A Device for Rapid, Automated Trimming of Insect-Sized Flying Robots

Successful demonstrations of controlled flight in flying insect-sized robots (FIRs) $< $500 mg have all relied on piezo-actuated flapping wings because of unfavorable downward size scaling in motor-driven propellers. In practice, the mechanical complexity of flapping wings typically results in large torque bias variability about pitch and roll axes, leading to rapid rotation in free flight for vehicles that are not properly trimmed. Manual trimming by watching high-speed video is tedious and error-prone. In this letter, we introduce an alternative, a trimming device that uses feedback from motion capture cameras to determine and correct for bias torques. It does so using an automated feedback loop, without the need for any visual feedback from the user, or airborne flights which can damage the robot. We validated the device on two different robot flies. After trimming with our device, the robots both took off approximately vertically in open-loop and were able to hover in free flight under feedback control. Our system, therefore, reduces the time of essential yet time-consuming step in robot fly fabrication, facilitating their eventual mass production and practical application.

A torque inherent to a robot which causes it to have some attitude during initial flight. This is generally introduced due to manufacturing inconsistencies in the robot.
TRIM TORQUE: A value of torque that counteracts the bias torque. These are generated by a specific set of trim values, in our case it is voltage offset (V o f f set ) and amplitude differential (δ A). Due to their small size and ability to explore confined spaces, flying insect-sized robots (FIRs)

ROBOFLY-EXPANDED
can be used in search and rescue missions. They are inexpensive and extremely lightweight-with a mass measured in milligrams-making them an appealing alternative to large rovers for space exploration. We can potentially send thousands of these robots in space at very low cost for expeditions and data gathering. They might also be used for crop monitoring in farming applications.
The motivation is to someday mass produce these at low cost like electronic chips which is perfect for use in dangerous environments where they might get damaged.
With the decline in bee population many varieties of fruits and vegetables can come to an end.
We need ways to pollinate plants without them. Due to their light weight and small size FIRs are viable alternatives to pollinate flowers or plants in future.

Background
The first feedback-controlled flying insect robot (FIR) was demonstrated in [2]. Since then, improvements to the basic design have explored increasing payload capacity, simplifying fabrication, and achieving passive attitude stability. In [3] the effect of relative position between the aerodynamics center and center of gravity on intrinsic attitude stability of the FIR was studied, and [4] provided better understanding of dynamics of a flapping wing mechanism. In [5] a four-wing design with increased payload capacity and steering actuation was demonstrated, this work also elucidated the controller design for FIRs. It focused on the adaptive component used to control four wing robots which is important in robots with flapping wing mechanism due error in thrust vector direction because of manufacturing uncertainties. [6] introduced an alternative design ac-tuated by uniomorph actuators. To expand the mobility of robot flies, [1] improved the design by reducing part count and lowering the center of mass, allowing landing and ground ambulation in addition to flight. An emerging alternative to flapping wings also suited to insect scale is miniaturized electrohydrodynamic thrust introduced in [7] and [8].
Each of the foregoing FIR flight demonstrations required that the robot be trimmed, regardless of the number of actuators or design of the robot. From undergraduate physics, an arbitrary set of forces and torques acting on a rigid body can be decomposed into a single force vector acting at its center of mass, and a torque vector. For flight control, we can make two statements about the force and torque acting on a properly-trimmed hovering device such as the Robofly [1]: 1. A zero commanded torque should result in zero net rotational acceleration.

A thrust force should result in a zero net lateral acceleration in the body frame.
Here, we are primarily concerned with (1) above, because a non-zero bias torque results in much larger flight path deviations, which make it hard to correct for in free-flight.
In the context of small flapping-wing robots like FIRs, trimming at such small scales entails two challenges that distinguish it from larger vehicles: (1) Rotational acceleration rates increase as size scale diminishes [9,10], making the dynamics of small vehicles particularly fast. The challenge is exacerbated by the fact that, like many flying insects including fruit flies and hawkmoths, their dynamics are unstable [4,11,10]. And (2) being based predominantly on flapping wings, FIRs consist of a flapping mechanism that, by virtue of its novelty, small size, and complexity, is subject to greater variability in performance than, for example, slightly larger quad-rotor helicopters. The result is that the magnitude of compensatory trim required is larger. As a result, in almost all cases, the first open-loop flights of such robots without trimming result in rapid inversion and a subsequent crash. If the vehicle does take off, it typically moves too far-out of the range of tracking cameras-before the controller is able to adapt for and correct for this irregularity. The trimming device we introduce in this work addresses both challenges.

Main Contribution
For this work, we define the torque trimming process to be the task of finding a trim torque, τ t , that exactly cancels the non-zero bias torque τ b . A bias torque τ b can arise from a) manufacturing inconsistencies, b) wear, and c) if there is damage to the FIR. The bias torque varies from robot to robot, as well as with changes in the payload carried by the robot, like a camera [12], boost converters for onboard power in [13], or an array of photovoltaic cells in [14], making trimming necessary for each robot. In current practice [15,16,5,1], trimming was performed by filming short flights <0.5 s using a high speed camera. The magnitude and direction of the bias torque vector were estimated manually by observing the slow-motion videos. This method requires many human handled, unstable, and thus crash-prone flights.
In this thesis, we introduce a new purpose-designed apparatus [17] that can trim FIRs precisely, rapidly, and automatically. In addition to reducing the operator time it takes to trim a robot, our trimming device reduces the amount of wear and tear on the robot. In comparison, trimming using open-loop takeoffs from the ground invariably involves impacts to the wings, and requires manual handling to re-right the vehicle, which often entails an even greater chance of damage. It is also possible to trim a vehicle hanging from a thin kevlar filament, eliminating wing impacts, but this brings its own set of problems including damage when the wing becomes entangled in this filament, and it is often difficult to disambiguate, in video footage, torques due to torque baises versus those arising from tension on the filament.
In our device, trimming is performed through closed-loop feedback. While the wings are flapped, a controller receives Euler Angles in real-time and continuously updates trim values to counteract bias torques. In particular, the device allows us to minimize two quantities: the pitch bias torque τ pitch b and the roll bias torque τ roll b . After doing so, the robot lifts off nearly vertically. This effectively places the flying system's state within the stability basin of our closed-loop freeflight controller. In the remainder of this report we describe the design, operation, and testing of this new apparatus.

Principles of Operation
The concept of trimming was first introduced in the ships [18] for achieving desired velocity and direction. This term was later adapted by the aviation community to indicate the process of moving on-board freight and trim tabs to achieve a stable flight condition. Trim analysis is a very fundamental and essential procedure in flight mechanics. Formally defined in [19], trim is a flight condition in which the rate of change of the state vector of an aircraft is zero when there are no net applied forces and moments. This definition holds a different significance depending on the type of air vehicle. In helicopters, [20] trimming analysis is a vital part of a stable flight and mid-air maneuvering, this is achieved by using three independent control inputs for the main rotor and one for the tail rotor . In airplanes, trim tabs are provided to a pilot for adjusting stick and rudder paddle forces [19]. In quad-rotor helicopters, pitch and roll trim is typically performed by adjusting the relative speeds of the rotors to compensate for weight or thrust imbalance. In FIRs, trimming consists of altering the wing kinematics so that there is zero net torque applied.

Dynamics analysis of an untrimmed flight
To understand the relevance of trimming analysis in FIRs, we will consider the trajectory of an untrimmed robot controlled by attitude and altitude controller in a 2-dimensional plane, actuated by a thruster on either side. The thrusters can be wings, motors or any source of producing upward thrust. We simulate the robot under the condition that it has a non-zero bias torque on its pitch axis.
The parameters used for the simulations are obtained from Robofly-Expanded, given in table 2.1; more details on the robot are presented in a later section.
The robot is simulated as a 3 degree of freedom system with state vector q = [θθ x w z wẋwżw ]. Here, θ is the angle andθ is the angular velocity of the robot in the body coordinate system. x w , z w ,ẋ w , andż w are position and velocity of the robot in world coordinate system. Body dynamics in this system are represented by Eq. 2.1. Because the wing amounts to 1% of body mass, we neglect the gyroscopic effect of wing inertial dynamics in our model.
Here x b and z b are positions in body coordinates, which are used to obtain x w , z w ,ẋ w , andż w , b w is the experimental value of aerodynamic drag on the wings [11], obtained from wind tunnel tests,

Parameter Value
Mass of the robot 120 mg body frame. We simulated this system using the ode45 solver in MATLAB with initial conditions This value is obtained using the frames of a high speed video of Robofly-Expanded without any trim compensation. The simulation predicts that under these conditions, the robot moves a long distance, more than 20 cm before its position reaches equilibrium ( Fig. 2.1). Moving this far is undesirable because it may be larger than the tracking volume of a motion capture system, or will lead to impacts with obstacles.
A trimming system that can measure such biases so that they can be compensated for before the first free flights can eliminate this hazard.

Trim plays an important role in a FIRs because: (1) A FIRs is inspired by flying insects like
Drosophila and hawkmoths, and it inherits highly unstable and fast dynamics from its paradigms [4] [10], (2) the assembly of these robots involve manually folding and gluing of a lot of discrete parts under a microscope which results in some variations in each half of the robots, and (3) insect sized flapping wings robots are subjected to a lot of wear even in flight times as low as 5 to 10 minutes, which often warrants re-trimming. Due to all these reasons even a simple closed loop takeoff on a FIRs without trimming would result in an imminent crash or the robot can drift too far before the controller can step in.

Trimming About an Elastic Rotation Axis
Torque sensing is commonly achieved by measuring small rotational deflections. One approach is to create a rigid system with sensors capable of detecting small deflections, e.g. the Nano17 Titanium (ATI Industrial Automation, NJ, USA). While this provides high bandwidth, the 8 µNm resolution is insufficient. Capacitive pickup is an alternative that has demonstrated sufficient precision [21], but requires costly electronics hardware and has not been demonstrated in two axes. Our approach is to instead use a low-stiffness spring. This sacrifices unneeded bandwidth in exchange for large deflections that can be measured using sensors commonly available in a robotics laboratory such as a motion capture system or accelerometer, and can be built using the same processes used to fabricate the robot itself.
We begin by introducing the underlying physics of a flying robot attached to a trimming device of our design, whose basic form is shown in Fig. 2.2(b). The principle of operation relies on the fact that the device constrains the robot to rotate around a single axis while keeping all other degrees of freedom fixed. The axis is subject to a spring-like restoring torque so that the robot remains upright at equilibrium. In our device, there are two such axes-pitch and roll-so that both can be trimmed simultaneously. When the wings are flapped, they in general produce both a thrust and a torque. Our device is designed so that applied torque, such as an undesirable bias torque τ b , results in a rotation in proportion to its magnitude. Whereas its design insures that thrust has no effect on rotation, regardless of magnitude. Trimming the robot then consists of determining the direction and magnitude of compensating trim torque τ t that reduces rotation approximately to zero.
For our system to operate in this way, we must make the following assumptions about the thrust vector: 1. Its direction is vertical (coincident with the body-Z axis) 2. It is nearly collinear with the axis of rotation of the flexure joint (that is, the lateral offset O R shown in Fig. 2.2 is small).
We will later show, in Section IIIC, how our device design includes a calibration process in which the robot is precisely positioned to insure assumption (3) above holds.
In our device, we use an integrating feedback control loop to find the compensatory trim torque τ t . The dynamical equation for how the system's rotation angle evolves with time is: Here J is the moment of inertia of the combined robot-trimming device system, θ is the rotation angle, τ b and τ t are the bias torque and trim torque respectively, k s is a spring-like stiffness constant (derived below), and c is a rotational damping coefficient due to aerodynamic drag forces on the flapping wings and damping in the flexure joints. We can solve for the angle at steady-state, giving This shows that the only way to make the angle zero is to make τ b = τ t . This provides a means to determine that the robot is trimmed, without the need to know the exact value of k s . Practical design considerations limit the range of k s , which we address below. If we can measure the angle θ of the robot in the trimming device, for example by using a motion capture camera or an on-board accelerometer, then we can use an integral controller to integrate this error in time to drive it to zero: where k i is the integral controller constant and θ d is the desired angle, which is zero in our case.
This concept can be used for finding both roll and pitch trim torques.

Mechanisms of Torque Actuation
For torque trimming, we are not concerned with the exact mechanism by which a bias torque τ b arises, but we must have the means to compensate for it using a trim torque τ t . In both quad-rotor In a quad-rotor, if rotor speeds are changed, the resulting differential force between propellers causes a torque (Fig. 2.3). Roll torques in the FIRs are produced through a similar means, by increasing the thrust magnitude of one wing (T 1 ) relative to the other wing (T 2 ), A pitch torque is produced by altering the position of the stroke-averaged center of aerodynamic thrust (Fig. 2.3),

For a vehicle actuated by other means, such as four electrohydrodynamic thrusters [8] [7], actuation
is very similar to quad-rotor devices.

Restoring Torque and Flexures
A flexure joint is a form of hinge that allows a rotation over a limited range [22]. Pin joints, bearings, and bushings are not suitable for small scale applications, due to friction scaling [23]. Ac-cordingly, rotation in our trimming device is through flexure joints. A simplified, two-dimensional free-body diagram of the device is shown in Fig. 2.4. The resulting torque on the system, neglecting bias and trim torques, can be calculated using a moment balance and is equal to k f θ − m R gl R sin θ + m b gl b sin θ , where l R and l b are the moment arm of the robot and balancing weight from the pivot point respectively, k f is the stiffness of the flexure joint, and m R and m b are the mass of the robot and counter-balance weight respectively. If we linearize the system using small-angle approximations around θ = 0, we can write the equivalent stiffness as The restoring torque approaches zero as θ approaches zero. Therefore, for a properly-trimmed system (τ b = τ t ), k s does not play a role in trim torque calculations. For practical purposes, however, to ensure that the deflections due to typical bias torques can be measured from our motion capture cameras, k s must not be too large. This is done by choosing the appropriate value of k f .
In early exploratory investigations, we constructed a trimming device with a negative k s , that is, without a counterbalance mass m b . Under these conditions, the system did not have an equilibrium at θ but instead the robot rested at the limit of rotation, tilted. Under these conditions, the integral controller performed a "wind-up" until the integrated commanded torque exceeded what was necessary to drive the robot away from its tilted configuration. But with a negative spring constant, the required torque is maximum at that point, and This had the additional advantage of allowing for the calibration step to eliminate O R described in

Trimming Device for Quadcopter
Crazyflie is mounted on a set of two flexure joints as shown in 3.1, limiting its unconstrained degrees of freedom to two, pitch and roll. We chose flexures instead of pin joints because the same concept will be applied to the FIR and we wanted the setup to be similar.

Trimming Controller for Quadcopter
Roll and Pitch angles feedback is obtained form the IMU at the frequency of 100Hz. These angles are supplied as input to two independent integral controllers which estimate the trim values between -1 to 1. These values are then mapped to the motor speeds of the quadcopter, the sign of the trim value will signify which motor to adjust the speed on, while the value defines the percentage of PWM signal for that motor.

Trimming results for Quadcopter
The results from the trimming experiment on quadcopter are shown in Fig. 3

Experimental Apparatus
After validating the concepts introduced in chapter 2 on a quadcopter. The next step is build an apparatus which can perform the similar function of finding trim values on a flying insect robot.
This chapter explains the design steps followed to build a trimming device and the results obtained by using that trimming device on Robofly-Expanded.

New Robot Design: Robofly-Expanded
As one of our contributions here, we introduce a new iteration of the Robofly design [1], called Robofly Expanded, that further simplifies fabrication. The new design integrates the wing hinge and legs directly into the main layup, reducing the part count for a complete Robofly, when legs are counted, from 12 in [1], to only 8, and far below the 18 of [2]. Additionally, the actuators are re-oriented so that their long axis is horizontal. This has two desirable results. First, by moving the wings farther apart from each other, torque around a vertical, or yaw axis is increased. This is necessary because the only known yaw actuation mode for this basic design consists of actuating the wing faster in one direction than the other to achieve a drag differential. However, this is known to produce a weak force [25]. Increasing the moment arm increases the net yaw force. In [5], this was shown to be sufficient to achieve consistent yaw actuation in either direction, something that was not possible in the design of [2]. Secondly, it allows for increased maneuverability in other directions, by orienting the long axis along the direction of greatest torque, the roll axis [21], and having a very little moment of inertia around its pitch axis. Measurements of pitch torque showed that they were substantially lower than roll torque, by a factor of approximately two [21].
A completed device is shown in Fig. 4.1.

Trimming Device Design
We chose as our performance specification a maximum bias torque error of 0.3 µNm. This is motivated by the estimated torque uncertainty induced by the thin wire tether that provides power and control signals to the robot. While it is hard to provide a simple model of its effect due to its widely variable conformation, one reasonable model for the tether is a torsional spring. Experiments performed in [11] indicated that a 45 • rotation causes a torque of approximately 0.3 µNm, leading to our performance target.
We then used our performance target to design the size of the flexure joints. Flexures were made of 12 µm polyimide film ("kapton"). The bending stiffness of the flexure joint, is calculated by using k f = Et 3 w 12L [22]. Here, t is the thickness of the flexure material, L is the length of the flexure joint (500 µm), w is the width of the joint (3 mm) and E is Young's modulus of 2.5 Gpa. At these values, the resulting flexure stiffness is 2.16 µNm/rad. The same value of flexure stiffness is used for both roll and pitch joints. With this stiffness, a bias torque of 0.3 µNm produces a rotation of approximately 8 • . This is easily measured by the motion capture arena, which can measure angles to within approximately 1 • , indicating that our device can provide the necessary accuracy. Note that we chose the counter-balance mass and position (Fig. 2.4) so that so that m b l b ≈ m R l R so that their equivalent stiffness counteracted the "negative stiffness" caused by the robot's COM being above the flexure rotation axis.
To mitigate buckling, all flexures were loaded in tension rather than compression. The remaining rigid structure was machined from inexpensive, rigid 254 µm fiberglass (FR4), which sandwiched the polyimide flexure material on both sides, following "smart composite microstructure" fabrication methods first introduced in [26]. A rigid part connects the two perpendicular pitch and roll flexures, which are designed so that their rotation axes are as close as possible to the robot's COM. Keeping that in mind the first iteration of the design (Fig. 4.4) kept this distance close to zero, but it was limited with the range of the laser. This impelled us to adopt to ( Fig. 4.2 (b)), with distance 10 mm from COM of robot to the pitch axis. This can cause an error torque if the true thrust vector direction deviates from vertical, violating assumption 1. Adaptive controllers, e.g. in [2,5], typically estimate this to be about 2 • . This results in an error of approximately 0.3µNm, within the specification. This could be eliminated in a future revision that brings these flexures nearly perfectly coincident with the COM, but would require parts to physically surround the Robofly's wings, which extend farther than the ≈ 50 mm cutting range of the galvanometer of our laser machining system. The robot is mounted on the moving part of the pitch link through a connecting rod. The width of the roll link is minimized, at just 15 mm, so that it does not affect airflow from the wings.

Calibration/Positioning the Robot
Here we describe features of our trimming device that allow us to minimize O R , the lateral displacement between the thrust vector and the trimming device's flexure-based rotation axis (Fig. 2.2(a)).
Without this step, we found that trim estimates exhibited large errors, manifested in free-flight as large undesirable rotational accelerations at takeoff. To understand how a non-zero offset O R could introduce error in our measurement, consider the case of robot displaced laterally by a small amount, such as O R =1 mm, on the trimming device. If thrust T is equal to the mass of the vehi- cle, T = mg = 1.2 mN, then the error in torque measurement T × O R is 1.2 µNm. This is large compared our 0.3 µNm accuracy target, and therefore represents a source of error that must be eliminated.
Our solution is to use the mass of the robot itself as the source of information about its positioning. If the wings are not flapping, then a lateral displacement of its COM (O R in Fig. 2.2(a)) induces a torque about the flexure due to gravity acting on the robot's body. Hence, the calibration procedure consists of moving the robot laterally on the the trimming device until its pitch and roll angles are equal to what they were before the robot was added (Fig. 4.3). After the robot is in its calibrated position, its feet are carefully glued to the surface with cyanoacrylate glue on a temporary basis. A soldering iron is used to carefully melt the glue and remove the robot when it is ready to fly.

Fabrication
Parts were machined using a diode-pumped solid state (DPSS) laser with a wavelength of 355 nM (Photomachining, Inc., Massachusetts). The roll link includes "castellated" cuts, which permit precise specification of the rotation axis, which are glued to a fixed angle as part of the assembly process ( Fig. 4.2 (a)). Layers were pin-aligned and bonded together using a thermal sheet adhesive (18 µm Pyralux FR-1500) using a heat press at 200 C under a force of 50 kg. A subsequent release cut separated the required links from scaffolding. The assembly process is shown in Fig. 4.2 (b) in which the two links are glued together. These are bonded to a stable base that holds the assembly away from the surface of the table at about 15 cm to minimize the ground effect due to the table surface below. A lightweight scaffold is then added to hold the retroreflective motion capture markers. The complete device with a Robofly is shown in Fig. 4.5. In future, the trimming device can also be used for the characterization of torque response of the robot as a function of frequency.
Its imperative to have a linear stiffness of the flexure joint in order to attain a consistent mapping between frequency and torque measurements. We loaded the pitch link (Fig 4.2(b)) with different static loads and noted the the deflection using a macro lens camera (Phantom v 5.1) to plot the data points in Fig. 4.6. The linear curve approximation of the data (Fig. 4.6(red)) has a mean squared error of 0.0027 rad suggesting the linearity in the stiffness of the flexure joints. The experimental value of stiffness obtained through this curve is 2.006 µNm which is consistent with its corresponding theoretical value.

Trimming Controller
A diagram showing the essential components of the closed-loop trimming system is shown in respectively. Thrust varies approximately linearly with flapping amplitude [27]. Here, A is the baseline voltage amplitude and ω is the flapping frequency. Roll torque is varied by varying δ A, the amplitude difference between left and right wings. Pitch torque is varied by varying V o , the mean voltage of the sinusoid. To avoid actuator breakage due to cracks, the controller includes saturation blocks to limit the range of these inputs [28].

Trimming Results
Voltage commands from the integral controller and output angles measured by motion capture for two different Robofly devices are shown in Fig. 4.8. In both cases, trim voltages appear to

Hovering
We confirmed that the trimming values from our trimming device could be used for hovering flight as well. We used the controller derived from the one in [5], which is an evolution of the one used in [2]. As in many controllers for underactuated systems, the controller operates by tilting the thrust vector in a desired direction to perform lateral motions [29,5]. The first Robofly was commanded       Chapter 5

Conclusion and Future Work
In this letter, we present a device for correcting the bias torques that are almost always present in small-sized airborne robots due to manufacturing irregularity in their complex flapping mechanics.
Our device operates in a feedback control loop using motion capture feedback. We performed validation experiments on two different Robofly devices, successfully trimming them. In both cases, before the devices were trimmed, they exhibited strong pitch and roll torque in free flight, tumbling almost immediately after take-off. The entire trimming process took less than 25 minutes including calibration, and less than fifteen seconds of wing flapping time. Compared to manual trimming, where the trimming time and number of airborne flights depends on the operator skill, our process is automatic, more predictable and causes less wear. After trimming, both devices were observed to lift off nearly vertically and did not tumble. Trim values consisted of commanded voltage offsets to the drive waveform of the piezo actuators. Subsequently, we showed that our estimated trim values could be used by our controller to perform stable hovering flight. By greatly speeding and automating an essential yet time consuming step in robot fly fabrication, our device will facilitate high volume manufacturing of FIRs.
Our device is also able to trim robots with payload such as a battery or sensor package not perfectly centered relative to the COM. Misalignment is equivalent to a nonzero O R that is corrected for using the calibration procedure in Fig. 4.3. An alternative way to build the trimming device is by tethering the robot to a thin metal rod. Although simple, this method would result in large estimation errors in the event that the thrust vector was not perfectly aligned with the body z-axis, because of the large moment arm.
Yaw trimming could be added by the incorporating a vertical-axis flexure between the align-ment plate and connecting rod. This addition would not be subject to the potential for the confounding thrust-induced torque that required calibration for the pitch and roll axes, making it a simple addition. Furthermore, thrust force trimming could be added by placing the entire device on a sensitive balance scale, positioning the lightweight robot and trimming device off of the side of the scale to minimize aerodynamic ground effect. If the spring constant of is known, a full characterization of torque response as a function of frequency can be done using this device.
While our system was shown in operation on two-winged devices, its design accommodates other designs, such as 4-winged robots [5], or micro-robots actuated by other thruster types such as electrohydrodynamic thrusters [8].
The trimming device presented in this letter uses a camera-based motion capture system to measure orientation on the trimming device, but this is not a requirement. It is expected that most fully-autonomous robots will incorporate an inertial measurement unit (IMU) onboard [31]. The accelerometer in the IMU can serve as an inclinometer on the trimming device, precisely measuring the rotation angle for both pitch and roll axes in place of the motion capture system.