year month201505
Department Electronic and Information Engineering
NameID099305

Wisnu Aribowo

day25

Kazuhiko Terashima
Supervisors Takanori Miyoshi
Jun Miura

ＡｂｓｔｒａｃｔTitle

Integrated Trajectory Planning and Vibration Suppression of Transfer Robots（800 words）
Automatic transfer systems are utilized to a great extent in various type of modern industry. Such systems
can transfer industrial work pieces in high speed with relatively consistent performance. The cycle time
reduction gained by utilization of such systems can increase throughput of the factory. However, high speed
operation often results in residual vibration as side effect, usually considered undesirable in many industrial
applications that require high precision such as semiconductor wafer pick-and-place system, where a multi-linkrobot arm is used to automatically pick up, transfer, and place semiconductor wafers. Vibration of the arm tip
that occurs after the robot motion causes the robot to wait for a moment until the vibration settles to an
acceptable level before performing next operation. This settling time should be reduced as much as possible inorder to increase production rate in semiconductor factory.
Other type of vibration problem caused by motion of the robot arm is sloshing, or the vibration of liquidsurface. Sloshing is not caused by the vibration of the mechanical structure of the robot. Instead, it is caused by
the motion in the task space of the container held by the robot arm. Sloshing may cause the liquid to spill out of
the container, and in the case of molten metal too much sloshing may affect the physical properties of theliquid. Moreover, other task, e.g. pouring, cannot be performed when residual sloshing still occurs, thereby
potentially reducing the system productivity.
The main challenge in this kind of problem is to generate trajectories with concurrent consideration ofmotion time minimization and vibration (or sloshing) suppression for point to point motion in a three
dimensional working space where static obstacles may exist. Minimizing motion time means that the trajectoryshould be designed in the joint space, where the main constraints of robot motion exist, for example thekinematic and dynamic constraints of the joint actuators. On the other hand, the existence of obstacle orworking boundary of the robot means that the solution has to consider the task space constraints as well. Inaddition, the vibration suppression should not increase the motion time too much.
This research proposes an integrated framework of trajectory planning and vibration suppression of multijoint robot arm to generate trajectories with quick motion time and low vibration. The framework uses twobuilding blocks: cubic spline trajectory and input shaping. The cubic splines trajectory has a few favorable
properties, for example the limited jerk, which provides smoother profile than acceleration-limited trajectories,and the quick computation. Nonetheless, it is relatively fast compared to other higher degree polynomials. Acubic spline trajectory is composed of several curve segments, each is represented by one cubic function. The

segments are bounded by knots. The shape of each cubic curve is determined by four parameters of the cubicfunction. The trajectory has to be continuous in position, velocity, and acceleration throughout the whole time.
By simplification, a system of linear equations involving the knot values, the segment times, and theaccelerations can be obtained.
Input shaping method is a simple yet effective method to reduce system vibration. Using value of natural
frequency and damping ratio of the vibrating system, the command input signal is decomposed into two. The
magnitude and time between those two signals are set such that the second signal can compensate vibration
coming from the first signal, thus effectively eliminate subsequent vibration. The input shaping has foundpractice in many real applications due to the combination of its simplicity and good performance. From thebasic principle of input shaping, researchers have come with numerous developments and modifications,
resulting in many types of input shapers for different kind of applications.
The framework is formulated as a non linear optimization model with motion time as the main objectivefunction. The constraints consist of the joint constraints (e.g. velocity and torque limit) and task spaceconstraints (e.g. working boundary and obstacle avoidance). The decision variables are both the segment times
and the knot values. This gives the framework enough flexibility to achieve quick motion time and to avoid
obstacles at the same time.
The integrated framework is applied for two practical cases: a semiconductor wafer transfer robot arm and aliquid container transfer robot arm. In the first case, a three-link planar robot arm works in small boundedworking space. In some area, the working space is so small such that the motion of the last link is constrained toa straight line only. In the second case, the system uses a seven degree-of-freedom robot arm that works in three
dimensional space, where obstacle may also exists.
Through simulation and experiments, the effectiveness of the proposed solution in generating quick motion
while keeping vibration (or sloshing) low is demonstrated. With only small increase in motion time, thevibration can be suppressed to a substantially smaller amount. The calculation time of trajectory generation
without vibration consideration is quick. If integrated with vibration suppression, the calculation takes
somewhat longer time, but is still acceptable for offline calculation.