06-07-2012, 11:55 AM
A RELAY-BASED APPROACH FOR ROBOT MOTION CONTROL WITH JOINT FRICTION AND GRAVITY COMPENSATION
A RELAY-BASED APPROACH FOR ROBOT MOTION CONTROL WITH JOINT FRICTION AND GRAVITY ......pdf (Size: 764.51 KB / Downloads: 38)
This paper introduces a relay-based approach to control the motion of robot joints with
friction and gravity load. This approach uses relay feedback tests to estimate the disturbances
including Coulomb friction, viscous friction, and the gravity load. The relay
feedback tests take the robot joint angular as the feedback signal and identify the friction
value and the gravity load at the same time. A control scheme is then presented including
a feedforward friction compensator and a feedforward gravity compensator based on the
estimated results. With the disturbances properly compensated, the proposed approach
improves the tracking performance of a robotic system. Simulation and experimental
results are presented to verify the effectiveness of the proposed method.
Keywords: Motion control; friction compensation; gravity compensation; describing function;
relay feedback.
1. Introduction
In robotic systems, no matter medical robots, industrial robot arms, or humanoid
robots, there is always a requirement of tracking the motion profile accurately.1
However, disturbances existing in robot joins greatly degrade the tracking performance
by inducing limit cycle and steady-state error. One major source of disturbance
is the frictional force related to the relative motion of robot joints. Extensive
researches were carried out to eliminate the effects of the friction2 including modelbased
friction compensation,3–5 adaptive compensation,6,7 and friction observers.8,9
Another disturbance source concerned in this paper is the external load caused by
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the force of gravity. In general mechanical systems such as CNC systems, the gravity
is considered as a constant value because the mass usually moves along a fixed
direction. However, in rigid robotic systems, the gravity load is modeled as a vector
related to the robot gesture due to its free movement in space. Many strategies
were performed to control robots with gravity compensation to achieve better control
performance.10–12 However, it would still be time costing to find the appropriate
parameters of the compensation algorithm. Thus, it is necessary to find a simple and
quick way to automatically identify the disturbances and design control algorithm
in robotic systems.
The relay feedback identification method was first proposed by Astr¨om and
H¨agglund and hence extensively explored in recent years due to its robustness and
simplicity. Astr¨om and H¨agglund suggested an oscillation generated around the
critical point of the system through the relay feedback test.13 The system characteristics
are derived by measuring the ultimate gain and ultimate frequency during
the process and could be used to identify the system parameters subsequently.14
More research works on improving the relay feedback autotuning method have been
reported.15 Saturation relay,16 asymmetrical relay,17,18 and two-channel relay19
have been studied to provide better approximation to the ultimate gain and ultimate
frequency. Further researches were conducted in systems with disturbances. Pu and
Wu gave a detail analysis on how the nonlinearity affects the parameter identification.
20 Wu identified the Coulomb and vicious friction through relay feedback tests
and designed feedforward and time delay compensator accordingly.21 Chen identified
the force ripple and friction through hysteretic relay feedback tests.22 However,
relay feedback identification toward the gravity load in robotic joints has not yet
been studied.
In this paper, a relay-based approach to control the motion of robot joints
with friction and gravity load is presented. Relay feedback tests are performed
by taking the robot joint angular as the feedback signal to estimate the disturbances.
The friction model consists of two components: Coulomb friction and viscous
friction. The torque caused by gravity is considered as an angular-dependent
variable. Coulomb friction, viscous friction, and the gravity load are identified at
the same time during two relay feedback tests using describing function approximation
in frequency domain.23,24 A control scheme is then developed including
a feedforward friction compensator and a gravity compensator based on the estimated
results. With the disturbances properly compensated, the control scheme
increases the positioning accuracy and improves the tracking performance of a
robotic system.
This paper is organized as follows: the dynamic model of the robot joints with
disturbances is presented in Sec. 2. In Sec. 3, we discuss the relay-based identification
method to estimate the disturbances and the control scheme is designed based on
the estimated results. In Sec. 4, simulation results are given to verify the estimation
accuracy of the proposed method. In Sec. 5, experiments are first conducted to
estimate the disturbances existing in a robot joint and then comparative tracking
A Relay-Based Approach For Robot Motion Control 675
performances are presented to show the effectiveness of the proposed control scheme.
Conclusions are drawn in Sec. 6.
2. Model of Robot Joints with Disturbances
The dynamical characteristics of a robot joint is described as
Tr = J ¨θ + Tdis, (1)
where Tr is the torque applied to the system, θ is the joint angular, J is the moment
of inertia, and Tdis is the torque caused by disturbances.
The disturbances concerned in this paper consist of the torque induced by the
frictional force and the gravity.
Tdis = Tf + Tg. (2)
The frictional torque is represented by Coulomb and viscous friction components
Tf = Tfc · sign(ω) + b · θ˙, (3)
where Tfc is torque of the Coulomb friction and b is the viscous coefficient. The
friction model is shown in Fig. 1.
Because of the free movement in space, the torque Tg caused by the gravity is
related to the load mass m and the position of gravity center.
As to a robot joint, the torque generated by gravity is shown in Fig. 2.
The gravity load is expressed as a function of the joint angular
Tg = TG · sinθ, (4)
where θ is the joint angular and TG is the maximum gravity torque at θ = π
2 .