rapid pressure changes. This can be understood by considering the simple example of a closed cylinder in compression due to force from a piston with cross-sectional area
Pressure consists of ambient plus that due to the applied force:
Differentiating produces the stiffness:
For fixed (or nearly fixed)
3.2. Interaction Control
Physical interaction requires control strategies that differ significantly from the more common position or velocity servo problems. Because of the unique characteristics of physical interaction described above, the prevailing approach is explicitly to regulate dynamic behavior at the port(s) of interaction, e.g. by using
A class of control methods has been developed that uses measured forces (torques) at the port of interaction to close a feedback loop and expand the range of apparent dynamics that can be presented. This approach has the potential to mask the physical properties of the hardware, presenting a desired dynamic response at the port of interaction that closely tracks target dynamics derived independent of the physical hardware. For instance, the apparent inertia and friction can be reduced below the physical values by using the actuators to drive the device in the direction of applied force. When the target impedance is zero, this is termed force control. Unfortunately this approach seriously threatens coupled stability; in fact passivity is lost whenever the apparent inertia is reduced by more than a factor of two below the physical inertia (Colgate & Hogan, 1988, Newman, 1992). Natural admittance control exploits the fact that loss of passivity derives from reducing the apparent inertia, rather than the friction. This method provides a means of theoretically ensuring passivity while aggressively reducing the apparent friction well below the physical level by keeping the inertia at a level that ensures passivity (Newman, 1992). This approach can dramatically improve feel by virtually eliminating static friction, but cannot mitigate high levels of physical inertia, which are particularly common in geared actuator systems.
An alternative approach recognizes that passivity, though sufficient to stabilize interaction with human subjects, is not necessary. Passivity ensures stability when coupled to a wide range of environments including large inertial loads, kinematic constraints, highly nonlinear frictional contact, etc. On the other hand, the dynamic characteristics of human limbs are considerably more limited, even as they vary in time, configuration and across subjects. Port stability can be posited as a robust stability problem with conservative bounding values used for operator dynamic properties, and robust control methods can be used to shape the dynamics of the force feedback control loop to maximize performance (by minimizing impedance error) while guaranteeing coupled stability (Buerger & Hogan, 2007).
3.3. Advanced actuators
In spite of significant progress in advanced interaction control, achieving all six required characteristics of high force haptic devices listed in section 1 remains a persistent challenge, particularly for complex and high-DOF devices. Several recent advances in actuator development offer promising future alternatives for the high force haptic designer’s toolbox.
Goldfarb has described monopropellant-powered actuators that chemically generate gas to produce pressure, and force output (Goldfarb et al., 2003). This approach dramatically improves energy density and eliminates the need for a compressor. However, force and impedance properties—and limitations—appear to be fundamentally similar to those of compressed-air systems. In particular, rapid changes of stiffness (to simulate contacting a surface) require high mass flow rates. Dramatic thermal changes would also impact endpoint impedance. In the authors’ opinion, this approach seems quite promising, though as yet unproven for high force haptics.
Series elastic actuators, which include compliant members placed between high-impedance source actuators and the environment and use force feedback control, can achieve high force-density and low impedance (Pratt & Williamson, 1995). The elastic element provides several advantages for certain applications, but does not guarantee passivity, and a careful tuning process is generally required to achieve stability. This is problematic when interacting with variable, unpredictable humans. An alternative design method that includes carefully controlled physical damping in conjunction with natural admittance control can theoretically guarantee passivity (Dohring & Newman, 2002). Generally, the more aggressive the reduction of apparent impedance from the physical actuator level, the softer the compliant element must be. This limits the utility of this approach by limiting achievable stiffness. Still, carefully designed series dynamics are an important tool.
Research into electroactive and dielectric polymers has shown potential for high achievable stresses. These muscle-like materials could one day produce effective high force haptic actuators, but have not yet been shown to scale up to the forces needed (Bar-Cohen, 2004).
To the best of our knowledge, no existing actuator technology or control strategy provides a comprehensive solution for high force haptics. Additional tools are needed to improve the tradeoffs between force capacity, DOFs, workspace size, interface fidelity, and coupled stability. An alternative way of evaluating the potential of major human-scale actuator technologies is by available stress, which is strongly related to force density. The force output of electromagnetic actuators is limited by the shear stress in the air gap between moving and stationary components, which is typically tens of pounds per square inch (psi). Pneumatic actuators can achieve hundreds of psi but rapidly introduce hazards as pressure is elevated, due to high levels of stored energy. By contrast, hydraulic actuators routinely achieve thousands of psi (McBean & Breazeal, 2004). This fundamental promise warrants a second look at hydraulics to see if the underlying high impedance of servovalves can be avoided, and if the tradeoffs between the six criteria listed in section 1 can be improved.
4. Hybrid hydraulic actuators for high force haptics
Among actuator technologies available at the human scale, hydraulic actuators are alone in offering high force density, high stiffness, and flexible connectivity between power sources and the interaction port. Their main drawback is high impedance, which derives primarily from servovalves, and because of this they have been little-used for haptic interfaces. By contrast, electromagnetic actuators are widely used for haptics due to their favorable force and impedance behavior, but suffer from dramatically inferior force density. A hydraulic actuator capable of controlling pressure with low impedance rather than a high impedance servovalve would be a powerful development. We have investigated a hybrid architecture for actuators that exploits the benefits of both hydraulic and electromagnetic actuation while circumventing the weaknesses of each. In this design, sketched in Fig. 4, a hydraulic element is used purely as a transmission, while a remotely-located source actuator provides force and motion, and dictates the representation of the virtual environment. The hydraulic transmission is stiff in the direction of actuation but is embodied in flexible tubing, such that motion of the interaction port is decoupled from motion of the source actuator, and the source actuator may remain stationary. Critically, this architecture obviates the need for a hydraulic servovalve, eliminating the main cause of high impedance. The hydraulic transmission is analogous to a mechanical transmission but, unlike cables, tapes or rods, does not require a deterministic coupling between source and interaction port locations. This architecture also enables the use of effective source actuators, particularly direct-drive electromagnetic actuators, that can provide favorable force, motion and impedance properties. The source actuator can have large mass, because it need not move.
While this proposed architecture can dramatically reduce endpoint mass, in its simplest form it actually increases the total system mass when compared to using only direct drive electromagnetic actuators. (The hydraulic transmission would be unnecessary if the actuator was connected directly to the endpoint.) Total mass is critically important for some applications (e.g. fully mobile exoskeletons), and this approach may not be suitable for those. However, in many cases the
4.1. Design Model and Tradeoffs
Figure 4 shows a schematic of one embodiment of this architecture that uses a linear electromagnetic motor as a source actuator and a passive hydraulic system as a power transmission. The hydraulic system consists of a piston/cylinder on each end for conversion between mechanical and fluid power, and a flexible hose connecting the two. One piston connects to the source motor, and the other acts as an actuator. Unlike servovalve-controlled hydraulics, the mechanical piston-cylinders, each of which acts as both an energy and signal source for the hydraulics, and the tubing that joins them need not include small orifices to regulate pressure, and can be designed to have relatively low intrinsic impedance.
If the source actuator is capable of providing the desired force and impedance, then an ideal transmission is mechanically
Any practical transmission will drain some energy and will therefore not be perfectly transparent. Furthermore any real physical system has nonzero inertial and compliant dynamics. To approach ideal behavior, the transmission should be designed to minimize inertia, compliance, and friction (although transmission dynamics may be used to advantageously shape the port impedance; see 4.3). While transparency is an important performance objective, an effective transmission must also be
From Figure 4 it is straightforward to envision the hydraulic components transmitting force, motion and power in compression. However most high force haptic systems must sometimes actuate bilaterally (pulling as well as pushing). If tensile forces are applied to a closed liquid volume, its pressure drops below ambient and the fluid evaporates locally (cavitates). If the seals are imperfect, air leaks in. Two simple options enable bilateral actuation: a bias pressure that exceeds the pressure needed to transmit tensile forces can be introduced, or actuator pairs can be used together. The latter is depicted in Figure 6, wherein the two actuation paths exist within the same two cylinders, joined by two separate fluid lines, one for “tension” and the other for “compression.” This configuration introduces several difficulties, including additional weight and complexity as well as additional seals. Seals where the pistons exit the cylinders are particularly problematic, as any liquid that leaks there leaves the constant-volume system and must be replaced.
A simpler method of tensile force transmission that uses a single fluid path requires mechanically creating a bias pressure such that the fluid pressure is elevated above ambient without force applied by the actuator or environment. This can be accomplished by applying a constant compressive force to each piston. When the system is at rest, the forces on each side cancel, but the fluid in the chamber is at an elevated pressure. Tensile forces reduce the pressure, but if the force does not exceed the bias force level, the fluid pressure remains above ambient and cavitation and gas leakage into the system are avoided. This approach requires additional hardware to create the applied load, and increases the operating fluid pressure, but requires only two moving seals rather than four.
Using this mechanical bias force approach, the transmission can be modeled for design purposes as the simple straight-pipe system shown in Fig. 7. This model, used as the design basis for determining transmission impedance, includes each of the piston-cylinders (with diameters
To be viable, the proposed actuator architecture must be amenable to control. By introducing a significant separation between the source actuator and the endpoint where behavior is controlled, with accompanying transmission dynamics, the structure of the system poses a potential challenge for effective and highly stable control. Because stability and passivity are paramount, one way to represent target impedance is to feed back motion only at the source actuator, closing a simple impedance control loop around only the well-characterized electromagnetic source actuator, yielding a robustly stable implementation. This arrangement depends on the transmission to reliably (and nearly transparently) transmit impedance between the source actuator and operator, but without using a sensor at the interaction port, it may be vulnerable to small and accumulating position errors. Fortunately, although humans excel at gathering information from physical contact, they are not generally sensitive to small changes in position. Provided that physical contact is represented as intended, small positioning errors can be tolerated with very little consequence, especially if the device is used in conjunction with a visual display. Compared to alternative transmission implementations (e.g. cable drives), a hydraulic transmission may provide superior damping of resonant transmission line modes via the intrinsic viscous behavior of the working fluid, and in fact the dynamics of the transmission may be intentionally sculpted to improve both interaction stability and performance via
To illustrate the key design issues for this architecture, a representative design problem is presented by applying the model in Fig. 7 to the specifications for an actuator for an upper-limb physical therapy robot device. This is intended as an out-of-plane “anti-gravity” addition to the planar MIT-MANUS robot, and has previously been addressed with two designs, one using a rotary electric motor and a low-friction roller screw and the other a direct-drive linear electromagnetic motor (Buerger et al., 2001, Krebs et al., 2004). The stringent and challenging target specifications for this application include a range of motion of 0.4 m, a force capacity of at least 65 N, a mass of less than 2 kg at the endpoint, a separation of at least 3 m between the stationary source actuator and the mobile endpoint, achievable stiffness of at least 2 kN/m, and minimal endpoint impedance including inertia less than 2 kg, Coulomb friction less than 2 N, and linear damping coefficient of no more than 10 Ns/m. Both previous designs violated the mass specification by nearly a factor of four. In this section the design model is developed to predict frictional and inertial dynamics of the transmission, and compliance is discussed. A prototype actuator (Fig. 8) was fabricated and its measured properties are discussed in the next section.
which also uses the relationship:
The head loss
The major damping at the piston is proportional to the
Turbulent damping is nonlinear in velocity, and even more highly dependent on the piston and line diameters.
Given the specification of a 3 m flexible line for the representative prototype, a design figure depicting the predicted friction versus velocity for several different hose diameters is shown in Fig. 9. A specification of a maximum of 10 Ns/m damping is also shown. Because the overwhelming majority of human patient subjects never exceed 0.4 m/s hand speed in the course of therapy, a hose with an inner diameter of 5/16” (0.79 cm) was selected for the prototype as it satisfies the design requirement for all relevant speeds. This hose has an outer diameter of approximately ½” (1.27 cm), and is comparable in size and flexibility to the electrical power cables that drive the source motor.
The resulting equivalent inertia is:
When the fluid line is long or narrow, the second term dominates. Decreasing the piston diameter
The simple calculations described above elucidate the geometric tradeoffs in the hydraulic transmission architecture. Because this application uses hydraulics differently from prior work, this model facilitates scaled designs for various applications and requirements. Transparency requires low friction, compliance, and inertia. From eqs. (14), (15) and (18), short and wide (large diameter) lines provide low friction and inertia. However, flexibility requires long and bendable (preferably small diameter) lines. Minimizing compliance requires using lines that are either materially rigid or thick-walled (and therefore unlikely to bend easily), or small in diameter and short. Design of line materials and geometry must include consideration of each of these requirements and the tradeoffs between them. Impedance can also be changed by altering the piston/cylinder geometry. Reducing the piston diameter can significantly reduce damping and inertia, as shown by Eqs. (14), (15) and (18), or permits smaller hose diameters for the same impedance properties, reducing compliance and improving flexibility. However, by Eq. (13) this increases the operating pressure, which has at least two negative consequences: greater part strength is required, and leakage is likely to increase, often requiring seals with greater friction. Thus changes in piston diameter can trade leakage and seal friction against reflected fluid friction and inertia.
Changes to system geometry improve certain aspects of performance at the expense of others. For any specific application the performance properties must be traded off against one another to find a suitable solution. Several rules of thumb should guide design:
1. To minimize reflected inertia, fluid friction, and compliance, the hydraulic line(s) should be made as large and radially rigid as possible.
2. Problem constraints should be used to determine how large, how heavy, and how rigid the line can be. These properties (related to flexibility) are traded against the endpoint impedance (transparency).
3. Decreasing the piston diameter decreases the reflected impedance but increases the operating pressure, and therefore the leakage rate and/or seal friction.
4.2. Proof of concept prototype and characterization
A prototype for the anti-gravity upper-limb application, shown in Fig. 8, was constructed to prove the concept of hybrid hydraulic actuation and to test the design model. A cogless tubular linear motor from CopleyTM, used previously as a version of the anti-gravity robot system, was selected as a source actuator for the system. A wound steel constant-force spring was used at each cylinder to apply the bias force. Springs are an advantageous means of applying a bias force because they contribute minimal inertia and friction.
In choosing a working fluid for this application, fluid dynamics including the viscosity, density, and compressibility are especially important because they contribute to the endpoint impedance and haptic feel. Other factors (e.g. lubricity) that are important for other hydraulic applications are not important here because of the mechanical simplicity of the design. Water is cheap and available in abundance, and has minimal viscosity and compressibility with modest density. Water also poses minimal environmental threats (provided that it be separated from electrical and electronic equipment), and was therefore selected. The fittings that connect the flexible fluid line to solid structures are a critical component for design of a system with no small orifices. The analysis in 3.1 shows that losses from small orifices in servovalves lead to high endpoint impedance; the same can be said of orifices in a transmission line. Typical pipe and tube fittings generally obstruct the interior passages, greatly reducing diameter (and increasing damping) in a local area. In servo systems this effect is usually insignificant because the losses in the servovalve are so great as to dwarf fitting losses. For this application, however, an unobstructed fluid path is critical, and small orifices must be aggressively eliminated. Quick-release hose fittings that grip only the outside of the hose and leave the inside unobstructed were chosen for this prototype. To use such fittings, only hoses with relatively rigid walls are acceptable. A fuel hose meeting the SAE30R3 specification was selected. Perhaps the most challenging practical issue in hydraulic transmission design is the selection of moving seals with sufficiently low friction. In general, sliding seals require increased friction to reduce leakage. Because of the extreme low-friction needs of high-force haptic devices, static and Coulomb friction must especially be minimized. A wide array of seal types were considered, including elastomeric sliding seals, rolling diaphragm seals, bellows designs, and non-contacting seals. While rolling diaphragm seals show great promise, they generally provide a small ratio of travel to diameter. Non-contacting AirpotTM piston-cylinders were selected to minimize friction. This technology uses a precision ground sintered graphite piston that is diametrically matched to a high-precision glass tube to clearances that are generally between.0001” and.001”. There is no physical seal, and the piston is designed to ride on a cushion of fluid between its outer edge and the cylinder’s inner edge. This design minimizes friction but, because there is clearance between piston and cylinder, inevitably permits some leakage. Some amount of leakage of the working fluid across a low-friction seal is inescapable. When fluid leaks, the
bias pressure prevents the replacement of the fluid with air. Instead the fluid volume is reduced. This is a positive feature of this bias pressure method; leakage produces a drift in endpoint position, but no significant change in dynamic transmission properties. To permit long-term operation, the leaked fluid must be replaced. For the prototype, a pump was used to replace leaked fluid. Because the pump is a high-impedance flow source, its supply rate is unaffected by changes in the transmission pressure, and it has a negligible impact on the system dynamics. Figure 10 shows the outer cylinder assembly.
Static and dynamic characterization tests were conducted to evaluate the prototype performance and validity of the design model. The force capacity, transmission stiffness, friction, inertia, weight and bandwidth were analyzed. The results are summarized and compared to the specification and the same quantities for a module based on the source actuator alone (Krebs et al., 2004) in Table 1.
|Specification||Linear Motor||Passive Hydraulic Transmission|
|Force capacity (N)||65||70||70|
|Endpoint weight (kg)||2||8.1||2.4|
|Core component weight (kg)||-||2.7||0.6|
|Endpoint inertia (kg)||2||2.7||4.5|
|Coulomb friction (N)||2||3.5||8|
To determine the force capacity in tension and compression a high stiffness was commanded with the source actuator and a force was applied (and measured) at the endpoint until saturation was reached. The transmission supported over 50 N in tension (exceeding the bias spring force) and almost 70 N in compression (meeting the saturation level of the source motor). The endpoint stiffness at DC is a series combination of the effective transmission stiffness and the source actuator stiffness. The source actuator controller was calibrated to achieve target endpoint stiffness using proportional motion feedback (simple impedance control). To determine the transmission stiffness, a virtual spring was imposed at the source actuator and the transmission endpoint force and position were measured as the endpoint was actuated slowly and steadily by hand. An example of the resulting data is shown in Fig. 11. The endpoint stiffness was determined from the slope of a linear fit to this data. The test was repeated at several different stiffnesses and the results were averaged, producing a measured transmission stiffness of 4020 N/m. When coupled to the source motor with maximum stiffness of 50,000 N/m, the resulting system can achieve stiffness up to 3700 N/m. This exceeds the specification by 85% and signals that radial hose flexibility does not prevent the creation of desired haptic sensations.
The endpoint friction profile was determined by measuring the force required to backdrive the system at constant speeds with a separate servo system. This test revealed approximately 8 N of Coulomb friction at the endpoint, in addition to viscous damping around 15 Ns/m. Coulomb friction appears as the separation between the upper and lower parts of the trace in Fig. 11. Approximately 3.5 N of Coulomb friction results from the source actuator, and the rest is mostly due to the bearings on the outer assembly. Significantly, a test on only the two pistons and the fluid, decoupled from mechanical bearings on each end, revealed less than 0.5 N friction from these critical parts. Viscous damping is approximately twice the estimate from the model. This results from viscous drag at the source motor as well as the fact that the transmission is not an ideal straight pipe, as modeled, and indicates a need for further model development to capture additional damping.
The model predicts over 2.5 kg of apparent fluid inertia, plus the inertia of the linear motor forcer and the moving hardware (handle, bearing carriage, sensors, etc.) in the endpoint package, totaling 4.9 kg. This significantly exceeds the 2 kg specification, because the design of this prototype erred on the side of making the hose extremely flexible yet radially stiff, and therefore very small. The most straightforward way to reduce inertia is by changing the hose geometry, as described in the previous section. A segmented line could help to balance hose flexibility and endpoint inertia. To measure the inertia, the source actuator was used to create a virtual spring. The transmission endpoint was displaced and released, creating an initial condition response. The transient of this response was fit with a second order initial condition response using the known endpoint stiffness. Inertia measured in several trials averaged to 4.5 kg. This is slightly less than the prediction because the inertia is actually partially distributed across a compliant part of the system (the transmission), while the model assumes a lumped mass with compliance originating only from the source actuator.
The weight of the endpoint package, including all parts of the assembly downstream of, but not including, the fluid line was 2.43 kg. Perhaps more importantly, the total weight of the (non-structural) components required to produce force (the cylinder, piston, piston rod assembly, fluid, and constant force spring assembly) was less than 630 g. By contrast, the weight of the linear motor magnet rod and forcer (for the same amount of travel) is over 2.7 kg. The weight of the core technology to produce force, excluding bearings and structure, is reduced by approximately 77%—more than a factor of four. Additional weight reduction is achieved because the structure need not support such heavy core components.
Although not a direct performance requirement for this application, bandwidth was also measured by fixing the endpoint and commanding a sinusoidal force profile at various frequencies, with a magnitude of 12 N (approximately 20% of the peak force specification). A resulting plot of magnitude versus frequency is shown in Fig. 12. The system has a resonant peak around 8 Hz with a damping ratio between 0.1 and 0.2, and an open-loop bandwidth of approximately 20 Hz. The system geometry could easily be altered to increase viscous drag and reduce the resonant spike (e.g. by using more constrictive fittings) should this be desired. The bandwidth is more than adequate for human arm movement.
A critical assessment of the model’s accuracy in predicting prototype impedance reveals moderate errors in the prediction of inertia, due to the assumption of lumped inertia in spite of the nonzero compliance, and somewhat larger errors in the prediction of damping, stemming primarily from the fact that damping is highly sensitive to tubing surface conditions, coiling, and interface losses. In general, over long stretches of tubing as implemented here, the primary goal is to keep friction below some level, rather than precisely achieve a specific value, so the simplified model suffices for this purpose. Prototype testing, along with the insights provided by the model, underscores the fact that seals are the core technology that determines performance. Smaller piston diameters can dramatically reduce apparent inertia and damping, but require higher pressures. At higher pressures, leakage increases unless seals are made tighter, which usually requires greater friction. It is clear from this work that improved seal technology that can better contain the fluid with minimal friction would substantially improve the capabilities of this technology.
4.3. Compliant Impedance Shaping
As discussed above, viscoelastic dynamics placed in series between a high-impedance actuator utilizing force feedback and the environment (termed series elasticity, mechanical filtering, or impedance shaping) can help to stabilize contact (Pratt & Williamson, 1995, Dohring & Newman, 2002).
A passive hydraulic transmission can implement selected dynamic characteristics and is situated to place these dynamics in series, providing another potentially valuable aspect of this architecture. In the prototype described above, the source actuator friction and inertia contribute significantly to the endpoint impedance (half the friction and 1/3 the inertia), suggesting that it may be useful to use force feedback control around the actuator to reduce its apparent impedance, with series dynamics to improve coupled stability. An
This simple impedance shaper can also introduce controlled inertia. The passageways can be designed to provide inertial forces that are proportional to the acceleration of the flow
This chapter presented and defined high force haptic systems, and articulated the specific constraints that make the selection of actuators for this application difficult. To provide context, the pioneering high force haptics application of therapeutic robotics, and the obstacles to continued advancement of the field, were discussed. We continue to develop therapeutic robots for human movement from lower body (including partial weight support) to fine finger motions, and the actuation problem is the core engineering challenge for almost all of the designs. Major actuation and control technologies suitable for human-scale interaction were explored and evaluated for their fitness for high force haptics. As existing technology does not meet all of the needs of this field, we described our development and proof-of-concept of a hybrid hydraulic actuation scheme. This approach exploits the high force density of hydraulic systems without producing inevitably high endpoint impedance. Though analogous to mechanical transmissions, the hydraulic approach enables a dramatically more flexible coupling between source actuators and interaction ports. The simplicity of this design architecture, and the relatively straightforward and validated impact of geometric design parameters, makes it amenable to scaling for use as modular actuators in robots of all shapes and sizes. With this architecture, a single integrated physical system, the passive hydraulic transmission, can provide remote power transmission (directly reducing endpoint actuator weight), intrinsic gear reduction (permitting variation in actuator sizing) and impedance shaping (stabilizing contact while more aggressive force feedback is used). The structure of hybrid hydraulic actuators may also permit operation in environments that are hostile to other actuator types, including near or inside medical neuroimaging equipment for use in concert with, for instance, functional magnetic resonance imaging (fMRI). Together with existing actuator and interaction control technology, as well as developing new capabilities for advanced interactive actuators, the hybrid hydraulic actuation approach contributes to a diverse and expanding suite of tools for addressing the high force haptics challenge. As a one-size-fits-all solution to this formidable challenge seems unlikely to emerge, the growing community of high force haptics researchers should consider each of these possible solutions for their applications and select those best suited to their needs.
Support: NDSEG Fellowship, NIH HD37397, Burke Medical Research Institute, New York State C019772.
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