THE performance achievable by a human operator using. Model-Based Cancellation of Biodynamic Feedthrough Using a Force-Reflecting Joystick

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1 SUBMITTED TO: ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL Model-Based Cancellation o Biodynamic Feedthrough Using a Force-Relecting Joystick R. Brent Gillespie and Szabolcs Sövényi Abstract Manual control perormance on-board a moving vehicle is oten impeded by biodynamic eedthrough the eects o vehicle motion eeding through the operator s body to produce unintended orces on the control interace. In this paper, we propose and experimentally veriy the use o a motorized control interace to cancel the eects o biodynamic eedthrough. The cancellation controller is based on a parametric model it to experimental data collected using an accelerometer on the vehicle and a orce sensor on a temporarily immobilized manual control interace. The biodynamic model and system identiication experiment are in turn based on a careully constructed model o the coupled vehicle-operator system. The impact o biodynamic eedthrough and the eicacy o the cancellation controller are estimated by comparing the perormance o 2 human subjects using a joystick to carry out a pursuit tracking task on-board a single-axis motion platorm. The crossover model is used as a basis or developing three perormance metrics. Ater irst conirming the deleterious eects o platorm motion, cancellation controllers derived rom individually it biodynamic eedthrough models were shown to signiicantly improve perormance. With the cancellation controller active on-board the moving platorm, perormance levels were almost hal-way restored to the levels demonstrated on the stationary platorm. Index Terms biodynamic eedthrough, vibration eedthrough, McRuer s crossover model, orce relecting interace. I. INTRODUCTION THE perormance achievable by a human operator using a manual control interace to track a moving target may be limited by various actors, including the kinematics o the interace device, its mechanical response, and parameters o the associated visual display. The limits o perormance in pursuit tracking and compensatory tracking have been extensively studied, especially in the ield o aviation, where the design o the aircrat dynamics and light controller must take pilot perormance careully into consideration [] [2]. A urther limiting actor arises i the tracking task is perormed on-board a moving vehicle. Motions o the vehicle can couple through the operator s body and accelerations can induce inertia orces that act on the joystick, giving rise to tracking commands quite outside the intentions o the human operator. The phenomenon o vehicle motion coupling through the operator s body has been termed biodynamic eedthrough or vibration eedthrough and has been studied extensively; a survey is contained in [3]. The systems in which biodynamic eedthrough plays a role can be divided into two classes according to whether or not the vehicle itsel is under the control o the manual control interace. Manuscript received April 4, 25 Both authors are with the Department o Mechanical Engineering, University o Michigan. For the class in which the vehicle is under control o the interace, a eedback loop is closed through the operator s body, as the vehicle accelerations produce joystick motions that in turn command vehicle motion. Oscillations may appear in the human-machine system oscillations that may grow or become unstable with suicient loop gain and accumulated phase dierence. Especially because these oscillations can jeopardize the sae operation o the vehicle, they have attracted signiicant attention in the literature. For example, oscillations appearing in the roll behavior o high-perormance aircrat have been analyzed in [4]. The dynamics o both motiontype and orce-type joystick interaces and the associated human-machine system were analyzed by Hess [4], [5]. Hess constructed a structural pilot-aircrat model to analyze the roll motion including a biodynamic eedthrough model, and models o pursuit tracking perormance, vestibular eedback, and manipulator orce response. Biodynamic eedthrough also appears in the drive dynamics o powered wheelchairs and hydraulic excavators [6], [7]. Biodynamic eedthrough might also play a role in inciting or exacerbating another eedback loop whose stability is oten compromised, namely Pilot Induced Oscillations (PIO). Time delays between the action and perceived response o the controlled element are at the root o PIO, and occasionally the gain or phase margins can be exceeded when the PIO loop is coupled with or disturbed by eedthrough dynamics [8]. The second class o system in which biodynamic eedthrough plays a role does not eature a eedback loop through the operator s body. In these systems the object being moved or steered with the interace is a machine or object other than the vehicle. Instead, biodynamic eedthrough may be interpreted as a path by which a disturbance enters the tracking loop (the control loop in which the operator acts as controller, and the interace and controlled object are plant). As vehicle passengers increasingly take on manual control tasks while on-board ground and air vehicles, the role o biodynamic eedthrough acting as disturbance or detractor rom perormance becomes more and more relevant. Especially in modern military operations, manual control input is demanded o crewmembers while underway. But even the design o interace to inormatics devices in civilian automobiles requires attention to the eects o biodynamic eedthrough. This second class o system has not been addressed in the literature. Various approaches have been proposed to mitigate the eect o biodynamic eedthrough. Perhaps the most straightorward and oten eective means is to redesign the kinematics o the interace or conigure an arm or handrest to stabilize the hand. A steering wheel, or example, is essentially immune

2 SUBMITTED TO: ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL 2 to translational accelerations whereas the largely translational displacements o the hand on a joystick make joystick interaces sensitive to translational accelerations directed perpendicular to the joystick axis o rotation. Another approach involves modiying the mechanical response o the interace device, such as increasing joystick damping [6] and/or stiness. Also, so-called motion sticks are considered more immune to biodynamic eedthrough than orce sticks (also called sti sticks) [3]. Short o interace redesign, signals within the system comprising the vehicle, human, and controlled element (whether or not the controlled element is the vehicle) can also be manipulated to mitigate biodynamic eedthrough. Gains can be reduced [6] or reduced selectively according to requency content using a ilter (although compromised tracking perormance oten results). Alternatively, a ilter can be used to remove that portion o the command signal that is due to biodynamic eedthrough, when such ilter is designed according to a model o biodynamic eedthrough. Grunwald et al.[9] demonstrated the utility o such a ilter and Verger et al.extended the approach to an adaptive ilter []. The use o a motorized control interace or cancellation o biodynamic eedthrough was proposed in [] and [2] and urther developed and applied in [3] and [4]. In this approach, an estimate o the biodynamic eedthrough orce acting on the joystick is generated and applied directly to the interace through the action o a motor coupled to its motion. Generation o the cancellation orce is accomplished with a controller based on an estimate o the biodynamic system transer unction and a measure o vehicle motion. Ideally the interace itsel, as the site at which the orces cancel, should respond as i biodynamic eedthrough were not present. As a result, the interace has a dierent mechanical eel to it. Sirouspour and Salcudean [3] [4] describe the use o a controller whose design is optimized to simultaneously cancel eedthrough eects and match a desired admittance o a joystick interace. The investigation covered only the case in which the vehicle was the controlled element, and used a model o biodynamic eedthrough based on the driving point impedance o the operator. In a related approach, Repperger [8] has investigated the use o a motorized joystick (haptic interace) or mitigating PIO. In this paper, we develop a model o biodynamic eedthrough and develop a system identiication experiment to be used as the basis o a cancellation controller that injects its eort through a motor coupled to the interace device. The system identiication experiment relies on a orce sensor integrated into the joystick and its temporary coniguration as a sti stick with a mechanical stop in the orm o a peg. Then during tracking operation, the peg is removed and the motor is employed as the control actuator. We investigate the utility o our compensation controller in the context o a pursuit tracking task, and use the well-known crossover model by McRuer [2] to analyze human perormance with and without the controller in place. We also incorporate trials without vehicle motion into our experiment to establish baseline tracking perormance by our subjects. Our model o biodynamic eedthrough is parametric (ARMA) but not based on a multibody dynamics model o the operator. Future work will include the development o physically-based models and perhaps the use o adaptive cancellation controllers. In this paper we address only the second class o systems, in which the controlled element is not the vehicle and thus the biodynamic eedthrough is a pathway or disturbance to enter the tracking loop. Our present experimental results indicate that the cancellation controller signiicantly improves human perormance in tracking tasks in a moving vehicle. In the ollowing, we begin in Section II by introducing a model o the human operator in terms o biodynamic coupling through his body and in terms o pursuit tracking control perormance per the crossover model. In Section III we develop the system identiication experiment and associated parameter it and present the means o characterizing pursuit tracking perormance. In Section IV we present our experimental results, grouped under three conditions: (A) stationary vehicle, (B) moving vehicle without compensation, and (C) moving vehicle with compensation. We end by discussing the merits o the cancellation approach in Section V. II. MODELING THE HUMAN-VEHICLE SYSTEM In this section we develop a mathematical model o the interacting human operator and vehicle a model aimed speciically at capturing the eects o vehicle motion on manual control perormance. Naturally, the most interesting part o the system model pertains to the human operator. Our model or the operator has two main sub-models: The irst is a description o the mechanics o the operator s body that is responsible or transmitting mechanical energy between the vehicle seat and the manual control interace. This sub-model, which we call the biodynamic model, does not include any volitional control. That is, it does not include human perception or action. The second component o the operator model describes volitional response to visual input pertaining to a pursuit tracking task. We call this sub-model the volitional tracking model. The development o the interacting biodynamic and tracking sub-models shall become the basis in Section III below or the design o a system identiication experiment that estimates parameters or a biodynamic model and the design and experimental veriication o a compensating controller based on that model. To begin the development o the system model, let us briely introduce our experimental apparatus in Figure. For now, the experimental apparatus serves our purpose as a convenient, i somewhat simpliied, representative o a ground vehicle. The apparatus will be more ully described in Section III, where the topic will be its use in experiments aimed at veriying the model and the cancellation o biodynamic eedthrough. Here, it suices to say that the apparatus is a single-axis motion platorm capable o simulating the lateral motions o a vehicle while an operator attempts to perorm a manual control task on-board that vehicle. The operator is seated in a chair on the platorm and uses his right hand to grasp a joystick mounted on the platorm. Through the joystick, and using visual eedback, the operator may cause a cursor on a computer screen to ollow a target that moves in an unpredictable ashion. The target ollowing task is modeled ater the well-known pursuit

3 SUBMITTED TO: ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL 3 tracking task and is representative o a large amily o manual control tasks that might be undertaken on-board a vehicle. By adopting pursuit tracking, we are able to draw upon well-known models o human perormance such as McRuer s crossover model and certain associated perormance metrics. Our apparatus produces motion in a lateral direction only, or which we draw justiication rom the observation that biodynamic eedthrough, when it appears in a real-world vehicle, produces motion predominantly in a particular axis and does not seem to depend on coupling between axes. Although our apparatus has limited workspace, it can nevertheless be used to induce biodynamic eedthrough since the phenomenon usually involves only small to moderate amplitude oscillations. Plant output cursor displacement, Reerence target displacement, Joystick displacement, x j x r x p how the vehicle velocity ẋ v and the joystick velocity ẋ j aect the joystick orce b and the vehicle orce s, respectively. The our transer unctions are assembled together in a two-port shown inside the dashed box in Figure 2. Note that although the joystick rotates about a horizontal axis, we deine the displacement x j o the hand as a translational displacement, measured relative to the platorm, since the angular workspace is small (< 3 ) and the distance rom pivot to hand is large ( cm). We use a eedback control model to capture the volitional actions that the operator applies to the joystick in response to visual input rom the screen. As shown in Figure 2, the operator applies a orce t to the joystick J in an attempt to minimize the error x e between the reerence signal x r and the output x p o the plant P. A transer unction T characterizes the input-output relationship o this tracking controller. The eedback path rom the plant output models visual input to the operator. The path rom ẋ v through the block s m j accounts or the eect o vehicle acceleration on the mass o the joystick. Assuming small joystick displacements x j, the equivalent mass m j accounts or the inertia orce that acts on the joystick due to the acceleration ẍ v o the moving vehicle. Port : trunk-seat Biodynamics Port 2: joystick-hand Ball screw and linear guides Capstan drive x v, Platorm displacement s x v _ Z vs js Z 2 vb x j _ Z 22 jb b Z 2 Fig.. A human operator seated on a single-axis motion platorm uses a joystick to cause a cursor on the screen to track a target that moves in an unpredictable ashion. The translational axis o the motion platorm is perpendicular to the rotational axis o the joystick, thus both the platorm and hand motions are in the lateral direction. xr _ x e s m j T t _ J x j x j s P x p As mentioned above, we begin by making a distinction between the passive biodynamics and the active sensorimotor unction o the human operator. The phrase passive biodynamics reers to the coupling o mechanical energy across the two mechanical interaces that exist between the operator s body and the environment. The irst mechanical interace lies between the seat and operator s trunk and the second lies between the joystick and the operator s hand. In contrast to the tracking model that captures the sensorimotor unction o the operator, the biodynamic model includes only unconscious responses, perhaps including stretch relexes. For now, we assume that the biodynamic model and tracking model superpose. For each mechanical interace, a orce and a velocity may be deined to characterize the interaction. Let the interaction orce s and common seat/trunk velocity ẋ v characterize mechanical interactions between the seat and trunk o the operator and let the interaction orce b and the hand/joystick contact velocity ẋ j characterize the hand/joystick interactions. Between these our variables, there exist our transer unctions. Two drivingpoint impedances, denoted Z and Z 22, describe how vehicle velocity ẋ v and joystick velocity ẋ j impact the vehicle orce s and the joystick orce b, respectively. The other two transer unctions are through-impedances Z 2 and Z 2 that capture Fig. 2. The human operator is modelled as a two-input, two-output system in which the input velocity ẋ s and output orce s comprising port capture the interaction between the trunk and the vehicle seat, while the output orce b and input velocity ẋ j comprising port 2 describe the interaction between the hand and the joystick. The our impedances capture the input-output maps o the two-port. The transer unction T describes how the operator responds to the visually observed dierence between the reerence signal x r and the plant output x p by imposing a orce t on the joystick J. The orce b enters the tracking loop as a disturbance. The orce b is the biodynamic response o the human operator to the joystick angular velocity ẋ j and the vehicle velocity ẋ v. A. Modeling the biodynamic system To highlight the role o biodynamic eedthrough as a disturbance to the tracking loop, the block diagram in Figure 2 may be re-arranged and simpliied to arrive at the block diagram in Figure 3. Since the vehicle mass is signiicantly larger than the mass o the operator, we model the vehicle as an ideal motion source and remove the transer unctions Z and Z 22. The two pathways rom vehicle velocity ẋ v through Z 2 and sm j may be combined by deining b b sm j ẋ v and by deining H Z 2 /s m j to create the single pathway rom vehicle acceleration ẍ v through the transer unction

4 SUBMITTED TO: ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL 4 H shown in Figure 3. Note that the input to H is now the vehicle acceleration ẍ v. A block diagram manipulation was used to move the driving point impedance Z 22 to its position in eedback around the joystick J. The role o the vehicle acceleration ẍ v acting through the biodynamic model H is now apparent as a disturbance acting on the tracking control loop. x v H ' b x r x e t T jb J Z 22 x j x j s Fig. 3. In this block diagram, biodynamic eedthrough can be recognized as a pathway or vehicle acceleration ẍ v to enter as a disturbance in the tracking loop. This block diagram ollows rom that in Figure 2 ater removing Z 2 and Z under the assumption that the vehicle acts as a motion source and ater deining H Z 2 /s m j and moving Z 22 into position as a eedback loop around the joystick J. We propose to mitigate the eects o biodynamic eedthrough on tracking by injecting an estimate ˆ b o the orce b into the tracking loop. We will inject ˆ b through the action o a motor coupled to the joystick such that its direction opposes that o b. Thus ˆ b should cancel the eect o biodynamic eedthrough. In Figure, the capstan drive that couples a DC motor inside the joystick box to the joystick is noted. To produce the estimate ˆ b, we assume that a measure o vehicle acceleration ẍ v is available (perhaps through an accelerometer). We urther require an estimate Ĥ o the biodynamic eedthrough unction H. Insoar that the model Ĥ is accurate, the action o ˆ b should reduce the eect o vehicle acceleration disturbance ẍ v on the tracking loop. Construction o the estimate Ĥ relies on data rom a system identiication test that involves the human subject and measurement o vehicle acceleration ẍ v and the hand/joystick interaction orce under special conditions. This system identiication step takes place prior to implementation o the cancellation controller, but using essentially the same hardware. The production o vehicle acceleration ẍ v (by virtue o the vehicle itsel) and its measurement with an accelerometer are already assumed or the operation o the cancellation controller. A orce (or torque) sensor on the joystick is the new sensor required or the system identiication step. A orce sensor on the joystick, however, can only measure the total orce, which is the sum o the biodynamic orce b, the volitional orce t, and the driving point impedance response jb o the operator (see Figure 3). However, i joystick motion is prevented, say, by a peg that locks it in a vertical position during the system identiication test, then the impedance Z 22 will not be excited and jb =. I urther the subject is not given any task and asked to not produce any orce by volition, then t can be assumed small. Under these conditions, and assuming the orce and acceleration signals in question can be represented as linear unctions o the Laplace variable s, P x p then H(s) = F b (s) s 2 X v (s) = F (s) s 2 X v (s) ẋ j=, t= A more complete description o the experiment used to construct the estimate Ĥ(s), using a pegged joystick and an idle operator shall be taken up in Section III below. B. Modeling volitional tracking In contrast to the biodynamic model, a model o an operator whose hand on the joystick responds to visual input to cause a cursor or cross-hairs to track a moving target cannot rely strictly on biomechanics. Cognitive processes, in particular visual perception and volitional muscle action are at play in the transer unction T that is the controller in the tracking loop. High-level cognitive processes such as eedorward control or path planning can be neglected, since the target moves in an unpredictable ashion, has no preview, and must thereor be continually monitored. I there exists a transer unction in the plant (or example an integrator rom steering angle to vehicle heading, as in the simplest model o driving) then the operator must take such behavior into account i he is to have any success at tracking with such a plant. Fortunately, pursuit tracking has been studied extensively and is richly reported in the literature [2]. We have adopted the pursuit tracking task precisely because such models exist, based on experimental observation o human behavior. The most amous o these models is the crossover model, irst introduced by McRuer [2]. McRuer s crossover model describes the human controller not as an isolated input-output system, but as a member o the open-loop transer unction. The open-loop transer unction, under unity gain eedback as in Figure 3, is the cascade o the controller T, the joystick dynamics, and the plant dynamics P. Let us denote the eedback interconnection o J and Z 22 together with the integrator as J. Then the crossover model states that the open-loop transer unction T J P has the requency response, in the region o crossover, o an integrator with a certain time delay. The crossover requency ω c is that requency or which the response has unity or db gain. In symbols, T (jω)j (jω)p (jω) = ω ce jωt d where the time delay T d depends on the operator, the type o plant and the reerence signal. According to the crossover model, this description o the open-loop transer unction holds true in a -.5 decade requency range centered about the crossover requency []. Such an open-loop transer unction (basically an integrator) is simply a good idea, in basic controller design terms. The high gain at low requencies acilitates good tracking o the slower components o the reerence signal (with requencies below the crossover requency). The low gain at high requencies ensures high requency noise suppression. Associated with an integrator is a 9 phase margin, some portion o which will be consumed by the pure time delay, another portion o which will remain as net phase margin at the crossover requency. The integrator, with its gross 9, is a suitable jω () (2)

5 SUBMITTED TO: ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL 5 compromise between perormance (which would produce less available phase margin) and stability robustness. What the human operator evidently does when acting as a controller in the pursuit tracking task is to choose (or achieve) a crossover requency w c and time-delay T d, then invert or compensate or the plant and joystick dynamics to produce an open-loop transer unction o an integrator with time delay (as in Eq. (2)). Ample experimental evidence reveals that trained human operators can extract good tracking perormance rom various plants, yielding open-loop transer unctions in the orm o Eq. (2). Values or ω c and T d have even been tabulated or various types o reerence signal and various types o plant dynamics, including K, K/s, and K/s 2, where K is a gain []. In general, the more diicult the task, the lower the crossover requency ω c and the higher the time-delay T d. In our experiments, we shall adopt a simple plant dynamics: unity gain or P =. We shall also propose the use o ω c as a perormance metric. Note that we have modeled the human as a orce source, not as a motion source, thus the joystick is a double-integrator and the plant is unity gain. An alternative would have been to model the human as a motion source, in which case the joystick impedance might have been neglected and the joystick/plant transer unction would simply be unity. III. METHODS Two distinct experiments were used in conjunction to construct and test our approach to biodynamic eedthrough cancellation. The irst is aimed at constructing the model Ĥ o the biodynamic system, or o determining parameter values or a model whose orm has been assumed. The particular model we used is a auto-regressive moving average (ARMA) model. This topic will be taken up in section III-A. The second experiment is designed to test the eicacy o the cancellation controller at improving tracking perormance. For the design o the second experiment, we pay particular attention to the choice o the reerence signal. Our aim is to choose a reerence signal that will maximize the inormation about tracking perormance that can be extracted rom the data. This topic is discussed in section III-B. Finally, subsection III-C presents the protocol used in the irst and second experiments, describing the tasks undertaken by the human subjects. A. Identiication o the biodynamic system For the biodynamic model, we assumed a model structure in the orm o a dierence equation with constant parameters c i, (i =,,..., 4) and d j, (j =,..., 4) b(n) = 4 c i ẍ v (n i) i= 4 d j b(n j), (3) j= where the signals b and ẍ v are represented in discrete time and n indexes discrete samples. The constants c i and d j are to be determined by it to experimental data. To re-arrange the dierence equation into a structure useul or itting parameter values, we deined a data matrix A and a parameter vector b as A = [ẍ v (n),..., ẍ v (n 4), (n, )..., (n 4)] b b b = [c,..., c 4, d,..., d 4 ] T, (4) where underbars on ẍ v and b indicate column vectors o discrete data that march back in time by row and arguments that indicate shiting o the entire column in discrete time. Thus the construction o matrix A acilitates the least-squares solution or the parameters contained in b using the wellknown pseudoinverse orm b = (A T A) A T (n) (5) b The orm o the model Ĥ in Eq. (3), in particular the ourth order and zero relative degree, were chosen based on observations o the experimental transer unction estimate (MATLAB unction te) constructed rom experimental data o acceleration and orce. Data were collected using white noise to produce motion o the platorm, whose acceleration ẍ v was measured with an accelerometer, iltered with an analog anti-aliasing ilter, and recorded. During this time the platorm reerence signal was white noise bandpass iltered to.7-4 Hz. The maximum amplitude accelerations recorded were.75 g. A human subject sat in the platorm chair with their hand grasping the joystick but not perorming any task. The joystick s angular position was ixed relative to the platorm with a snug-itting steel peg inserted through its structure. A load cell in the stem o the joystick sensitive to shear orces measured the joystick orce b, which in turn was anti-alias iltered and recorded. Although platorm motion control was managed at Hz, data recording occurred at Hz and the test lasted or 2 minutes. Beore processing, the data were low-pass iltered (ith order Butterworth ilter, c =Hz) and down-sampled to 5 Hz. A typical experimental run or a representative human subject produced the transer unction estimate shown in Figure 4 as a swath o dots on the magnitude and phase versus requency axes. Two peaks separated by a notch at about 6 Hz appear in the magnitude plot, supporting the choice o a ourth order model. Higher order models did not produce better its. Since the magnitude is approximately lat at high requencies and the phase generally starts and returns to 8 at high requencies (a trend observed to hold generally across subjects), a relative degree o zero was chosen or the model. The continuous traces on the Bode plot in Figure 4 show the requency response o the model it to the same data. The model parameters, or coeicients in the dierence equation were computed using Eq. (5) and this model was excited with white noise as vehicle acceleration to produce a simulated joystick orce response that in turn was ed into the MATLAB te unction. B. System identiication o volitional tracking In contrast to the parametric orm o the model used or system identiication o the biomechanical subsystem, we used a non-parametric model or the tracking loop. We are primarily interested in an expression o the tracking loop in

6 SUBMITTED TO: ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL 6 Magnitude, [db] Phase [deg] 3 2 Experimental data and itted model Exp. data Model Fig. 4. The requency response o the orce b to the excitation ẍ v during the system identiication test is shown or one subject. The Bode plot o the model Ĥ itted on the experimental data is shown in a continuous line. the requency domain, in particular the magnitude and phase response o the open-loop transer unction rom the error signal x e to the plant output x p. This orm is inspired by the crossover model. We chose this orm in the hope that certain characteristics such as the crossover requency might become suitable perormance metrics. To maximize the inormation to be extracted rom the data, we paid particular attention to the design o the reerence signal x r to be tracked. r(t) T y l (t) Fig. 5. A generic nonlinear system expressed as the sum o a describing unction T and a remnant n(t). To introduce the design o a reerence signal x r that best acilitates the identiication o the open-loop transer unction o the tracking loop, let us consider the generic system shown in Figure 5. Let the transer unction G rom r(t) to y(t) be expressed as the sum o a describing unction T and a remnant or noise input n(t). Since we assume that the signals y l (t) and n(t) are not measurable, the challenge is to design r(t) such that the best estimate Ĝ o T can be extracted rom the signals r(t) and y(t). Beginning with the cross-correlation unction φ ry (τ), deined as φ ry (τ) = lim θ n(t) y(t) θ 2θ r(t τ)y(t)dt, (6) θ and the autocorrelation unction φ rr (τ) deined similarly, one may divide the cross-correlation spectral density (CSD) Φ ry (jω) by the power spectral density (PSD) Φ rr (jω) to obtain an estimate Ĝ or the transer unction g(jω), where Φ ry (jω) and Φ rr (jω) are the Fourier transorms o φ ry (τ) and φ rr (τ), respectively. Because the Fourier transorm and cross-correlation are linear operators, one may write: Ĝ(jω) = Φ ry(jω) Φ rr (jω) = Φ r(y l n)(jω) Φ rr (jω) = T (jω) Φ rn(jω) Φ rr (jω) R e jωτ φ rn (τ)dτ = T (jω) Φ rr (jω) (7) which expresses the estimate Ĝ as the sum o a describing unction T (jω) and a remnant or error term. The error term can be made small i r(t) and n(t) are uncorrelated by using a maximally long test time. Alternatively, the error term may be minimized by increasing its denominator, or increasing the value o the PSD o the reerence signal or the requency range o interest. Since the expression in Eq. (7) holds at any requency ω = ω k, an estimate Ĝ(jω k) closest to T (jω k ) at that requency can be obtained by exciting the system with r(t) = L sin(ω k ), where L is a limit set to avoid saturations in the signals r(t) or y(t). This observation suggests a test paradigm in which the requency response Ĝ is reconstructed rom a set o estimates o T (jω k ), each taken at a particular requency ω k. The collection o test requencies are chosen to span the requency range o interest. For the describing unction T, the estimates can be made at the same time using a sum o sinusoids or the input signal r(t). I it is urther supposed that T is linear and time invariant (LTI), then superposition holds and the resulting estimate is not dependent on the particular amplitudes or requencies chosen in r(t). The magnitude and phase estimates are available only at each requency ω k, and appear as isolated dots on a Bode plot. The estimate Ĝ is then constructed by itting or interpolating among these dots. This approach has been used in previous work on pursuit tracking. It is common practice, in act, to report the requency response o pursuit tracking using isolated points on a Bode plot [5], [2], [5], [6] and [7]. In the present work, a sum o iteen sinusoids was used or the reerence signal x r (t). Even though this signal is periodic, it is random appearing due to its complexity and thereor eliminates precognitive tracking. Special attention was paid to the choice o requencies and their amplitude, ollowing in part the recommendations in [8]. To ensure that the reerence signal had zero mean over the 8 second test time, the period o each sinusoid was chosen to be an integer ratio o 8. This guarantees that each sinusoid starts and ends at the same phase. Also, the requencies o the component sinusoids were chosen to be relative prime multiples o the undamental requency o.55 Hz. Since the crossover requency or each subject was expected to lie between. Hz and.6 Hz, the requencies o the iteen sinusoids were distributed evenly (on a logarithmic requency scale) in the range between. Hz and 4 Hz. The prime multipliers were: 2, 3, 5, 7,, 7, 23, 37, 59, 87, 3, 99, 3, 467, and 79. The amplitudes o the 5 sinusoids were enveloped with an exponential unction o requency as ollows: 5 x r =.75 e.4(k ) sin(ω k t φ k ) (8) k=

7 SUBMITTED TO: ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL 7 The decay rate.4 and the scaling actor.75 were determined experimentally so as to keep the cursor inside the screen but utilize much o the available space. Also, attention was paid to make sure the signal would contain suicient energy at high requencies to impose a suitable tracking challenge. The phase angles φ k o the sinusoids were randomized beore each test to eliminate any use o memory. Once the iteen sinusoids were constructed, a code was written to extract the open-loop transer unction o tracking, G(ω k ) = X p (ω k )/X e (ω k ) or the iteen angular requencies k =, The integral in Equation 6 and the Fourier transorms needed to compute the CSD and the PSD were carried out numerically in MATLAB. C. Human subject test protocol Human subject tests were used to experimentally veriy the proposed solution. The subjects carried out a pursuit tracking task with a motion stick in the motion platorm under three conditions. First, the subject used the joystick to track a target while the platorm remained stationary. Tests under this condition were used to establish baseline tracking perormance or each subject. Second, the subject used the joystick to track a target while the platorm moved under white noise input and without cancellation torque on the joystick. Tests under this condition were used to demonstrate tracking perormance degradation due to ride motion. In tests under the third and inal condition, the subject used the joystick to track a target while the platorm moved under white noise input and and while the cancellation controller imposed torques on the joystick through the joystick motor. Tests under this third condition were used to determine the extent to which the controller restores tracking perormance in a moving environment. Twelve subjects were tested, ten men and two women aged The subject pool did not include the authors. Each subject provided inormed consent according to University o Michigan human subject protection policies. Each subject had several hours o past experience with our apparatus using the joystick or tracking with and without the platorm moving. Each subject was given at least three minutes o additional practice time beore each test to decrease learning eects. The three tests were carried out in a randomized order or each subject to average out the eects o learning and atigue. The subjects were not told when the compensator was on or o. Each subject was buckled up in a seat attached to the platorm using a our-point harness. Each subject grasped the singleaxis joystick with his or her right hand and were instructed not to use the elbow rest. Our experimental apparatus, introduced above in Figure, eatures a 2.24 kw brushless DC servo motor (Koll Morgan Goldline B 44-B-A3) that moves the platorm on linear guides by means o a ball screw. The platorm moves only in the lateral direction, and has a ±.5 m workspace. A high-resolution resolver is integrated into the motor housing and the motor moves under the control o a position eedback loop closed within the motor ampliier. This position ollower is commanded with iltered white noise generated by a PC and transmitted through an interace card by ServoToGo Corp. To ensure that the platorm excursions do not exceed its workspace, the position reerence signal was digitally bandpass iltered to.7-2 Hz, as mentioned above. The platorm bandwidth was conirmed to exceed 6Hz. The resulting accelerations were characterized as.6 m/s 2 RMS and 7.5 m/s 2 peak. The joystick has an angular workspace o ±3 and eatures encoder output with a resolution o 496 counts per revolution. The joystick is coupled to a 5W DC servo motor (Maxon RE 4) through a capstan drive. A 5 inch computer monitor was positioned on ixed ground about.5 m in ront o the subject. White lines mm thick on a black background were used to draw a square target box o 3 mm width that moved horizontally on the lower part o the screen according to the signal x r (t). White lines were also used to draw a cursor in the orm o a cross that moved under the control o the plant output x p (t). The vertical position o the joystick placed the cursor in the center o the screen. The plant output x p was proportional to joystick angular displacement rad=.6 m screen displacement. ) Perormance Metrics: To quantiy the success o tracking under the various experimental conditions, three perormance metrics were deined. The irst metric is the root-mean square average tracking error, denoted RMS. The second, called Dwell Ratio and denoted r d, was deined as the ratio o time the cursor lay inside the square target relative to the total test time. This time-on-target deinition is based on the notion that in many applications the target can be hit even i the aiming device does not point exactly at the center. The third is the crossover requency c in Hz, deined as the requency at which a line o -2 db/decade slope it to the magnitude requency response estimate crossed the db axis. Ater the iteen dots were obtained on a requency domain plot using Equation 7, a straight line with a slope constrained to -2 db/dec was it to the irst eleven points using the method o least squares. The lowest eleven requencies range up to Hz, which is the typical upper limit o human tracking perormance. A small RMS error, a large Dwell Ratio and a large crossover requency are indicative o good tracking perormance. In addition to using single numbers that characterize an entire three minute tracking task or each human subject, we also deined two moving averages. The irst such average was deined or the Dwell Ratio using an indicator unction returns one whenever the cursor is inside the target box, and zero otherwise, then averaging this unction over a running second window throughout the test. The mean and standard deviation o the results obtained or the twelve subjects were computed and plotted against time or each test condition. The second moving average was deined or RMS error, also computed as the average over a running ten second time window. IV. RESULTS Ater itting an individualized biodynamical model to the characterization data taken with the pegged joystick, the

8 SUBMITTED TO: ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL 8 tracking perormance o each subject was tested under each o three conditions: (A) baseline (stationary platorm), (B) motion disturbance uncompensated and (C) motion disturbance compensated. Results indicate that motion disturbance has a signiicant deleterious eect on tracking perormance and that compensation signiicantly reduces that eect. Perormance was signiicantly improved with the compensating controller, but not quite restored to baseline levels. Since the compensating controller used or each subject was based on a biodynamical model individualized to that subject, we irst present and compare the 2 biodynamical model its. We then review the perormance dierences between the three conditions using our various perormance metrics, including RMS error, Dwell Ratio (time on-target), and crossover requency. A. Biodynamical model its Using the technique based on a least squares it to the ẍ v and b data presented in the previous section, a biodynamic model was constructed or each o the 2 subjects. Values or the 9 parameters in the dierence equation model locate our zeros and our poles in the discrete z-plane or equivalently, certain notches and peaks in the requency domain. Although the it was perormed using time-domain techniques, here we present and compare the requency responses o the 2 biodynamic models. Figure 6 shows the requency response o the 2 biodynamic models on 2 Bode plots. Each biodynamic model it eatures a notch in magnitude between 5 and 8 Hz ollowed by a small peak. Because a orm with zero relative degree was chosen, the magnitude lattens and phase returns to 8 at high requencies. We are most interested in the eatures that appear in the.- Hz range, since this is the requency range that characterizes human tracking perormance and biodynamic eedthrough (crossover requencies are expected to lie between. and Hz []). The nominal 8 phase dierence between ẍ v and b is appropriate to our sign convention adopted or x v and b and Newton s irst law (that inertia orces oppose the direction o acceleration). Note that i one uses db to approximate the magnitude at low requencies (which appears in Figure 6 to generally correspond to the DC gain) then the biodynamic orce b is moderately small at 3.2 N per m/s 2 acceleration or 32 N per g o acceleration. Note that the biodynamic model can be expected to be a unction o the subject s body posture, the restraints used, the coniguration o the joystick axis, the joystick length, and the degree o muscle co-contraction adopted by the subject, and tightness o grip. The biodynamic model also relects such eects as the stretch relex and possibly other relex loops, but hopeully does not relect any eects o volitional control (something that certainly depends on conormance by each subject to experiment instructions). B. Tracking Perormance Results Beore presenting summary results and statistics across the 2 subjects and across the 8 second trial time, let us irst present some time trajectories. Figure 7 shows trajectories o the reerence x r (t) and plant output x p (t) or one subject during a typical 2-second period o the 8 second trial. In Magnitude, [db] Phase [deg] 2 Results o twelve system ID tests Fig. 6. System identiication results or twelve subjects. The models show similar trends, but they can not be substituted with a single, average model. The current solution necessitates the construction o a separate controller or each individual. separate plots, tracking perormance is shown or each o the three conditions (A) stationary platorm, (B) moving platorm uncompensated and (C) moving platorm compensated. In each o the three plots, the solid line is the reerence signal x r and the dashed line is the plant output x p. It can be seen in (A) that the operator produces an output x p that is a delayed and low-pass iltered version o x r. In plots (B) the tracking perormance is noticeably deteriorated by the presence o platorm motion eeding through the biodynamic subsystem. In (C) the compensator has restored tracking perormance almost back to the level o the stationary platorm case (A). For each condition, the tracking error or dierence between the x r and x p signals was used to compute an average error across the 2 subjects. These average errors are urther processed using RMS computed over a moving second window and presented as the thick black line in Figure IV- B. Gray shading extends one standard deviation above and below the RMS trace. Comparing plots or the conditions (A), (B), and (C) in Figure 8 reveals that platorm motion degrades perormance and increases variance across the 2 subjects and that compensation partially restores that perormance but does not signiicantly decrease the variance across the 2 subjects. Figure 9 shows similar moving averages o the Dwell Ratio (time-on-target) or the 2 subjects. The Dwell Ratio is the raction o time the cursor lay inside the box-shaped target relative to the total test time. The traces in Figure 9 indicate the raction o time that all 2 subjects located their cursors within target during a second moving window. A Dwell Ratio value o is always and is never on target: higher values indicate better perormance. Figures 9 (B) and (C) show that platorm motion degrades perormance while Figure 9 (C) shows again that compensation partially restores perormance. Note that the traces in Figures 8 and 9 show traces over the ull 8 seconds o test-time per trial, rom which trends across the 8 seconds might be inerred, trends such as learning,

9 SUBMITTED TO: ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL A, No motion Reerence Output 4 3 B, Motion, no compensation Reerence Output 4 3 C, Motion, compensation Reerence Output Tracking signals Tracking signals Tracking signals Fig. 7. Twenty seconds o the reerence x r and plant output x p signals are shown or a typical subject under the three experimental conditions: (A) stationary platorm (B) moving platorm without compensation (C) moving platorm with compensation or biodynamic eedthrough. loss o attention, or atigue. Perormance seems steady or the most part, with the possible exception o condition (B)-Moving platorm without compensation, where a slight increase in RMS error and drop in Dwell Ratio over the 8-second trial is apparent. We did not, however, evaluate the signiicance o this trend. Summary statistics were computed or the RMS error and Dwell Ratio by condition across the 2 subjects and collapsed over the 8 second trial period. The median RMS errors or the three conditions are presented as lines through the middle o the boxes in the box-and-whisker plot in Figure. The boxes enclose the lower and upper quartiles and the whiskers show the range o the data. Similarly, the box-and-whisker plot in Figure shows the summary statistics or the Dwell Ratio by condition across the 2 subjects and collapsed over the 8 second trail period. Dierences in RMS error and Dwell Ratio by condition are clearly evident in Figures and Boxplot o RMS error values across twelve subjects No motion Motion, no comp. Motion, comp. Fig.. Boxplot o RMS error values across the twelve subjects under the three test conditions Boxplot o dwell ratios across twelve subjects No motion Motion, no comp. Motion, comp. Fig.. Boxplot o Dwell Ratios across the twelve subjects under the three test conditions We are particularly interested in the nature o the lowpass ilter that characterizes the dierence between the reerence signal x r (t) and the plant output x p (t). A requency response plot o the closed loop transer unction Xp(jω) X r(jω can be expected to have lat response or low requencies and by the same token, the open-loop transer unction Xp(jω) X can e(jω be expected to show higher magnitude at low requencies. Also, the requency response under conditions (B) or (C) could be expected to see increased amplitude at those requencies where signiicant energy eeds through the biodynamic system, disturbing the tracking loop. Using the methods outlined in Section III above, we extracted the magnitude and phase response at a set o 5 requencies or a particular set o input sinusoid amplitudes. In accordance with the crossover model, we it lines o -2 db/decade slope to the series o magnitude response points, using only the irst points (those near the resulting crossover requency). Figure IV-B presents the requency response o the transer unction G that relates the output x p to the error x e or a representative subject, or each o the conditions. The estimates at each o the 5 requencies are shown as dots in both the magnitude and phase plots. For each condition a line o -2 db/decade slope was it to the irst magnitude points, as shown. From those best-it lines, the crossover requencies were determined or each condition. In Figure 2 a crossover requency o.4 Hz can be seen or the stationary platorm case in (A), o. Hz or the moving, uncompensated case in (B) and o.25 Hz in the moving, compensated case in (C). This trend (lower crossover with a moving platorm, but partial restoration with compensation) is typical o all 2 subjects. Figure 3 presents a box-and-whisker plot o the crossover requency values obtained or the twelve subjects under the three experimental conditions. The changes in crossover requency demonstrate tracking perormance degradation as a result o platorm motion and a largely restored tracking perormance as a result o compensation. To analyze statistical signiicance o the dierences by condition, multiple-actor analysis o variances (MANOVA) was applied to the three perormance metrics (RMS error, Dwell Ratio, and crossover requency), revealing signiicant main eects due to condition and subject, with no signiicant interaction eects. Thereater, paired t-tests were applied to each o the perormance metrics comparing conditions (A)