Implementation
6.1 Suspension clamp manoeuvre
6.1.1 Simulink model test
The trajectory and simulation predictions were generated using the PLIR Trajectory Solver application with the detailed Simulink model. The results presented here show the commanded, simulated and measured performance of the PLIR. Figure 6.1 shows the commanded, simulated and actual movements of the robot’s joints.
The robot followed the trajectory that was commanded, but with lag. There is a significant delay from the time the position command changes to the time the robot begins to move due to static friction (discussed below). Also, the rear arm joint does not keep up with the commanded trajectory due to it reaching its velocity limit, as marked in the “Rear Arm Velocity” graph of Figure 6.2.
The Simulink model of the PLIR is sufficiently accurate to predict this behaviour. The simulated and actual joint movements correspond closely, and this verifies the Simulink model. The noise present in the actual velocity measurements is due to noise in the current measurements, which is discussed below.
Figure 6.1: Simulink model optimised trajectory: commanded, simulated and actual robot joint angles for the suspension clamp manoeuvre.
The trajectory command has a time of 1.8 s and optimised interval times of ¯r= [0.7 s,0.6 s,0.5 s], with a 1 s and a 2 s trajectory command holding time at the beginning and end of the trajectory respectively.
The delay in movement can become a problem in obstacle avoidance situations when the joints do not move in a synchronised manner. In this particular case, the core joint completes its movement significantly sooner than the other joints. This means that the end effector moved back toward the power line before it had properly passed the AABB obstacle representation. This can be clearly seen in Figure 6.3.
In this experiment, the AABB violation was not a problem. The AABB had over bounded the suspension clamp in the first place, and the end effector did get around it as shown from Figure 6.4 to Figure 6.7. Also, the robot achieved the final set-points with sufficient accuracy to get the end effector back onto the line.
As mentioned above, static friction present in the robot joints is the primary reason for this delay in motion, with the integrator action in the PID controller not being fast enough to compensate. The position error at the controller input begins to drive the controller output and hence the actuator when the position command begins to change. However, due to the static friction, the joints can only move when the controller output (actuator current) is large enough to overcome the friction.
Figure 6.2: Simulink model optimised trajectory: simulated and actual robot joint velocities for the suspension clamp manoeuvre.
Figure 6.3: PLIR simulation environment showing AABB collision.
Figure 6.4: PLIR simulation together with the laboratory test video frame of the suspension clamp obstacle avoidance manoeuvre at timet= 0.
Figure 6.5: PLIR simulation together with the laboratory test video frame of the suspension clamp obstacle avoidance manoeuvre at timet= 2.09.
Figure 6.6: PLIR simulation together with the laboratory test video frame of the suspension clamp obstacle avoidance manoeuvre at timet= 2.48.
This effect is highlighted in Figure 6.8. The “Break-away” labels show where the static friction was overcome and the joints began to move. As seen in Figure 6.8, the current decreased after the break-away point because the torque due to viscous and Coulomb friction is less than that of static friction, and the position error was decreasing. The break-away points in Figure 6.8 can be matched up with the same time points in Figure 6.1 where the joints began to move.
Furthermore, the static friction plays a part at the end of the trajectories where the joints may have not met the end set-point exactly. There are clear cases in Figure 6.8 in the “Gripper Current”
and “Front Arm Current” graphs; there is integrator wind-up in the PID controller due to the static friction. This will cause a limit cycle if the controller is left to hold the robot’s position. An improvement to the PID controller would be to “switch-off” the integrator once the robot had met the desired set-point with sufficient accuracy.
From Figure 6.8, it is clear that the Simulink model of the robot is sufficiently accurate to predict the current profile for each actuator during a manoeuvre. From these profiles, the profile for the total current required can be calculated which can be used to determine the charge required from the battery for the manoeuvre. Not only does this verify the model used for charge requirement predictions, but in turn it verifies the optimisation techniques presented in Chapter 4 using the Simulink model. The cost at each optimisation iteration for a set of time intervals can be predicted with sufficient accuracy, and at each iteration, the interval time adjustments are being made according to a model that closely represents reality.
Developing the Simulink model provided much insight to the behaviour of the joint angle and current profiles seen in Figure 6.1 and Figure 6.8. Apart from the break-away current required to get the joints moving, there are some other noteworthy details in Figure 6.8.
The high frequency noise present in the actual current measurements is due to noise present in the position measurement signals. This is because the current command is derived from the
Figure 6.7: PLIR simulation together with the laboratory test video frame of the suspension clamp obstacle avoidance manoeuvre at timet= 4.5.
Figure 6.8: Simulink model optimised trajectory: Simulink model and actual robot actuator currents for the suspension clamp manoeuvre.
position error of the controller input, and of course, this noise propagates through the controller and out to the actuators. The cause of the position measurement noise is due to the existence of noise in the potentiometers’ reference voltage. The noise source is the 3.6864 MHz oscillator on the microcontroller board. Attempts were made to filter out the noise, but with limited success.
However, this is not of major concern, since the successor to this first PLIR prototype makes use of digital position encoders which are immune to such noise sources.
The “noise spikes” present in the “Gripper Current” window are due to momentary communication glitches between the master microcontroller and on-board PC. When a communication packet between the on-board computer and the master microcontroller is dropped (lost), the slave microcontroller receives an erroneous current set-point command, causing an ephemeral spike in the PWM voltage and hence the current. This bug was not a cause for major concern during these tests because it did not affect the overall performance of the robot. Furthermore, this robot is to be superseded by a superior prototype, and so fixing this bug would be pointless at this stage.