Quadcopter control in three-dimensional space using a noninvasive motor imagery-based brain–computer interface

The study consisted of training and calibration phases, an experimental task phase, and an experimental control phase. In addition, the intrinsic ease of the experimental task was quantified to serve as a baseline comparison to better characterize the achievements of the subjects. Prior to participation in the experimental phase of the study, each subject had received exposure to 1D and 2D cursor movement tasks using motor imagery. One of the subjects had also received training in virtual helicopter control experiments (Royer et al 2010, Doud et al 2011).

Regardless of training background, subjects were asked to demonstrate proficiency in 1D and 2D cursor control prior to progression to the AR Drone quadcopter training. Subjects who demonstrated the ability to correctly select 70% or more of valid targets in each of four consecutive 2D cursor trials, or who achieved an average of 70% or more of valid targets over ten consecutive 2D trials, were deemed proficiently skilled in BCI control for participation in the AR Drone quadcopter study.

During the initial training period, a statistical optimization of the control signal was performed using the Offline Analysis toolbox released with the BCI2000 development platform (Schalk et al 2004). This software allows researchers to identify the specific electrodes and frequencies that were most differentially active during the actuation of a given imagination pair. Spectrograms of the R² value, a statistical measure of degree of correlation of temporal components of the EEG signal with different imagination state pairings, were created so that the electrode and frequency bin (3 Hz width) with the highest correlation value to a given imagination state could be used. In this way, the training period was crucial in determining an optimal, subject-specific control signal that prepared each subject for entry into the real-world task. Figures 2 and 3 show the statistical analysis involved in selecting a control signal for a representative subject. The Offline Analysis toolbox produces a feature map of the R² value at each frequency and electrode, a topographical representation at a user-specified frequency, and a single-electrode representation of the R squared value that varies with frequency. By evaluating these three figures, a researcher may quickly identify a subject specific electrode-frequency configuration that will best serve the subject as a control signal for a motor imagery-based BCI. Electrode selection for each subject can be seen in table 3 in the supplementary materials (available at stacks.iop.org/JNE/10/046003/mmedia).

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Five human subjects, aged 21–28 (three female and two male), were included in the study. Each subject provided written consent in order to participate in a protocol approved by the Institutional Review Board of the University of Minnesota. Four of the subjects had not been exposed to BCI before this study, while the fifth subject had been trained and participated in the previous virtual helicopter study detailed in Doud et al (2011).

The initial training phase of the study was aimed at achieving competence in 2D control in the standard BCI 2000 cursor task in addition to a virtual helicopter simulator program developed and described in Royer et al (2010). The reductionist control strategy that was employed in the Royer protocol proved to be a robust control system that was relatively quick and easy to learn. Thus, this protocol was chosen for the transition from virtual to real-world control. Subjects were introduced to and trained in the 1D cursor task (Yuan et al 2008, Royer and He 2009) until they achieved a score of 80% or above in four consecutive 3 min trials, or until they achieved a score of 80% or more when performance was averaged across ten or more consecutive trials. In the 1D cursor task, a target appeared on either the left or right side of the screen and was illuminated with a yellow colour. The subject was instructed to perform motor-imagery of left or right hand movement to guide a cursor to the illuminated target, while avoiding an invisible target, which was located on the side of the screen opposite the desired target. Subjects were given three experimental sessions, each consisting of at least nine experimental trials (3 min each) to complete this first phase.

A second dimension was then trained independently of the first. Subjects were presented with a second cursor task in which targets appeared at either the top or bottom of the screen. In this task, subjects were instructed to move the cursor up by imagining squeezing or curling both hands and to move the cursor down through the use of a volitional rest. The rest imagination often consisted of subjects focusing on a non-muscular part of the body and relaxing. In this task, addition of the normalized amplitude of the desired frequency components produced the up-down control signal, whereas the left-right control signal was generated from the subtraction of these same frequency components. This allowed for independent control because simultaneous imagination of the hands cancels out the subtracted left-right component, while a lateralized left or right imagination in isolation causes a difference in signal sign that cancels the additive up-down component. Rules for progressing from this phase were the same as in the previous phase, with a limit of three experimental sessions for completion.

The third phase paired the control signals from the first two phases together in a 2D cursor task with an array of four targets in positions on the top, bottom, left, and right sides of the monitor. Subjects progressed to the next phase of training when they could correctly select 70% or more of valid targets in four consecutive 2D cursor trials or an average of 70% or more of valid targets over ten consecutive 2D trials.

After meeting these criteria, subjects progressed to controlling a virtual helicopter (Royer et al 2010). The kinetics of this virtual helicopter operated according to a linear tie of velocity to the normalized amplitude of EEG signal components. After up to three sessions (for a total average of about 1 h of flight time) of training to gain familiarity with this virtual helicopter control protocol, subjects were trained with an enhanced virtual simulation of the AR Drone quadcopter. This improved simulator included an updated virtual model of the AR Drone quadcopter, similar in appearance to the physical quadcopter subjects would eventually be flying in 3D real space. The new simulation program also had an improved control algorithm. It used the same Blender platform physics simulator that was used in Doud et al (2011), but the new algorithm employed force actuation of the drone movement to better approximate the behaviour of the actual AR Drone in a real physical environment. This new algorithm linked subjects' BCI control signal to the acceleration that was applied to the quadcopter rather than to the velocity of the quadcopter. By actuating the virtual quadcopter through force, we excluded from the system some unrealistic movements that could arise from directly updating the velocity of the model in coordination with the control signal. While this force actuation presented a novel challenge to the subjects, it was an important step in exposing the subjects to the real-world forces that must be managed in order to successfully control the AR Drone. More information on the simulator and its control setup can be found in the supplementary materials (available at stacks.iop.org/JNE/10/046003/mmedia). Subject interaction with this simulation system was qualitatively evaluated with the major goal being to familiarize the subject with the control setup, without the pressure of steering an actual robotic drone.

After one to three sessions (consisting of at least nine 3 min experimental trials each) of training with the virtual AR Drone, subjects started to train with the real AR Drone. The four subjects that were naïve to BCI prior to this study spent an average of 5 h and 20 min of virtual training over an average period of three months before starting to train with the real AR Drone. This time includes the 1D left versus right, 1D up versus down, and 2D cursor tasks, in addition to the virtual helicopter simulation. The order of progression of training can be seen in the flowchart in figure 4.

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Upon completion of the virtual tasks, subjects were given an opportunity to calibrate their control signals and familiarize themselves with the robotic system by way of a novice-pilot training task. In both the experimental task and the novice-pilot training task, subjects were asked to pilot the AR Drone quadcopter safely through suspended-foam rings. However, in the novice-pilot training task, the rings were spaced further apart and subjects were instructed to fly back and forth such that no ring was acquired more than once in a row. The design of the novice-pilot training task encouraged the user to explore the control space, and gave the subject an opportunity to suggest refinements to the sensitivity of each of the BCI controls. The experimental group spent an average of 84 min over three weeks on the novice pilot training task. When the subject felt comfortable with the calibration of the control signal in the novice-pilot training task, they were moved to the experimental protocol where speed, accuracy and continuity of control were assessed with the experimental task described below.

Subjects sat in a comfortable chair, facing a computer monitor in a standard college gymnasium. The experimental set-up was such that a solid wall obscured the subject's view of the quadcopter. A 64-channel EEG cap was securely fitted to the head of each subject according to the international 10–20 system. EEG signals were sampled at 1000 Hz and filtered from dc 200 Hz by a Neuroscan Synamps 2 amplifier (Neuroscan Lab, VA) before they were imported into BCI2000 (Schalk et al 2004) with no spatial filtering. Details of electrode and frequency selection can be seen in the supplementary materials (available at stacks.iop.org/JNE/10/046003/mmedia).

The parameterization of BCI2000 during the AR Drone task was such that 4 min runs consisting of 6 s trials ran in the background of the drone control program and communicated the raw control signal via the UDP packet protocol. The trials were set to have no inter-trial interval or post feedback duration. During each BCI2000 trial, the standard cursor moved through a 2D control space for 6 s before being reset to the centre of the control space for the next trial. Since there was no inter-trial interval, this 6 s trial pacing was not perceptible by the subject, but was performed to ensure that the system was normalized regularly. Normalization to impose a zero mean and unit variance was performed online with a 30 s normalization buffer. The output signal during cursor movement for all target attempts entered the normalization buffer and was recalculated between trials. The control signal was extracted as the spectral amplitude of the chosen electrodes at the selected frequency components. This was accomplished using BCI2000's online Autoregressive Filter set with a model order of 16 operating on a time window of 160 ms for spectrum calculation. Effectively, this configuration resulted in continuous output of control signal, pauses for recalculation of normalization factors imperceptible to the subject.

Subjects attended three days of the experimental protocol with each daily session consisting of 6–15 trials, lasting up to four minutes each. Subjects were visually monitored for inappropriate eye blinking or muscle activity during each session and were regularly reminded of the importance of minimizing movement. However, observed eye blinking and muscle movement were minimal during all of the experimental sessions. The time-varying spectral component amplitudes from the EEG at predetermined subject-specific electrode locations and frequencies were selected and then integrated online by BCI2000 to produce a control signal that was sent every 30 ms via a UDP port to a Java program that communicated wirelessly with the AR Drone.

The quadcopter flight environment was set up in a standard college gymnasium. Figure 5 illustrates the experimental setup of the flight environment, and the quadcopter's starting position relative to the two ring-shaped targets. These targets were made of lightweight foam and were suspended so that the internal edge of the bottom of the ring was approximately 1 m above the ground. Each ring had an outer diameter of 2.7 m and an inner diameter of 2.29 m. Subjects were situated to be facing a solid wall on the side of the gymnasium to ensure safety and to obstruct the subject's view of the AR Drone quadcopter. Thus, subjects did not directly see the quadcopter, but watched a computer monitor with a first person view from a camera that was mounted on the hull of the quadcopter.

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The AR Drone 1.0 quadcopter (Parrot SA, Paris, France) in the described control space was chosen for the experiments because it provides strong onboard stabilization while allowing for a wide range of programmable speeds and a smooth range of motion. It is a relatively low-cost option for robust control in 3D space with extensive open source support. In addition, the AR Drone provided access to two onboard cameras, and the accelerometer, altitude, and battery data were all reported to the control software and recorded in real time.

The experimental protocol consisted of three experimental sessions for each subject, with 6–15 trials per session and a maximum flight time of 4 min per trial. Each trial began with the AR Drone quadcopter 0.8 m off the ground. Imagining use of the right hand turned the quadcopter right, while imagination of the left hand turned it left. Imagining both hands together caused the helicopter to rise, while intentionally imagining nothing caused it to fall. A constant forward signal was sent to the quadcopter such that the linear velocity was measured to be 0.69 ± 0.02 m s⁻¹ in the absence of rotational movement. Figure 6 displays the actuations of the quadcopter that correspond to the subjects' motor imaginations. Turning the quadcopter attenuated its forward velocity significantly. This is an example of a real-world control parameter that was absent in virtual simulations. An example of this attenuation can be seen in supplementary video 3 (available at stacks.iop.org/JNE/10/046003/mmedia). Subjects were allowed to pass through the rings in any order, on the condition that no event (i.e. ring collision or target acquisition) occurred within 5 s of the previous event. A demonstration of two short, yet separable, acquisitions can be seen in supplementary video 4 (available at stacks.iop.org/JNE/10/046003/mmedia). This time requirement prevented multiple successes from a single target attempt.

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In comparison to the novice-pilot training task, the experimental protocol allowed subjects to expand their strategies, while still ensuring that no two events came from the same intentional act. In the experimental task, the rings were positioned such that each ring was 4.6 m from the take-off location of the drone.

In order to maximize control, subjects were given a system of actuation that is commonly used for remote control vehicles. This was accomplished by using a nonlinear transformation of the EEG signal before the control signal was sent to the quadcopter. A graph of this transformation can be seen in figure 7. The signal used a threshold to remove minor signals that were not likely to have originated from intentional control. Beyond this threshold, the signal was transformed by a quadratic function so that the subjects were able to alter the strength of imagined actions to either achieve fine control for acquiring rings or to make large turns for general steering purposes and obstacle avoidance.

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If a subject successfully navigated the quadcopter to pass through a ring, a 'target hit' was awarded; however, if the subject only collided with the ring, a 'ring collision' was awarded. If the quadcopter collided with a ring, and then passed through that same ring within 5 s, a target hit but not a ring collision was awarded. Finally, if the quadcopter went outside of the boundaries of the control space, the trial was ended and the subject was assigned a 'wall collision'.

Trials that lasted for less than four minutes ended because the quadcopter either prematurely exited the bounds of the control space (i.e. a wall collision) or a drone malfunction occurred; malfunctions consisted of occasional wireless network failures or mechanical errors that were outside of the users control. These occasional malfunctions due to mechanical errors or the loss of wireless signal caused a small subset of trials to end early. The data from these trials were analyzed prior to the malfunction, but no wall collision was assigned to the subject's performance log, as the error was not within their control.

A control was performed using an experimental protocol in which one naïve subject and two experimental subjects controlled the flight of the quadcopter using keyboard control instead of a BCI. In this protocol, the quadcopter was given the same constant forward velocity, as well as maximum altitude gains and turning speeds that were equivalent to the average of all trained subjects. This protocol allowed for a comparison between a standardized method of control and BCI control. The keyboard control had one advantage in that a 'total zero' signal could easily be maintained such that no left/right or up/down actuation occurred. This allowed for easier achievement of straight-line flight in the control experiments. Although it can be argued that a joystick or a remote control box would be a more nuanced method of controlling the quadcopter, this control paradigm employed the discrete keyboard actuation to ensure that the actuated control was the fastest possible within the constrained parameters. In the keyboard control task, subjects were given the same instructions with regards to the manner in which the rings were to be acquired.

In addition, the intrinsic ease of the experimental task was assessed. It is common practice in the field of BCI to propose a new and novel task for a BCI to perform. When such a task has not yet been explored by other researchers, it can become difficult for readers to determine how much of the subject's success is attributable to the control system, and how much is attributable to the inherent characteristics of the task. In a task that reports that a subject acquires a target 100% of the time, it is important to also know the target density and how well the system performs when given random noise. If the system can still acquire 100% of the targets in the absence of user intent, the result becomes trivial. To evaluate the intrinsic ease of the presented experimental task, a naïve subject was shown a sham video feed of the helicopter moving in the control space. The subject was instructed to simply observe the screen while sitting quietly and still. In all other ways the system was set up in a manner that is identical to the experimental protocol. The subject wore an EEG cap and signals were acquired that controlled the action of an AR Drone quadcopter in the control space. The performance of the AR Drone in the absence of user intent was measured. This setup was preferred to ensure that realistic biological signals were used as the input of the system; thus, poor performance could not be attributed to a choice of random noise of inappropriate magnitude or characteristics.

The performance of BCIs has been quantified by various metrics. Unifying these standard metrics is an important part of establishing a common ground for assessment within the BCI community and encouraging progress from a mutual reference point. In 2003, McFarland et al described a simple, yet elegant ITR metric based on Shannon's work (Shannon and Weaver 1964). However, it has been postulated that this metric cannot be directly applied to asynchronous (self paced) or pointing device BCIs (Kronegg et al 2005). As it has been postulated that such BCIs may nevertheless be used to assist clinically paralyzed patients, the need has arisen for the development of an analogous assessment for BCI's that do not require a fixed schedule of commands. An unfixed schedule of commands would allow users to choose and perform activities as they would in a realistic manner (such as picking up a spoon but thereafter deciding they want to switch to a fork instead). In one particular study, subjects successfully navigated a 2D maze using a forward, left, and right command, but the subjects were limited to a maximum of 15 s to make a choice (Kus et al 2012). If no choice was made, the movement selection was restarted. Furthermore, if subjects in the 2D maze test performed a task incorrectly by moving into a wall, this did not cause the cursor to move incorrectly or stop the navigation task, which allowed for continual trials. Recently Yuan et al (2013) discussed the difficulty in comparing ITR because of the many intricate differences, including the aforementioned error correction, in BCI systems. The need for explicitly redefining tasks, even if there are multiple choices, is a current limiting factor in the utility of BCIs. However, having an unfixed schedule of commands to reach a target in a dynamic path requires the user to re-plan their path to the target in order to account for mistakes.

In order to create an ITR for an asynchronous BCI system that does not limit user attempt time, the same mathematical basis (established by Shannon and Weaver) used by the current BCI ITR standard was used to quantify an analogous ITR for the present study.

It should be noted that with an unfixed trial length and a large field of operation for the user, the ITR may be lower than comparable BCI systems due to the fact that a long trial, regardless of success or failure, lowers the overall average. This is important in that a BCI system can provide more autonomy in the real world if the system does not require the user to be reset to a position or state after a fixed interval of inactivity. Instead, pursuit of the target should be continuous until the task is achieved.

Using these requirements and the basic equation for bits that was developed by Shannon, we were able to create a metric that would be suitable for an asynchronous real-world BCI task, in which only the initial and final positions of the user are required. The following derivation was used. The index of difficulty (ID) from Fitt's law in the form of Shannon's equation uses units of bits. Therefore, using the ID equation from Fitt's law

$$\begin{equation*} ID = \log _2 \left( {\frac{D}{W} + 1} \right), \end{equation*}$$

where D = the distance from the starting point to the centre of the target, and W = the width of the target, we were able to calculate bits (Soukoreff and MacKenzie 2004). Dividing this by the time needed to perform the action of reaching the target, we attained bits/min. The ITR in bits/min was thus calculated by

$$\begin{equation*} {\rm ITR} = \frac{{\log _2 \left( {\frac{{{\rm Net}\,{\rm Displacement}\,{\rm Traveled}\,{\rm to}\,{\rm Target}}}{{{\rm Diameter}\,{\rm of}\,{\rm Target}}} + 1} \right)}}{{{\rm Time}\,{\rm to\, Reach\, Target}}}. \end{equation*}$$

This equation was used to calculate the ITR for the first event after take-off (with an event defined as either a target acquisition, ring collision, or wall collision). The net displacement travelled to the target for this study, as seen in figure 5, is 4.6 m. An example of a first ring acquisition can be seen in supplementary video 5 (available at stacks.iop.org/JNE/10/046003/mmedia). The diameter of the target, calculated as the inner diameter of the ring, was 2.29 m. It should be noted that a ring collision, although close to target acquisition, was counted as a failure to transfer any information. Furthermore, this ITR does not account for the nuance that the users started each run with a forward velocity, and without facing the target. However, it does allow for a simple calculation, taking into account only the initial user position and target positions. Such strict guidelines enable the user to give specific instructions throughout the entire time to target acquisition. As we have pointed out, this metric is a coarse approximation of ITR, but it has been alluded to in the BCI field that ITR is often calculated incorrectly when using the standard metric (McFarland et al 2003, Yuan et al 2013).

Speed of performance was assessed through the use of two metrics. The average rings per maximum flight (ARMF) metric reports how many targets a subject can acquire on average, if the quadcopter were to remain in flight for the full 4 min trial. In addition, the average ring acquisition time (ARAT) metric was also used to evaluate the subjects' speed of control. Continuity of control was evaluated by using the average crashes per maximum flight (ACMF) metric, which reports the average number of crashes that would occur in four minutes given their average rate of occurrence.

ARMF was calculated by

$$\begin{equation*} \frac{{{\rm Number\ of}\,{\rm Target}\,{\rm Acquisitions}}}{{\left( {{\rm Total}\,{\rm Flight}\,{\rm Time \,\div }\, {\rm Four}\,{\rm Minutes}} \right)}}. \end{equation*}$$

ARAT was expressed as

$$\begin{equation*} \frac{{{\rm Total\, Flight \,Time}}}{{{\rm Number \,of\, Target\, Acquisitions}}}. \end{equation*}$$

In addition, ACMF was calculated by

$$\begin{equation*} \frac{{{\rm Number \ of \ Wall \ Collisions}}}{{\left( {{\rm Total \ Flight \ Time} \div {\rm Four \ Minutes}} \right)}}. \end{equation*}$$

The success rate of the present BCI system was assessed by three metrics: percent total correct (PTC), percent valid correct (PVC) and percent partial correct (PPC). If the subject successfully controlled the quadcopter to pass through a ring, one target hit was awarded. If the quadcopter collided into a ring without passing through it, a ring collision was designated. If the quadcopter collided with a ring and then passed through that same ring, only the target acquisition was counted and the ring collision was not awarded. PTC is the number of target acquisitions divided by the number of attempts (total number of target acquisitions, ring collisions and wall collision). In contrast, PVC was calculated as the total number of target acquisitions divided by the total number of valid attempts (total number of target hits and wall collisions). A valid attempt occurred when a definitive positive or negative event occurred. In addition, PPC was evaluated to demonstrate how many perfect completions of the tasks were completed versus how many partial successes were achieved.

PTC was calculated by

$$\begin{eqnarray*} &&\frac{{\rm Number \ of \ Target \ Acquistions}} {{{(\rm Number \ of \ Target \ Acquisitions}} +\,{{\rm Number\ of\ Ring\ Collisions}} +\, {\rm Number\ of\ Wall\ Collisions})}. \hspace{17.5pc} \end{eqnarray*}$$

PVC was given by

$$\begin{eqnarray*} &&\frac{ {\rm Number \ of \ Target \ Acquisitions}} { ({\rm Number \ of \ Target \ Acquistions} +\,{\rm Number \ of \ Wall \ Collisions} ) }.\hspace{17.5pc} \end{eqnarray*}$$

Lastly, PPC was calculated by

$$\begin{eqnarray*} &&\frac{ ( {{\rm Number \ of \ Target \ Acquisitions}} +\, {{\rm Number \ of \ Ring \ Collisions}}) } { ( {{\rm Number \ of \ Target \ Acqusitions}} +\, {{\rm Number \ of \ Ring \ Collisions}} +\, {{\rm Number \ of \ Wall \ Collisions}} )}.\hspace{17.5pc} \end{eqnarray*}$$

The subjects were successful in achieving accurate control of the quadcopter in 3D real space. Table 1 displays the performance results. PVC is the subject success rate in all trials in which a result (either correct or incorrect) was achieved. The PTC metric was used as a stricter metric to ensure that each subject made a significant effort towards passing through the target rather than just reaching it. The PPC metric was most analogous to previous BCI experiments in which subjects solely had to reach a target, and not perform the task of passing through the target in a particular orientation after reaching it. The group per trial weighted average for PTC was 66.3%. The PPC weighted average was 82.6%. A summary of these and all other metrics can be seen in table 1.

Subjects demonstrated the ability to acquire multiple rings in rapid succession by minimizing turning actuations of the quadcopter. Some subjects were able to do this by temporarily minimizing their left/right signal in order to achieve a more direct path. This is demonstrated in video 2 (available at stacks.iop.org/JNE/10/046003/mmedia). Furthermore, subjects were able to achieve fine turn corrections as they approached the rings in order to rotate the quadcopter to pass through the target (seen in video 1 available at stacks.iop.org/JNE/10/046003/mmedia). All subjects were able to successfully achieve high degrees of accuracy by using their motor imaginations to approach and pass through the targets.

The five subjects who participated in this protocol displayed an average ITR of 6.17 bits min⁻¹ over 10 characteristic trials in a 2D cursor control task in which they were given 6 s to reach the target, or were otherwise reset to the centre of the screen and given a new target.

During the AR Drone experimental protocol, the five subjects performed at an average ITR of 1.16 bits min⁻¹. Individual subject values can be seen in table 2. While lower than those reported in the 2D task, these values represent an important step towards providing BCI users with more autonomy, by not mandating a fixed schedule of events or limiting time. The difference in ITR, while partially due to the strict enforcement of ITR calculation in the real world, could represent some challenges in bringing BCI systems to the real world. While the drop off from 2D cursor is noteworthy, so is the fact that the subjects' average ITR was 8.29 times higher than the ITR from the ease of control assessment task, a good indication that the subjects were intentionally interacting with the environment via the BCI system. The ease of control assessment used a random biological signal to control the helicopter, and shows that the task could not be completed at a high success rate without an intentionally modulated signal.

Because of the importance of ITR, it was necessary to ensure that the system did not artificially transfer information without user input, or allow the user to inflate the ITR without using a full range of controls. Therefore, during the period of flight during which ITR was calculated, the direction of control of the user was also tracked, and figure 8 shows the comparison of left to right control together with the comparison to up and down control. This demonstrates that the users had the ability to actuate all dimensions of control in order to move the AR Drone throughout the field to the target.

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For the purposes of this study, a constant forward command signal was sent to the quadcopter; however, the subjects were able to manipulate the speed by rotating and adjusting the altitude of the quadcopter. It was found that large turns in a single direction tended to increase the velocity, whereas temporarily changing directions decreased the forward linear velocity. Individual subject performance and group average performance for speed of control metrics can be seen in table 1.

The ARMF metric was calculated in order to better quantify the speed performance for each subject. If a subject reached the maximum flight time of four minutes, the quadcopter was automatically landed in order to assure that the battery life had at most a minimal effect on homogeneity of control. The group trial weighted average for ARMF was 3.1 rings per maximum flight.

Subjects were given control of the quadcopter in 3D space for flights of up to 4 min. During this time, subjects were able to modulate the movements of the quadcopter as they strategized, in order to acquire the most possible rings. However, if the subjects were to collide with the boundaries of the field, then the trial was ended. By calculating the number of boundary collisions that occurred per maximum length of flight (4 min), an ACMF metric was developed to compare subject performance. The group trial weighted average for ACMF was 0.8 crashes per maximum flight. Subject progress was tracked over each session and a comparison of subject performance, including metrics of accuracy, speed, and continuity, can be seen in figure 9. Subjects demonstrated the ability to maintain smooth control, while avoiding crashes. Video 1 (available at stacks.iop.org/JNE/10/046003/mmedia) demonstrates subject 1 continuously acquiring targets, while avoiding wall collisions and ring collisions in between, thus demonstrating a high level of continuous control.

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In the keyboard control paradigm, in which a naïve subject and two experimental subjects completed the experimental task using keyboard control instead of BCI, the subjects were able to achieve a group weighted average of 12.0 rings per 4 min trial. In contrast, the trained subjects were able to achieve 3.1 rings per 4 min trial using BCI. Thus, our BCI system demonstrated the ability to acquire 25.8% of the rings that were acquired via keyboard control, which is a method considered to be the gold standard in terms of reliability and prevalence for our current interactions with computer technology.

For the experimental ease of control assessment (in which a naïve BCI user was given sham feedback), the naïve subject was able to acquire only one target acquisition and no ring collisions over a total flight time of about 7.5 min. The reason for the short flight time, despite a normal session of 12 trials, was that the subject crashed the quadcopter quickly after take-off in each trial. The subject had a notably high ACMF of 5.9, indicating the high number of rapid crashes that were observed.

In summary, the trained subjects were able to acquire an average of 3.1 rings per maximum flight time compared to only 0.5 rings per maximum flight for the subject with no training or feedback in the ease of assessment task. The ratios of weighted average performance metrics for keyboard control as compared to BCI control, in addition to the ratios of weighted average performance metrics for BCI control compared to the intrinsic ease of the experimental task are reported in figure 10.

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