10 A Technique for Minimizing Robot-Induced Modal Excitations for On-Orbit Servicing, Assembly, and Manufacturing Structures 91 Fig. 10.2 Partially assembled OSAM telescope example model with attached notional assembly robot; each different-colored hexagonal backplane segment represents an assembly unit Table 10.1 Frequencies of the first eight flexible modes of the partially assembled OSAM telescope # Mode description Frequency (Hz) # Mode description Frequency (Hz) 1 Forward bend 3.18 5 System yaw twist 8.42 2 Base truss roll twist 3.43 6 Second roll twist 9.48 3 Fwd bend w/ storage 3.49 7 Truss bend +backplane yaw 10.8 4 Mixed backplane twist and fwd bend 7.07 8 Backplane yaw 12.1 10.2 Demonstration Model For evaluation and demonstration purposes, a mobile robot arm based on those found on the International Space Station and envisioned for the lunar gateway [8] is used in conjunction with an exemplary OSAM structure based on the in-space astronomical telescope (iSAT) reference design [9]. A partially assembled version of the iSAT telescope was developed and consists of a space platform and several hexagonal truss segments that constitute the telescope mirror backplane (Fig. 10.2). During construction, the robotic arm will assemble the backplane segments before mounting mirror segments. Analytical modal characteristics of this model obtained via Nastran and substructuring routines within IMAT™ [10] are provided in Table 10.1. Modal damping of 1% is applied to the assembled structure. The robotic arm is modeled as a set of three rigid bodies and simulated via a multibody dynamics solver coupled to the iSAT model within IMAT. The angle of two joints of the robotic arm (one elbow joint and one shoulder joint near the connection to the iSAT structure) are independently controlled to follow defined trajectory profiles via PD controllers implemented within MathWorks’ Simulink. More details about this combination of iSAT and robotic arm models can be found in Refs. [3, 4]. 10.3 Selection of Minimal Excitation Poses Our goal in this chapter is to define a technique that allows for selecting robot poses and trajectory motions that minimize robot-induced modal excitations. We start by exploring the relationship between modal excitation and robot actuation. Then we develop a metric that can be used to guide robot path and trajectory planning. Finally, we verify our findings through an analytical demonstration of two otherwise equivalent robotic motions that induce different modal responses, with one clearly preferred over the other. As discussed in detail in Ref. [3], there exists an intricate relationship between robot pose and transmissibility between the robot actuator torque and the structural modes. In short, as the robot arm changes orientation, its ability to excite a given
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