Robot and control method of optimizing robot motion performance thereof
A robot and a method of controlling the same are disclosed. The robot derives a maximum dynamic performance capability using a specification of an actuator of the robot. The control method includes forming a first bell-shaped velocity profile in response to a start time and an end time of a motion of the robot, calculating a value of an objective function having a limited condition according to the bell-shaped velocity profile, and driving a joint in response to a second bell-shaped velocity profile that minimizes the objective function having the limited condition.
1. A method of controlling a robot, the method comprising:
forming a first bell-shaped velocity profile according to a start time and an end time of a motion of a joint of the robot;
calculating a value of an objective function having a limited condition according to the first bell-shaped velocity profile; and
driving the joint of the robot in response to a second bell-shaped velocity profile that minimizes the objective function having the limited condition,
wherein the forming of the first bell-shaped velocity profile in response to the start time and the end time of the motion includes:
forming a trajectory of a center of gravity of the robot,
wherein the limited condition includes a velocity of a joint, a torque of the joint, and a Zero Momentum Point (ZMP) of the robot.
2. The method according to claim 1 , wherein the forming of the first bell-shaped velocity profile in response to the start time and the end time of the motion includes:
forming a trajectory of a joint needed for motion of the robot.
3. The method according to claim 2 , wherein the trajectory includes information of a joint angle, a joint velocity, and a joint acceleration needed to perform the motion.
4. The method according to claim 1 ,
wherein the objective function having the limited condition recognizes a value (J min ) using the following Equation:
min
P
CoG
,
q
(
-
w
1
J
performance
+
w
2
J
velocity
+
[
Equation
]
w
3
J
torque
+
w
4
J
balance
)
=
J
min
where J peformance is a value of an objective function to maximize a velocity of an end effector of the robot, J velocity is a value of an objective function to limit the velocity of the joint used in the motion, J torque is a value of an objective function to limit the torque of the joint, J balance is a value of an objective function to limit the Zero Momentum Point (ZMP) of the robot within a specific range, w 1 , w 2 , w 3 , or w 4 is a constant, PCoG is a position of the overall center of gravity of the robot, and q is an angle of the joint.
5. The method according to claim 1 , wherein the bell-shaped velocity profiles represent a variation of velocity with time of a robot profile.
6. The method according to claim 1 , wherein the forming of the first bell-shaped velocity profile according to the start time and the end time of the motion of a joint of the robot includes:
forming a plurality of initial bell-shaped velocity profiles according to certain start times and certain end times of the motions of a plurality of joints of the robot.
7. The method according to claim 6 , wherein the calculating of the value of the objective function having the limited condition according to the first bell-shaped velocity profile includes:
repeatedly calculating the value of the objective function having the limited condition in response to the initial bell-shaped velocity profiles.
8. The method according to claim 1 , wherein the second bell-shaped velocity profile is determined by determining a start time and an end time at which the objective function having the limited condition is minimized.
9. The method according to claim 8 , wherein a trajectory is formed by the start time and the end time at which the objective function having the limited condition is minimized, and the trajectory is determined to be the second bell-shaped velocity profile.
10. A robot, comprising:
an input unit to receive a motion command of a robot; and
a controller to form a first bell-shaped velocity profile according to a start time and an end time of a motion of a joint of the robot and to calculate a value of an objective function having a limited condition according to the first bell-shaped velocity profile; and
a driver to drive the joint of the robot in response to a specific second bell-shaped velocity profile that minimizes the objective function having the limited condition,
wherein the controller forms a trajectory of a center of gravity of the robot,
wherein the limited condition includes a velocity of a joint, a torque of the joint, and a Zero Momentum Point (ZMP) of the robot.
11. The robot according to claim 10 , wherein the controller forms a trajectory of a joint needed for motion of the robot.
12. The robot according to claim 10 ,wherein the controller recognizes a value (J min ) of the objective function having the limited condition using the following Equation:
min
P
CoG
,
q
(
-
w
1
J
performance
+
w
2
J
velocity
+
[
Equation
]
w
3
J
torque
+
w
4
J
balance
)
=
J
min
where J performance is a value of an objective function to maximize a velocity of an end effector of the robot, J velocily is a value of an objective function to limit the velocity of the joint, used in the motion, J torque is a value of an objective function to limit the torque of the joint, J balance is a value of an objective function to limit the Zero Momentum Point (ZMP) of the robot within a specific range, w 1 , w 2 , w 3 , or w 4 is a constant, PCoG is a position of an overall center of gravity of the robot, and q is an angle of the joint.
13. The robot according to claim 10 , wherein the controller forms a plurality of initial bell-shaped velocity profiles according to certain start times and certain end times of the motions of a plurality of joints of the robot.
14. The robot according to claim 13 , wherein the controller calculates the value of the objective function having the limited condition according to the initial bell-shaped velocity profiles, and drives a joint in response to a specific second bell-shaped velocity profile that minimizes the value of the objective function.
15. The robot according to claim 13 , wherein the controller drives each joint or the center of gravity needed for the motion in response to the second bell-shaped velocity profile that minimizes the value of the objective function.
16. The robot according to claim 10 , wherein the controller arbitrarily determines the start time and the end time of the motion, and forms an initial bell-shaped profile of either a joint needed for the motion or a center of gravity of the robot.
17. The robot according to claim 10 , wherein controller determines the second bell-shaped velocity profile by determining a start time and an end time at which the objective function having the limited condition is minimized.
18. The robot according to claim 17 , wherein a trajectory is formed by the start time and the end time at which the objective function having the limited condition is minimized, and the trajectory is determined to be the second bell-shaped velocity profile.
19. The robot according to claim 10 , wherein the controller includes a command interpreter to interpret the received motion command, and a command generator connected to the command interpreter to generate a motion command.
20. A method of controlling a robot, the method comprising:
forming a plurality of first bell-shaped velocity profiles corresponding to a start time and an end time of motions of a plurality of joints of the robot;
calculating a value of an objective function having a limited condition according to the first bell-shaped velocity profile;
optimizing a plurality of second bell-shaped velocity profiles to minimize the objective function having the limited condition and to perform a dynamic motion of the robot, which includes moving the plurality of joints, based on the plurality of first bell-shaped velocity profiles; and
driving the plurality of joints of the robot in response to the plurality of second bell-shaped velocity profiles that minimize an objective function having a limited condition,
wherein the forming a plurality of the first bell-shaped velocity profiles corresponding to the start time and the end time of the motions of the plurality of joints of the robot includes:
forming a trajectory of a center of gravity of the robot,
wherein the limited condition includes a velocity of a joint, a torque of the joint, and a Zero Momentum Point (ZMP) of the robot.