Human-Inspired Hyper Dynamic Manipulation
73
subject to Equations (4.16), (4.17), (4.18), (4.19) and the initial conditions
θ θ ( )
0 = θ θ θ
, q ( ) qq
0 θ 0 = 0, θ θ ( )
0 = 0 ,
where
C
)
Τ
τ
=
Τ
( τ, ,
t m t f
e ( τ τ, t m ) w 1 e (τ τ, t m ) + e ( τ τ, t f ) w 2 e ( τ τ, t f f ) + w 3 J ( )
τ τ
e(τ τ, t m ) = ⎡θ θ
⎣ t − θ θ
( )
m
m ; v x ( )
t m − v xm ; v y ( ( )
t m − v ym ⎤ ⎦
e ( τ τ, t f ) = ⎡ θ θ q ( )
t − θ θ θ
q
f ; qq
f
θ ( )
t f − θ qq θ f ⎤
⎣ ⎣
⎦
θ θ = ⎡ ⎣ θ 1 , θ ⎤
T
2 ⎦
The other parameters for simulation are determined according to the average values of human beings and are omitted here.
The following cost function toward minimizing the total work consumed
by the actuators of joint 1 and joint 2 is used.
=
∫
t f
t
J
τ 1 ( )
f
t ⋅ θ q
1 ( )
t dt +
∫
τ ( ) q
2 t ⋅ θ 2 ( )
t dt
(4.22)
0
0
DD motors are set to torque mode and are controlled by torque (voltage) reference from the computer. Angular positions of joints are measured through
resolvers and counters by a board computer.
As characteristics of DD motors, coulomb friction torque and viscous
friction torque must be compensated for because they cannot be neglected
in the case of DD motors. Coulomb friction torque is calculated according to the relation between the reference voltage input to the motor driver
and the output torque produced by the motor and is calibrated by experiments. Viscous friction coefficients are also calculated according to the
experimental results of the relation between the voltage reference and the
angular velocity.
As an implementation of the control system to the real manipulator, we
constructed a controller shown in Figure 4.7. Considering the features of
the robot, such as high speed, strong nonlinearity, and dynamic coupling, a
feed-forward compensation is introduced with a PD controller. That is, the
torque feed-forward compensations of joints combined with PD controllers
for the angular positions of joints are used. The torques of joints for feed-forward compensation and the reference motions of joints for PD controller are
generated by offline calculation according to the method described previously, before the swing starts. Sampling time for a feed-forward and feedback loop is 1 ms.
73
subject to Equations (4.16), (4.17), (4.18), (4.19) and the initial conditions
θ θ ( )
0 = θ θ θ
, q ( ) qq
0 θ 0 = 0, θ θ ( )
0 = 0 ,
where
C
)
Τ
τ
=
Τ
( τ, ,
t m t f
e ( τ τ, t m ) w 1 e (τ τ, t m ) + e ( τ τ, t f ) w 2 e ( τ τ, t f f ) + w 3 J ( )
τ τ
e(τ τ, t m ) = ⎡θ θ
⎣ t − θ θ
( )
m
m ; v x ( )
t m − v xm ; v y ( ( )
t m − v ym ⎤ ⎦
e ( τ τ, t f ) = ⎡ θ θ q ( )
t − θ θ θ
q
f ; qq
f
θ ( )
t f − θ qq θ f ⎤
⎣ ⎣
⎦
θ θ = ⎡ ⎣ θ 1 , θ ⎤
T
2 ⎦
The other parameters for simulation are determined according to the average values of human beings and are omitted here.
The following cost function toward minimizing the total work consumed
by the actuators of joint 1 and joint 2 is used.
=
∫
t f
t
J
τ 1 ( )
f
t ⋅ θ q
1 ( )
t dt +
∫
τ ( ) q
2 t ⋅ θ 2 ( )
t dt
(4.22)
0
0
DD motors are set to torque mode and are controlled by torque (voltage) reference from the computer. Angular positions of joints are measured through
resolvers and counters by a board computer.
As characteristics of DD motors, coulomb friction torque and viscous
friction torque must be compensated for because they cannot be neglected
in the case of DD motors. Coulomb friction torque is calculated according to the relation between the reference voltage input to the motor driver
and the output torque produced by the motor and is calibrated by experiments. Viscous friction coefficients are also calculated according to the
experimental results of the relation between the voltage reference and the
angular velocity.
As an implementation of the control system to the real manipulator, we
constructed a controller shown in Figure 4.7. Considering the features of
the robot, such as high speed, strong nonlinearity, and dynamic coupling, a
feed-forward compensation is introduced with a PD controller. That is, the
torque feed-forward compensations of joints combined with PD controllers
for the angular positions of joints are used. The torques of joints for feed-forward compensation and the reference motions of joints for PD controller are
generated by offline calculation according to the method described previously, before the swing starts. Sampling time for a feed-forward and feedback loop is 1 ms.