# Space Robot Sensor Noise Amelioration Using Trajectory Shaping
## 1 Introduction  
The solutions and methods developed in this manuscript are applicable to a wide range of dynamics problems. A robotic arm is chosen here as an example of a highly flexible system, with implications across the industry. Robots are deployed in space for a variety of purposes. Figure 1a shows one such robot, NASA's Robonaut 2. In addition to space applications, robotic arms can be deployed underwater, as evidenced by Figure 1b. Whether in space or underwater, the commanded trajectory can influence the tracking error of the robotic arm. Minimizing tracking error can allow for more precise movements and support the execution of detailed motion. In-orbit servicing is an example of the need for precise control over a robotic arm's movement. By identifying the most appropriate trajectory to command, the error in angular movement can be minimized. Towards in-orbit servicing, the importance of spacecraft-mounted robotics missions is highlighted in reference [3] which stipulates:  
\"...environmental, economic, and strategic considerations support the claim that the future of a space infrastructure will depend on the ability to perform on-orbit servicing, encompassing a broad array of in-space operations, such as inspection, berthing, refueling, repair, assembly, and so on.\"  
According to a 2010 study by the U.S. National Air and Space Administration (NASA), [4] a key to enabling robotic servicing missions in space leading to advantageous future strategic impact, cost effectiveness, and environmental sustainability. Cost effectiveness is manifest in the ability to relatively cheaply replace spacecraft components rather than launch a replacement spacecraft. Reference [5] indicates since 1957 roughly 5400 space missions have been flown, while nearly twenty-thousand space objects are tracked by the north American air defense command (NORAD), where over two thousand are rocket upper stages spent of fuel and over ten thousand additional items are classified as debris. Current proposals [6; 7] indicate intentions for very large future constellations together comprising another twenty thousand objects in orbit. Such a large number of craft in orbit constitute a potentially lucrative business model for system repair [8] and refueling on-orbit. Discovery of the very origins of life and human long-term habitability are postulated to be aided by space robotics in [9]. This manuscript investigates the importance of the trajectory shaping fed to the control method used to rotate the space robot. The flexible spacecraft system examined in this manuscript is indicative of a larger dynamics problem. The solutions and methods explored are applicable to that larger set of dynamic problems. The requisite equations of motion are derived and feedback controllers and second-order structural filters are applied, following the methodology developed in [10]. Initially, sinusoidal trajectory generation is used to drive the controllers. Whiplash compensation is additionally investigated as a solution, per [11]. Three methods of trajectory shaping are applied to the flexible spacecraft robotic system and compared critically: step shaped, sinusoidally shaped, and whiplash shaped. The state errors, rate errors, and control efforts are compared for each of the three methods of input control to determine which is most appropriate for the flexible spacecraft system application. Elder techniques for controlling highly flexible systems relied foremost on feedback necessitating construction of feedback linearizing control laws [12]. The linear-quadratic regulator approach, robust control approaches minimizing the H\(\infty\) and H2 norms, and  
Figure 1: (**a**) NASA’s Robonaut 2, built at Johnson Space Center, became the first android astronaut to go to space in 2011.