When operating a general robot, electrical energy loss from the actuator's required current and mechanical energy loss from the mechanical requirements of actuators occur. This algorithm's goal is to maximize the energy saving effect by analyzing a consumed electrical power model.
Introduction
Background and Motivation
For these reasons, previous work has reduced these loss energies through careful manipulation of the robot's task trajectory. The required currents and mechanical force of actuators can be divided and rearranged by this theory.
Previous Work
Agrawal[11] and Wongratanaphisan[12] studied gravity compensation devices using springs and added structures as Fig. As described above, previous research on improving energy efficiency has been conducted to optimize the task trajectory and design the gravity compensation device.
Objective and Scope
With this algorithm, energy saving can be possible by simply using the general operation algorithm. By using this algorithm, the consumed electrical energy can be further reduced than the minimum norm torque distribution algorithm.
Energy saving concept and Operation algorithm plan
Energy saving concept using redundant actuation
2.1(b) shows that the system holds the object with two actuators, including one additional redundant actuator. In this redundantly actuated system, the required force of 100 N to hold the object can be distributed between the two actuators. The force in this case is distributed as 50 N. The gravitational acceleration is 10 m/s2 and the internal resistance of the actuator is 10 Ω. In a general system, the current flow in the actuator is proportional to the required actuator force. Assuming a proportional constant of 10, a current of 10 A flows into the actuator in the figure. This means that the current flow can be distributed by distributing the actuator forces using redundant triggering. This distribution of currents can reduce the overall accuracy of power loss inferences. This is because the heat loss of the actuator is proportional to the square of the current flowing. The heat loss appears as 1000 J in one actuator in the case of Fig. Energy saving concept and operation algorithm design. a) sum of squared torques in a general manipulator with 2 DOF. b) sum of squared torques in a 2-DOF redundant manipulator of 10 kg. Despite this concept, force distribution with redundant actuation can reduce the power loss of the entire system.
Analysis of consumed electric power of actuation part
- Analysis of electrical energy loss
- Analysis of mechanical energy loss
- Consumed electric power model of actuation parts
This mechanical energy loss occurs because the actuator cannot regenerate the energy supplied to negative work. The mechanical energy loss due to the conflict between jobs can be reduced by redundant propulsion.
Operation algorithm plan
- Minimum-norm torque distribution algorithm operation
- Minimum-energy consumption algorithm operation
This algorithm can be implemented by setting the same control gains and performing synchronous position control. The loss of electrical energy, which is proportional to the sum of τ2, can be minimized through this operation algorithm.
Kinematic analysis
Kinematic structure
Kinematic analysis
- Inverse kinematic analysis
- Forward kinematic analysis
The forward Jacobian is defined as the relation between the velocity of an independent node and the velocity of the robot's end effector. The relationship between the linear velocity of the robot end effect and the velocity of the independent nodes qu is as shown below.
Kinematic calibration
Error modeling
The kinematic calibration of the test robot was carried out taking into account the angular displacement errors of the actuation joint. ˆdqm is the following error vector measured by experiment, and qr is the angle offset error.
Process and result of kinematic calibration
As a result, the objective function of the kinematic calibration was reduced to about 99.9% of what it was before.
Dynamic analysis and derivation of consumed electric power model
Dynamic analysis
- Overall structure dynamic model
- General robot dynamic model
- Redundantly-actuated robot dynamic model
The value of fv and fc can be derived by subtracting the torque values of the servo motor from the torque values of the gearbox shaft. Due to this null space, the actuation torque of redundant actuated robot is not uniquely determined and can be chosen in certain combinations of solution.
Analysis of consumed electric power model
Simulation of energy saving effect
Operation condition
Simulation of energy saving effects with minimum-norm torque
- Simulation of consumed electrical energy of a general robot
- Simulation of the consumed electrical energy of a redundantly-
- Simulation result of energy saving effect with minimum-norm torque
6.8(a), the red solid line is the consumed electrical power of a general robot, and the blue dotted line is the consumed electrical power of a redundantly operated robot with torque distribution according to the minimum standard. 6.8(b) shows the saved electrical power of the redundantly operated robot with torque distribution according to the minimum standard. By working with a minimum standard torque distribution algorithm, an estimated 107 W of average electrical power or 8,364 J of electrical energy is saved after expanding the general robot to a redundantly driven robot.
As a result, it is estimated that 41.0% of electrical energy is saved by the redundantly driven robot with minimum standard torque distribution algorithm. The estimated electrical energy loss of a general robot and a redundantly operated robot with a minimum standard torque distribution algorithm is shown in Figure. The blue dotted line is the electrical energy loss and the sum of the mechanical energy of a redundantly operated robot with minimum -norm torque distribution algorithm.
Simulation of energy saving effect with minimum-energy consumption
- Simulation of consumed electrical energy of general robot
- Simulation of consumed electrical energy of redundantly-actuated
- Simulation result of energy saving effect with minimum-energy
By operating with the minimum power consumption algorithm, after extending the general robot to the redundantly activated robot, it is estimated that 117 W of average electrical power or 9.105 J of electrical energy will be saved. As a result, 44.6% of the energy electricity is estimated to be saved by the over-activated robot with the minimum energy consumption algorithm. The alternating long and short green dash line is the electrical energy loss and the sum of the mechanical energy of the over-actuated robot with a minimum energy consumption algorithm.
The blue dashed line is the electrical energy consumed by redundantly actuated robot with minimum-norm torque distribution operation. The green alternate long and short dashed line is the consumed electrical energy from redundantly activated robot with minimal energy consumption. The redundantly actuated robot operated with a minimum norm torque distribution algorithm and a minimum energy consumption algorithm.
Experiment system
- Mechanical part
- Driving part
- Control part
- Measurement part
The amounts of electrical energy consumed are measured when the generic robot and the redundantly actuated robot operate on the same task trajectory. The servo motor is of the AC type and operates on a three-phase current supplied by the servo drivers. An additional absolute encoder is installed at the front of the gearbox to compensate for the backlash of the planetary gearbox.
The position control of the servo motor is monitored by this encoder, and the servo driver operates the servo motor using the signals of this encoder. This part also monitors the torque control of the servo motor through the command of torque values with the DAC signal. The torque value is measured by a DAC signal which is transferred from the main controller to the servo driver[41].
Experiment of energy saving effect with minimum-norm torque
- Experiment of consumed electrical energy of general robot
- Experiment of consumed electrical energy of redundantly-actuated
- Experiment result of energy saving effect with minimum-norm
7.22(a), the red dashed and solid lines are the simulation and experiment result of consumed electrical power of the general robot, respectively. The blue dashed and solid lines are respectively the simulation and experiment result of consumed electric power of the redundant light-driven robot with minimum-norm torque distribution operation. 7.22(b) shows the simulation and experiment result, respectively, for the saved electrical power of redundant-powered robot with minimum-norm torque distribution operation.
Operating with the minimum rate torque distribution algorithm after extending the general robot to the overactuated robot saves an average of 112 W of electricity or 8,703 J of electricity. As a result, 41.4% of the electricity is saved by the robot redundantly activated with minimum rate torque distribution algorithm. The blue dotted and solid lines are the electrical energy loss and the sum of the mechanical energy of the overactuated robot with the minimum-rate torque distribution algorithm, respectively.
Experiment of energy saving effect with minimum-energy consumption
- Experiment of consumed electrical energy of general robot
- Experiment of consumed electrical energy of redundantly-actuated
- Experiment result of energy saving effect with minimum-energy
The dotted and solid green lines are the simulation and experiment results, respectively, of the consumed electrical energy of the over-activated robot with the minimum power consumption operation. 7.31(b) shows the simulation and experiment result, respectively, of the saved electrical power of the redundantly actuated robot with the minimum power consumption operation. As a result, 45% of the electrical energy is saved by the redundantly activated robot with the minimum energy consumption algorithm.
And by using minimum energy consumption algorithm, the redundantly powered robot can operate with minimum electric power as green line. The electrical energy loss of the general robot and redundantly powered robot with minimum energy consumption algorithm is shown in Fig. The green dashed and solid lines are the electrical energy loss and the sum of mechanical energy, respectively, of the redundant light-driven robot. with minimum energy consumption algorithm.
Summary of experiment result
The red dotted and solid lines are the electrical energy loss and the sum of the mechanical energy, respectively, of the overall robot. 7.35, the red dotted and solid lines are the simulation and experiment results, respectively, of the consumed electric power of the overall robot. The blue dotted and solid lines are the simulation and experiment results, respectively, of the consumed electrical energy of the overactuated robot with the minimum-rate torque distribution operation.
The green dotted lines and solid lines are the simulation and experiment result of the consumed electrical energy of the redundantly powered robot with minimum energy consumption, respectively. The redundantly operated robot with minimum torque distribution consumes an average of 158 W of electrical power, or 12,319 J of energy, and with minimum energy consumption consumes an average of 148 W of electrical power, or. The energy savings percentage and energy are calculated as an average electrical power of 41.4% and 112 W, or 8,703 J, when used with a minimum standard torque distribution algorithm.
Conclusion
12] Wongratanaphisan, T., Chew, M., "Gravity compensation of spatial two-DOF serial manipulators", in Journal of Robotic System, vol. Antagonistic Stiffness Optimization of Redundantly Actuated Parallel Manipulators in a Predefined Workspace”, IEEE/ASME Transactions on mechatronics, vol.18, no.3, 2013. 21] Kim, J., Hwang, J.C., Kim, J.S., Iurascu, C. , Park, F.C., Cho, Y.M., "Eclipse II: a new parallel mechanism enabling continuous 360-degree rotation plus three-axis translational motion", IEEE Transaction on Robotics and Automation vol.
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Consumed electric power comparison between redundantly actuated system
As analyzed in the above section, the consumed electric power of the general system is 520 W. Therefore, reducing the sum of absolute torque value is also important to minimize the consumed electric power. In the case of the redundant driven system, this can reduce the sum of the absolute torque value.
In addition, mechanical energy loss may occur during the use of the actuator's mechanical energy during robot operation. 53 6.2.2 Simulation of the consumed electrical energy of a redundantly controlled robot with a minimum standard torque distribution algorithm. Mechanical energy loss occurs when the mechanical energy of the actuators is used to operate the robot.
Finally, the analysis of the consumed electricity model is done including these energy losses. In this situation, the loss of mechanical energy does not occur and the mechanical energy used to operate the robot is equal to the sum of the total mechanical energy of the actuator.
