Professor Jean-Jacques Slotine is Professor of Mechanical Engineering and Information Sciences, Professor of Brain and

the Nonlinear Systems Laboratory. He received his Ph.D. from the Massachusetts Institute of Technology in 1983, at age 23. After working at Bell Labs in the computer research department, he joined the faculty at MIT in 1984. Professor Slotine teaches and conducts research in the areas of dynamic systems, robotics, control theory, computational neuroscience, and systems biology.

The course is designed for the first-year graduate program in either mechanical or electrical engineering. The course gives a thorough treatment of the kinematics and dynamics as well as key advances in motion control of robot manipulators. Students will develop proficiency in using homogeneous transformation for complex kinematic structures, in analyzing forward and inverse dynamics of linked mechanisms, and in developing motion control techniques for machines in 6-dimensional space. Along with issues in real-time control, the course covers practical issues related to sensing, feedback control under modeling inaccuracies, and parameter variation. The control techniques treated in the course have a wide range of applications in various industries such as in aerospace, machine tool, and heavy-equipment. The course will conclude with practical applications and emerging topics and future directions in robotics.


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In this paper, we present a tentatively comprehensive tutorial report of the most recent literature on kinematic control of redundant robot manipulators. Our goal is to lend some perspective to the most widely adopted on-line instantaneous control solutions, namely those based on the simple manipulator's Jacobian, those based on the local optimization of objective functions in the null space of the Jacobian, those based on the task space augmentation by additional constraint tasks (with task priority), and those based on the construction of inverse kinematic functions.

Using the Unity game engine, we built a method for measuring the potential implicit cues used during Japanese rice cake (mochi) making. Figure 1 is a representation of the designed environment. Movement of the pestle was measured and recorded by attaching VIVE trackers, a motion tracking accessory, calculating its position based on infrared signals emitted by virtual reality base stations [27], to its handle and head. VIVE trackers were also attached to each glove worn by the person kneading the dough. The mortar and dough were respectively represented by a stool with a height of 0.5 m and a seat of 0.4 m in diameter, and a disk shaped sponge with a radius of 0.3 m. Participants were asked to position themselves on opposite sides of the stool, facing each other.

Participants, 20 in total (Male/ Female: 13/7, age 22 to 35), were divided into two groups. Participants put into the first group were in charge of the pestling, participants in the second group were in charge of the kneading. Each participant from the first group performed the task 6 times for 60 s with each of the members from the second group (between-subjects study design). Evaluation was done both qualitatively and quantitatively. The former was done using a Likert scale based questionnaire with questions shown in Table 1.

For the quantitative evaluation, we focused on the relative distance between the hands of the individual kneading and the pestle using the index in Eq. 1. Here \(x _a\) represents the position of the hand and \(x _k\) is the coordinate of the pestle.

To verify our hypothesis of implicit communication through unconscious cueing, we chose to analyse and compare participant motion data at points where the smoothness of the collaboration was most likely to be disturbed (and therefore mutual understanding between participants seemed most crucial).

As mentioned, the interval during which the rice cake is turned over is the main element that disrupts the established punch-knead, punch-knead of the collaboration (the pace established up to that point). Attention was therefore focused on methods used by participants to proceed with this action as smoothly as possible, with minimal impact on the overall task rhythm. To observe the periodic change caused by the turning of the rice cake, the overall motion of the person performing the kneading was divided into three phases:

When paying close attention to the cycles of each participant, a major difference was noticed. While for some participants, the action cycle remained constant, increasing only for the turning over, for others, the kneading cycle preceding the turning over (\(T_{br}\)) was slightly shorter.

Figure 6a and 6b show the comparison between the group averages of the time length of \(T_r\), \(T_{br}\) and \(T_t\) for implicit and explicit pairs. As can be seen, depending on the technique used by the kneading participant, the rhythm of the person pounding the rice cake was affected.

The authors believe that the increase in kneading pace observed in the behaviour of individuals, in the cycle preceding the turning over of the cake was directly correlated to the awareness of the participant that the following action would require more time. The participant therefore unconsciously used this as a signal to the individual pounding the cake to slow down his/her pace during the next cycle.

Answers collected from the survey are displayed in Fig. 7a. As can be seen in Fig. 7a, for both questions, the experiment scenario where the robot used implicit signal received much better ratings than when the robot did not rely on it.

Figure 7b shows the measured difference in the coefficient of variation of the relative distance \(\Delta x\) both with and without the use of preliminary indication. The Wilcoxon signed rank test was used to evaluate the difference between the result pair of each participant. As shown in Fig. 7b a significant difference (\(p < 0.05\)) was found in the coefficient of variation between the two experiment variants. Results suggested that the use of the preliminary indication facilitated the synchronization between the kneading and pounding and therefore allowed for a more stable \(\Delta x\) with less variation from one motion cycle to the next.

Work performance was first (Fig. 8) evaluated by observing the number of times the rice cake making process was completed within the imparted 45 s. This was done by recording the number of times the rice cake was pestled by the participant. From Fig. 9b, it can be seen that using the implicit indication resulted in a higher performance, with the participant pounding the rice cake, on average, an additional 7 times. This improvement was apparently due the quicker response/reaction time from the participant. With the use of implicit cues, not only was the participant able to anticipate potential changes in the work rhythm, but also became more confident and less fearful of any unexpected behaviour. In situations where the robot did not use the implicit cues, the user became more uncertain and slowed his/her pace down as a cautionary measure (to compensate for any unexpected movement or behaviour from the robot).

In the future, it would be interesting to pay closer attention to the division of control between the human and the robot in order to ensure that the artificial agent, in this type of task, is capable of adapting to demands of the user just as much as the user can adapt to the robot.

To satisfy the first requirement, no task-related information was provided to the system. In addition, we avoided the use of any kind of image/visual data as input data to the system, to ensure minimal context dependence. Regarding the second requirement, to prevent the motions of the user from being restricted or obstructed by heavy data collection equipment, a minimally invasive sensing system was used. Therefore, the placement of Inertial Measurement Unit (IMU) sensors was limited to strategic locations. The following four locations were used: head (eyeglasses), torso and wrists. The IMU sensors used were Bluetooth 9-axis inertial sensor TSND151 [30], with 3 axes of acceleration, 3 axes of angular velocity, and 4 axes of posture (quaternion), for a total of 10 dimensions.

With X the original sensor data, Y the same data after normalization, \(x_{min}\) and \(x_{max}\) as the maximum and minimum values recorded for the sensor over the period of time. Collected training data was divided by time steps and shaped into three dimensional input. During collection of the training data, matching label for each movement of the users was collected by having them vocally express which action they wished for the robot arm to perform at that instant (in the designed experiment, 5 options were avalable: reach, grasp, release, return, wipe).

To verify the capacity of the robot to learn and identify the implicit cues in real time, a final experiment was conducted. For the present study experiments and data collection were performed using a static robot, as shown in Fig. 11. For this part of the study, the experiment was conducted over the span of 3 days (each participant had to participate for three consecutive days, Fig. 13). On the first day, participants performed tasks together with the robot arm by explicitly expressing commands (voicing them), while wearing the IMUs at the locations indicated on Fig. 11. The second day, participants performed the same tasks as the previous day, only this time, whether the collaboration would be done using voiced (explicit) commands or only the user motion data (implicit cues) was randomly determined. On the third day, whichever operation method (implicit or explicit) had not been used the previous day was used for the collaboration. Each day, the participants performed a task for 10 min, since their were a total of four task, the experiment lasted 40 min per person. Data collected from the experiments was used as training data for the system at the end of each day.

Task 1 - Wiping Task The user lifts a basket of dimensions 61 cm x 44.1 cm x 26.4 cm (length x width x height) from the desk while pointing the head IMU towards the area to wipe. The robot arm (already holding a piece of cloth) is expected to move and start wiping the instructed area (horizontal back and forth motion over a 30 cm distance). As the person starts lowering the basket back on the table, the robot arm is retracts. 152ee80cbc

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