KINEMATIC AND DYNAMIC CALIBRATION OF HYDRAULICALLY ACTUATED MANIPULATORS by MASOUD KHOSHZABAN- ZAVAREHI B.Sc. (Mechanical Engineering), Sharif University of Technology, Tehran, Iran, 1986 A THESIS SUBMITTED IN partial FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Mechanical Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December 1992 ©Masoud Khoshzaban- Zavarehi, 1992 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature) Department of ['A •z_k\f, sIN \ C Er IN• (NICx. t(A_. The University of British Columbia Vancouver, Canada Date \ 2, yI ") 2 DE-6 (2/88) ABSTRACT Important industries such as construction, mining, and forestry make use of heavy-duty hydraulic machinery with manipulators usually controlled manually by expert human operators. The hand controls that operate most articulated machines today do not take advantage of recent developments in robotics and control technology. There are thousands of industrial hydraulic machines in existence that can potentially benefit from improved computer-assisted controls such as the ones which are under development at UBC. To control such manipulators properly, however, precise link parameters should be known in advance in order to obtain inverse kinematics, Jacobians, and inverse dynamics used in various control algorithms. Accurate measurement of link parameters is made possible by using calibration techniques. The theme of this thesis involves calibration (measurement) of kinematic and dynamic parameters of hydraulic manipulators. In the category of kinematic calibration, we have presented and experimented with a new algorithm and instrumentation for automatic measurement of the geometric parameters of such robotic manipulators when forming mobile closed-chains. The contribution of the work proposed here, in the face of a large literature in kinematic calibration, is that there is no need for joint and end effector sensing of the manipulator. Instead, an external linkage-type sensing instrument, called "calibrator" has been introduced. One end of the calibrator is attached to the manipulator endpoint, while the other end is attached to a passive task fixture which is a spherical joint fixed to the machine's chassis. A special hierarchical identification algorithm using iterative least-squares technique has been developed based on link-by-link movement of the manipulator, starting from the end effector. By using the joint angle sensory data from ii Abstract the calibrator, all the geometric parameters of the moving link, as well as the kinematics of the actuator and the task fixture, were identified for a Caterpillar 215B excavator. In the area of dynamic calibration of hydraulic machines, a new methodology for the dynamics of a complex hybrid open-closed chain hydraulic manipulator was derived based on the Newton-Euler formulation. It was shown by simulation that neglecting the dynamics of the minor links (hydraulic actuators) may dramatically underestimate the forces/torques applied to the joints/links. By measuring the joint positions and the oil pressures inside the hydraulic actuators and applying the proposed dynamic equations, we attempted to calibrate the dynamic parameters (inertias, friction forces/torques, and transducer offsets) of both major and minor links of a typical hydraulic manipulator, the UBC Caterpillar 215B excavator. Simulation results showed that with the current accuracy of the sensors and transducers, it was not possible to obtain a good estimate of the parameters. The poor estimates of the individual parameters of the UBC hydraulic manipulator confirmed the simulation indications. Nevertheless, the estimated torques/forces obtained from the calibrated parameters appeared to be closer than the ones calculated from the existing nominal model to the actual measured torques/forces of the actuators. Although the formulation was much more mathematically and computationally involved, the complete model predicted the actuator forces/torques better than both reduced and nominal models. There are a number of potential advantages of the calibration techniques developed in this work over the existing methods in the literature. The techniques have the potential of being industrially feasible, fast, inexpensive, automatic with minimum human involvement and engineering supervision, and ready to apply on-site. iii Table of Contents ABSTRACT^ ii LIST OF TABLES^ vii LIST OF FIGURES^ ix ACKNOWLEDGMENTS^ xii 1 GENERAL^ 1 1.1 Introduction ^ 1 1.2 Robot Calibration ^ 2 1.2.1 Calibration Levels ^ 3 1.2.2 Calibration Steps ^ 4 1.3 Motivation and General Objective ^ 4 1.4 Scope of Present Work ^ 6 1.5 Contributions ^ 8 2 A HEAVY-DUTY HYDRAULIC MANIPULATOR^ 10 2.1 Introduction ^ 10 2.2 The Experimental Machine ^ 10 2.3 Link Specifications ^ 12 2.3.1 Geometric Parameters ^ 13 2.3.2 Inertial Parameters ^ 16 2.4 Actuator Specifications ^ 18 2.4.1 Geometric Parameters ^ 19 2.4.2 Inertial Parameters ^ 20 2.5 Sensors ^ 20 iv 3 KINEMATIC CALIBRATION^ 22 3.1 Introduction ^ 22 3.2 Previous Work ^ 22 3.3 Problem Statement ^ 26 3.3.1 Endpoint Sensing Problem ^ 26 3.3.2 Mobility Problem ^ 27 3.3.3 Joint Sensor Problem ^ 30 3.4 Model ^ 31 3.4.1 Geometric Parameters ^ 32 3.4.2 Nongeometric Parameters ^ 37 3.4.3 Manipulator Kinematics ^ 38 3.4.4 Actuator Linkage Kinematics ^ 43 3.5 Measurement ^ 44 3.5.1 The Calibrator ^ 45 3.5.2 Measurement Procedure ^ 47 3.6 Identification ^ 48 3.6.1 Differential Relations ^ 48 3.6.2 Jacobian Calculation ^ 49 3.6.3 Iterative Parameter Estimation ^ 50 3.6.4 Identifiable versus Unidentifiable Parameters ^ 52 3.7 Simulation Results and Discussion ^ 56 3.7.1 Effect of Actuator Drift ^ 58 3.7.2 Effect of Joint Sensor Accuracy ^ 60 3.7.3 Effect of Joint Flexibility ^ 60 3.8 Experimental Results and Discussion ^ 62 3.8.1 Major Links ^ 62 3.8.2 Improving the Major Link Identified Parameters ^ 67 3.8.3 Minor Links ^ 71 4 DYNAMIC CALIBRATION^ 79 4.1 Introduction ^ 79 4.2 Previous Work ^ 81 4.3 Estimation Procedure ^ 84 4.3.1 Newton-Euler Formulations for a Major Link ^ 84 4.3.2 Newton-Euler Formulations for Chained Links ^ 88 4.3.3 Newton-Euler Formulations for a Minor Link ^ 90 4.3.4 Global Newton-Euler Equations for a Hydraulic Manipulator ^ 96 4.3.5 Estimating the Link Parameters ^ 99 4.4 Simulation Results and Discussion ^ 100 4.4.1 Complete Model versus reduced Model ^ 101 4.4.2 Identifiability of Dynamic Parameters ^ 106 4.4.3 Effect of Sensor Accuracy ^ 107 4.5 Measurement Procedure ^ 111 4.6 Experimental Results and Discussion ^ 113 5 CONCLUSION^ 120 5.1 Kinematic Calibration Issues ^ 121 5.2 Dynamic Calibration Issues ^ 122 5.3 Further Issues ^ 124 REFERENCES^ 126 vi LIST OF TABLES Table 1^Nominal inertial parameters for the major links. ^ 18 Table 2^Nominal D-H parameters for the UBC hydraulic machine and calibrator. ^ 56 Table 3^Nominal kinematic parameters for the minor links of the UBC hydraulic machine. ^ 57 Table 4^Identified D-H parameters — simulation for the effects of actuator drifts. ^ 59 Table 5^Identified D-H parameters — simulation for the combined effects of sensor accuracy and actuator drift. ^ 61 Table 6^Identified D-H parameters — simulation for the combined effects of joint flexibility and actuator drift^ 61 Table 7^Identified D-H parameters for the UBC hydraulic machine and calibrator. ^ 63 Table 8^Distance error comparison between the nominal and identified models. ^ 66 Table 9^Reidentified D-H parameters for the UBC hydraulic machine and calibrator. ^ 70 Table 10^Distance error comparison between the previously identified and the re-identified models. ^ 71 Table 11^Identified versus nominal parameters for minor links. . . ^ 76 Table 12^Error parameters for the minor links of the manipulator. ^ 77 Table 13^Hypothetical dynamic parameters of a hydraulic machine for simulations^ 106 vii ^ Table 14^Identified dynamic parameters of a hydraulic machine with sensor errors (complete model). ^ 109 Table 15^Identified dynamic parameters of a hydraulic machine with sensor errors (reduced model)^ 110 Table 16^Identified dynamic parameters of the UBC hydraulic manipulator (complete model) 115 Table 17^Identified dynamic parameters of the UBC hydraulic manipulator (reduced model) ^ 116 LIST OF FIGURES Figure 1 A hybrid position/force feedback controller. ^ 2 Figure 2 Schematic of a typical excavator with "bucket"^ 11 Figure 3 Schematic of a modified excavator having "grapple" instead of "bucket". ^ 12 Figure 4 Plan view of the excavator with grapple, showing the swing parameters^ 13 Figure 5 Schematic diagram of the "boom"^ 14 Figure 6 Schematic diagram of the "stick". ^ 15 Figure 7 Schematic Diagram of the "grapple". ^ 16 Figure 8 Local coordinate frame attached to the C.G. of link i. .^. 17 Figure 9^Nominal geometric parameters for the boom actuators.. . 19 Figure 10 Nominal geometric parameters for the stick's actuator. ^ 20 Figure 11 Establishing link coordinate systems based on the modified D-H parameters. ^ 33 Figure 12 The kinematics of a cylindrical hydraulic actuator. ^ 44 Figure 13 The calibrator designed for machine calibration. ^ 45 Figure 14^The combined hydraulic machine and the calibrator during the kinematic calibration process ^ 47 Figure 15^Establishment of the coordinate systems for the links of the closed-chain. ^ 53 Figure 16^Experimental trajectories of the manipulator links used in simulations when only Link 3 (stick) is active. ^ 57 ix