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Figure 6. Comparison of the demonstrated position trajectories against the results of the motion planning model (5) [14]

Figure 6 Comparison of the demonstrated position trajectories against the results of the motion planning model (5) [14]

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Figure 1. Forwarder crane [14]: hydraulic manipulator with four main degrees of freedom without counting the end-effector’s tool; the sensors measure the joints known as the slewing q;, inner boom q2, outer boom q3, and telescope qz; the end-effector tool is a grapple used to grab logs and it is attached to move freely at the boom-tip The machine used for recording data is a Komatsu Forwarder 830 [20] equipped with a crane from the company CRANAB (model CRF 5.1) having a maximum length of 9.3 m when the crane is fully extended [21]. This machine has been used in many of our previous studies, e.g. [4], [13], [15]. Referring to Figure 1, the crane was equipped with four high resolution quadrature encoders able to measure the joint rotations with a resolution of 0.072 degrees (0.0012 rad) for the angular joints and 0.0007 m (0.7 mm) for the telescope. A real-time data acquisition unit (DAQ) was installed to record the data. This DAQ operated at a frequency of 1 KHz, i.e., 1,000 recordings per second.
Figure 1. Forwarder crane [14]: hydraulic manipulator with four main degrees of freedom without counting the end-effector’s tool; the sensors measure the joints known as the slewing q;, inner boom q2, outer boom q3, and telescope qz; the end-effector tool is a grapple used to grab logs and it is attached to move freely at the boom-tip The machine used for recording data is a Komatsu Forwarder 830 [20] equipped with a crane from the company CRANAB (model CRF 5.1) having a maximum length of 9.3 m when the crane is fully extended [21]. This machine has been used in many of our previous studies, e.g. [4], [13], [15]. Referring to Figure 1, the crane was equipped with four high resolution quadrature encoders able to measure the joint rotations with a resolution of 0.072 degrees (0.0012 rad) for the angular joints and 0.0007 m (0.7 mm) for the telescope. A real-time data acquisition unit (DAQ) was installed to record the data. This DAQ operated at a frequency of 1 KHz, i.e., 1,000 recordings per second.
Figure 2. The paths described here refer to those for performing the actions of grabbing logs from one side of the machine, and accumulating them in the trailer [12]
Figure 2. The paths described here refer to those for performing the actions of grabbing logs from one side of the machine, and accumulating them in the trailer [12]
Figure 3. Cartesian coordinate trajectories p(t) found after trimming the original data set, including the telescopic link qs. The bold signal represents the average of all trajectories [14] The data is shown in Figures 3 and 4. They correspond to the Cartesian trajectories of the boom tip and the telescopic link used to retract the crane from the left side of the vehicle. The dark bold signals are the averaged trajectories that are used in the learning process of the DMPs method. Figure 3 shows data plotted according to a monotonic parametric variable 6(t). This variable is the path curve length and it is shown in Figure 4 plotted with respect to time to show the duration of motions. Note that the duration of motion varies between trajectories because it depends on how much load the crane is holding: the higher the load, the slower the movement.
Figure 3. Cartesian coordinate trajectories p(t) found after trimming the original data set, including the telescopic link qs. The bold signal represents the average of all trajectories [14] The data is shown in Figures 3 and 4. They correspond to the Cartesian trajectories of the boom tip and the telescopic link used to retract the crane from the left side of the vehicle. The dark bold signals are the averaged trajectories that are used in the learning process of the DMPs method. Figure 3 shows data plotted according to a monotonic parametric variable 6(t). This variable is the path curve length and it is shown in Figure 4 plotted with respect to time to show the duration of motions. Note that the duration of motion varies between trajectories because it depends on how much load the crane is holding: the higher the load, the slower the movement.
Figure 4. Normalized curve length in respect to time [14] (the bold signal is the averaged length used for interpolations)
Figure 4. Normalized curve length in respect to time [14] (the bold signal is the averaged length used for interpolations)
Test 1 consists of simulating the standard and optimized motion planner using as initial condition: all those from the machine operator’s demonstrated trajectories. A graphical representation of these initia conditions is sketched in Figure 5. The total energy is determined by summing up the energies of al trajectories. This process is performed a) for the standard motion planner, b) for the optimized motior planner, and c) for the machine operator. Consequently, a quantitative comparison of energy among these three cases can be provided. The objective is to assess the energy efficiency improvements achievable through automation as opposed to manual crane control by operators. Test 2 consists of simulating the final motion planers using different initial conditions, resembling the act of collecting logs from different locations. These locations are chosen as the places where the machine operator grabs logs more frequently and would use the automatic motion planner to bring the logs into the machine’s log bunk. Figure 5 depicts six different variations around the y-axis, located on both sides of the machine, selected based on the operator’s crane control patterns [15]. It is assumed that five similar loads are collected at each location, giving a total of thirty motions. The goal is to demonstrate the motion planners’ capability to handle differences in initial conditions, motion amplitude, and velocities, despite training with only one dataset. Additionally, the comparison of energy for the standard and optimized model’s trajectories is presented to showcase their performance differences.
Test 1 consists of simulating the standard and optimized motion planner using as initial condition: all those from the machine operator’s demonstrated trajectories. A graphical representation of these initia conditions is sketched in Figure 5. The total energy is determined by summing up the energies of al trajectories. This process is performed a) for the standard motion planner, b) for the optimized motior planner, and c) for the machine operator. Consequently, a quantitative comparison of energy among these three cases can be provided. The objective is to assess the energy efficiency improvements achievable through automation as opposed to manual crane control by operators. Test 2 consists of simulating the final motion planers using different initial conditions, resembling the act of collecting logs from different locations. These locations are chosen as the places where the machine operator grabs logs more frequently and would use the automatic motion planner to bring the logs into the machine’s log bunk. Figure 5 depicts six different variations around the y-axis, located on both sides of the machine, selected based on the operator’s crane control patterns [15]. It is assumed that five similar loads are collected at each location, giving a total of thirty motions. The goal is to demonstrate the motion planners’ capability to handle differences in initial conditions, motion amplitude, and velocities, despite training with only one dataset. Additionally, the comparison of energy for the standard and optimized model’s trajectories is presented to showcase their performance differences.
Figure 7. Results of (a) comparison of the standard and optimized telescope motion qa(t) and (b) calculation of energy as result of using these two variations (grey signal: standard motion planner black signal: optimized one) Referring to Figures 3 and 7, results show that the operator in this study uses the range of motion of the telescope within small ranges compared to its maximum. As explained in [15], this differs from operator to operator and it mainly depends on their multitasking skills. Nevertheless, using the telescope while coordinating the remaining joints is commonly difficult for machine operators.
Figure 7. Results of (a) comparison of the standard and optimized telescope motion qa(t) and (b) calculation of energy as result of using these two variations (grey signal: standard motion planner black signal: optimized one) Referring to Figures 3 and 7, results show that the operator in this study uses the range of motion of the telescope within small ranges compared to its maximum. As explained in [15], this differs from operator to operator and it mainly depends on their multitasking skills. Nevertheless, using the telescope while coordinating the remaining joints is commonly difficult for machine operators.
Figure 8. The comparisons of (a) the standard model energies in relation to the operator’s trajectories and (b) the optimized model energies in relation to the operator’s trajectories (grey: the DMPs model, black: operator’s data) i a I I I Figure 8 shows an example comparing energy for a total of 38 trajectories out of the whole data set shown in Figure 3. The black bars represent the energy spent by the trajectories of the operator. The grey bars represent the energy spent by the trajectories from motion planning. Figure 8(a) is a graphical representation showing that the standard motion planner has the ability to reduce energy for most trajectories. However, it is notorious that the optimized motion planner, shown in Figure 8(b), can substantially reduce energy in relation to the standard case.
Figure 8. The comparisons of (a) the standard model energies in relation to the operator’s trajectories and (b) the optimized model energies in relation to the operator’s trajectories (grey: the DMPs model, black: operator’s data) i a I I I Figure 8 shows an example comparing energy for a total of 38 trajectories out of the whole data set shown in Figure 3. The black bars represent the energy spent by the trajectories of the operator. The grey bars represent the energy spent by the trajectories from motion planning. Figure 8(a) is a graphical representation showing that the standard motion planner has the ability to reduce energy for most trajectories. However, it is notorious that the optimized motion planner, shown in Figure 8(b), can substantially reduce energy in relation to the standard case.
Figure 10. The grey signals are the trajectories planned by the model (5) (solid bold lines: trajectories used as data set for learning) Figure 9. Cartesian coordinate plot for all simulated paths (grey signals: trajectories planned by the model (5), dark dots: new initial conditions used for the simulation, solid bold line: the path used as data set for learning)
Figure 10. The grey signals are the trajectories planned by the model (5) (solid bold lines: trajectories used as data set for learning) Figure 9. Cartesian coordinate plot for all simulated paths (grey signals: trajectories planned by the model (5), dark dots: new initial conditions used for the simulation, solid bold line: the path used as data set for learning)
Figure 11. Comparison of the standard model energies in relation to the optimized model (grey signal: the energy of the optimized model, black signal: the energy of the standard model)
Figure 11. Comparison of the standard model energies in relation to the optimized model (grey signal: the energy of the optimized model, black signal: the energy of the standard model)
Related topics:
Energy OptimizationDynamic Movement Primitives
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