Timothy Sands

Operations by space drones mandate significant autonomy. This study experimentally evaluates key proposed applications of autonomy. Center of gravity auto-location is proposed using autonomous identification of mass properties, necessitating nonlinear state estimation. Nonlinear, coupled governing kinetics are strictly adopted as the control, and inversion provides closed-form estimates of mass properties. Seminally neglecting the diagonal inertia moments, the inertia cross-products are utilized to exactly find the mass center coordinates using the parallel axis theorem to parameterize the location coordinates. In December 2024, experiments were performed in space for hours, validating the approaches proposed. The findings indicate the longitudinal distribution was quite symmetric. Meanwhile, the lateral distribution was quite off-balance. Estimation convergence of the mass center coordinates was improved compared to the state-of-the-art comparative benchmark. In hundreds of days, the latter achieved millimeter convergence, while in minutes, the former achieved hundreds of millimeters convergence.

Maintaining a spacecraft’s center of mass at the origin of a body-fixed coordinate system is often key to precision trajectory tracking. Typically, the inertia matrix is estimated and verified with preliminary ground testing. This article presents groundbreaking preliminary results and significant findings from on-orbit space experiments validating recently proposed methods as part of a larger study over multiple years. Time-varying estimates of inertia moments and products are used to reveal time-varying estimates of the location of spacecraft center of mass using geosynchronous orbiting test satellites proposing a novel two-norm optimal projection learning method. Using the parallel axis theorem, the location of the mass center is parameterized using the cross products of inertia, and that information is extracted from spaceflight maneuver data validating modeling and simulation. Mass inertia properties are discerned, and the mass center is experimentally revealed to be over thirty centimeters away from the assumed locations in two of the three axes. Rotation about one axis is found to be very well balanced, with the center of gravity lying on that axis. Two-to-three orders of magnitude corrections to inertia identification are experimentally demonstrated. Combined-axis three-dimensional maneuvers are found to obscure identification compared with single-axis maneuvering as predicted by the sequel analytic study. Mass center location migrates 36–95% and subsequent validating experiments duplicate the results to within 0.1%.

Grappling actions by space robots for the purposes of stabilizing, refueling, repair, and equipment replacement necessitate the autonomous abilities of a single grappling space robot to rapidly contend with large variations in total system inertia rapidly shifting a system’s center of mass, as targets can be massive with possibly unknown or poorly known mass inertia properties. Grappling actions yield opportunities for a novel online calculation of the time-varying location of the combined system’s center of mass. Two-norm optimal nonlinear, projection regression-based learning is implemented and juxtaposed to a comparative benchmark both qualitatively and quantitatively supported by a comparison of enhancements of Luenberger observers. Analysis precedes modeling and simulation to verify the design, and then, spaceflight experiments are proposed for the sequel to validate the simulation results. Time-varying mass locations are discerned, and the time-varying location of the mass center is revealed to be 36–95 percent different than initially assumed, and 58–317 percent corrections to inertia identification are demonstrated. Combined three-dimensional maneuvers obscures identification compared to single-axis maneuvering.

Grappling actions by space robots for the purposes of stabilizing, refueling, repair, and equipment replacement necessitate autonomous abilities of a single grappling space robot to rapidly contend with large variations in total system inertia rapidly shifting system center of mass, as targets can be massive with possibly unknown or poorly known mass inertia properties. Proposing time–varying inertia identification yields opportunities for novel online calculation of time–varying location of the combined system’s center of mass. Two–norm optimal nonlinear, projection regression–based learning is implemented and juxtaposed to a comparative benchmark both qualitatively and quantitatively supported by a comparison of enhancements of Luenberger observers. Following analytical development, simulations are used to verify the design, and then spaceflight experiments are proposed for the sequel to validate the simulation results. Time–varying mass locations are discerned, and the time–varying location of the mass center is revealed to be 36–95 percent different than initially assumed, and 58–317 percent corrections to inertia identification is demonstrated. Combined three–dimensional maneuvers obscure identification compared to single–axis maneuvering.

Within the past decade, the aerospace engineering industry has evolved beyond the constraints of using single, large, custom satellites. Due to the increased reliability and robustness of commercial, off-the-shelf printed circuit board components, missions have instead transitioned towards deploying swarms of smaller satellites. Such an approach significantly decreases the mission cost by reducing custom engineering and deployment expenses. Nanosatellites can be quickly developed with a more modular design at lower risk. The Alpha mission at the Cornell University Space Systems Studio is fabricated in this manner. However, for the purpose of development, the initial proof of concept included a two-satellite system. The manuscript will discuss system engineering approaches used to model and mature the design of the pilot satellite. The two systems that will be primarily focused on are the attitude control system of the carrier nanosatellite and the radio frequency communications on the excreted femto-satellites. Milestones achieved include ChipSat to ChipSat communication, ChipSat to ground station communication, packet creation, error correction, appending a preamble, and filtering the signal. Other achievements include controller traceability/verification and validation, software rigidity tests, hardware endurance testing, Kane damper, and inertial measurement unit tuning. These developments matured the technological readiness level (TRL) of systems in preparation for satellite deployment.

Controlling robots in space with necessarily low material and structural stiffness is quite challenging at least in part due to the resulting very low structural resonant frequencies or natural vibration. The frequencies are sometimes so low that the very act of controlling the robot with medium or high bandwidth controllers leads to excitation of resonant vibrations in the robot appendages. Biomimetics or biomimicry emulates models, systems, and elements of nature for solving such complex problems. Recent seminal publications have re-introduced the viability of optimal command shaping, and one recent instantiation mimics baseball pitching to propose control of highly flexible space robots. The readership will find a perhaps dizzying array of thirteen decently performing alternatives in the literature but could be left bereft selecting a method(s) deemed to be best suited for a particular application. Bio-inspired control of space robotics is presented in a quite substantial (perhaps not comprehensive) comparison, and the conclusions of this study indicate the three top performing methods based on minimizing control effort (i.e., fuel) usage, tracking error mean, and tracking error deviation, where 96%, 119%, and 80% performance improvement, respectively, are achieved.

Robots in space are necessarily extremely light and lack structural stiffness resulting in natural frequencies of resonance so low as to reside inside the attitude controller's bandwidth. A variety of input trajectories can be used to drive a controller's attempt to ameliorate the control-structural interactions where feedback is provided by low-quality, noisy sensors. Traditionally, step functions are used as the ideal input trajectory. However, step functions are not ideal in many applications, as they are discontinuous. Alternative input trajectories are explored in this manuscript and applied to an example system that includes a flexible appendage attached to a rigid main body. The main body is controlled by a reaction wheel. The equations of motion of the flexible appendage, rigid body, and reaction wheel are derived. A benchmark feedback controller is developed to account for the rigid body modes. Additional filters are added to compensate for the system's flexible modes. Sinusoidal trajectories are autonomously generated to feed the controller. Benchmark feedforward whiplash compensation is additionally implemented for comparison. The method without random errors with the smallest error is the sinusoidal trajectory method, which showed a 97.39% improvement when compared to the baseline response when step trajectories were commanded, while the sinusoidal method was inferior to traditional step trajectories when sensor noise and random errors were present.

Controlling robots in space with necessarily low material and structural stiffness is quite challenging at least in part due to the resulting very low structural resonant frequencies. The frequencies are sometimes so low, the vary act of controlling the robot with medium or high bandwidth controllers lead to excitation of resonant vibrations. Biomimetics or biomimicry emulates models, systems, and elements of nature for solving such complex problems. Recent seminal publications have re-introduced the viability of optimal command shaping, and one recent instantiation mimics baseball pitching to propose control of highly flexible space robots. The readership will find a perhaps dizzying array of thirteen decently performing alternatives in the literature but could be left bereft selecting a method(s) deemed to be best suited for a particular application. Bio–inspired control of space robotics is presented in a quite substantial (perhaps not comprehensive) comparison, and the conclusions of the study indicate the top three performing methods based on minimizing control effort (i.e., fuel) usage, tracking error mean, and tracking error deviation include.

Gain-scheduled autopilots have emerged as a dominant strategy to achieve adaptive control of coupled, non-linear engineering complexities, owing to an ability to adapt to changing operational conditions and uncertainties. This study focuses on utilizing bilinear interpolation of gain-scheduled autopilots, emphasizing enhanced system performance and robustness. Through a comprehensive investigation and comparative analysis using three disparate cases, advantages over conventional methods are revealed. Strengths and weaknesses of both simple and specialized variants (such as linear, and real-time gain-scheduling) are introduced. Three missile guidance case-studies utilize simulation time and miss distance figures of merit. Comparing the performance of bilinear interpolation and automatic instantiations to index-search, over comparable traveled distances, missile miss distances were improved 179% and 196% respectively with slightly improved computational burden.

Calculating a minimum-time trajectory requires the solving of a boundary value problem resulting from invocation of necessary conditions of optimality to set up a set of ordinary differential equations to solve the trajectory between the initial position and desired ending position with set constraints on the path between the two. This manuscript expresses the minimum time optimum trajectory between a satellite in a geosynchronous orbit and a target set on earth’s surface utilizing a non-rotating earth centric coordinate system. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Simulation precision (validated by the quaternion normalization condition) reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the ubiquitous 321 “aerospace” rotation sequence and a 99.84% increase over the so-called 313 “orbital” rotation sequence. Utilizing the proposed optimal trajectory candidate yields a total flight time of 2 hours, 34 minutes and 46 seconds, or an average velocity of 3.85 kilometers per second, while impacting the target with a velocity of 11.54 kilometers per second.

Robots in space are necessarily extremely light and lack structural stiffness resulting in natural frequencies of resonance so low as to reside inside the attitude controller’s bandwidth. A variety of input trajectories can be used to drive a controller’s attempt to ameliorate the control-structural interactions where feedback is provided by low-quality, noisy sensors. Traditionally, step functions are used as the ideal input trajectory. However, step functions are not ideal in many applications, as they are discontinuous. Alternative input trajectories are explored in this manuscript and applied to an example system that includes a flexible appendage attached to a rigid main body. The main body is controlled by a reaction wheel. The equations of motion of the flexible appendage, rigid body, and reaction wheel are derived. A feedback controller is developed to account for the rigid body modes. Additional filters are added to compensate for the system’s flexible modes. Sinusoidal trajectories are autonomously generated to feed the controller. Whiplash compensation is additionally implemented for comparison. The control method without random errors with the smallest error is the sinusoidal trajectory method, which showed a 97.39% improvement when compared to the baseline response when step trajectories were commanded, while the sinusoidal method was inferior to traditional step trajectories when sensor noise and random errors were present.

Gain-scheduled autopilots have emerged as a dominant strategy to achieve adaptive control of coupled, non-linear engineering complexities, owing to an ability to adapt to changing operational conditions and uncertainties. This study focuses on utilizing bilinear interpolation of gain-scheduled autopilots, emphasizing enhanced system performance and robustness. Through a comprehensive investigation and comparative analysis using three disparate cases, advantages over conventional methods are revealed. Strengths and weaknesses of both simple and specialized variants (such as linear, and real-time gain-scheduling) are introduced. Three missile guidance case–studies utilize simulation time and miss distance figures of merit. Potential to achieve precise control across various mission scenarios, while ensuring reduced computational complexity is revealed by nearly two–hundred percent improved missile miss distances with comparable distances traveled and slightly improved computational burden.

The goal of the manuscript is to design a relatively good control structure for the noise suppression of a drone’s camera gimbal action. The gimbal’s movement can be simplified as a rest-to-rest reorientation system that can achieve the boundary result of a dynamic system. Six different control architectures are proposed and evaluated based on their ability to control the trajectory of the dynamic-system position and speed, their running time, and their quadratic cost. The robustness of the control architecture to uncertainties in inertia and sensor noise is also analyzed. Monte Carlo figures are used to assess the performance of the six control systems. The conditions for applying different architectures are identified through this analysis. The analysis and experimental tests reveal the most suitable control of the drone’s camera gimbal rotation.

This study was conducted to understand the response of hearing aids to different inputs and propose a novel technique to significantly improve performance of hearing aid implants. The motivation behind this study is to represent behavior of hearing aid system with simple input-output relation rather than complicated models. This representation offered a better understanding of the system and inspired an innovation to improve the hearing aid implants. A model of a hearing aid system called cochlear transplants is generated and used to simulate the system response. Using multiple methods, simplified input-output relations are derived. Results from these methods are compared and conclusions are drawn regarding which method is best for this application. One of the methods used resulted in 69.7 % error measure reduction compared to the benchmark method. This method was later used to produce a simplified model, which was then used as the basis for analysis of different configurations. A qualitative comparison of model was made, and significant improvement of cochlear transplants was achieved. Received: 17 February 2023 | Revised: 29 May 2023 | Accepted: 8 June 2023 Conflicts of Interest The authors declare that they have no conflicts of interest to this work.

In the era of electrification and artificial intelligence, direct current motors are widely utilized with numerous innovative adaptive and learning methods. Traditional methods utilize model-based algebraic techniques with system identification, such as recursive least squares, extended least squares, and autoregressive moving averages. The new method known as deterministic artificial intelligence employs physical-based process dynamics to achieve target trajectory tracking. There are two common autonomous trajectory-generation algorithms: sinusoidal function- and Pontryagin-based generation algorithms. The Pontryagin-based optimal trajectory with deterministic artificial intelligence for DC motors is proposed and its performance compared for the first time in this paper. This paper aims to simulate model following and deterministic artificial intelligence methods using the sinusoidal and Pontryagin methods and to compare the differences in their performance when following the challenging step function slew maneuver.

The goal of the manuscript is to design a relatively best control structure for the noise suppression of a drone’s camera gimbal action. The gimbal’s movement can be simplified as a rest-to-rest reorientation system that can achieve the boundary result of a dynamic system. Six different control architectures are proposed and evaluated based on their ability to control the trajectory of the dynamic-system position and speed, their running time, and quadratic cost. The robustness of the control architecture to uncertainties in inertia and sensor noise is also analyzed. Monte Carlo figures are used to assess the performance of the six control systems. The conditions for applying different architectures are identified through this analysis. The analysis and experimental tests reveal the most suitable control of the drone’s camera gimbal rotation.

Compared with the traditional robots on earth, space robotics present additional difficulties including complicated, multi–body dynamics (including anti–resonances absent with earthly robotic systems), space environmental forces and torques, communication delays, and high expense. Pointing accuracy requirements necessitate control algorithms that can accommodate flexible, multi–body dynamics particularly. The high cost of placing systems in space drives necessarily lightweight systems lacking structural stiffness. Natural frequencies of space robot vibration are often so low, the act of implementing control torques causes structural resonance. Seeking improved performance, this manuscript introduces and compares a dozen options, revealing seventy–percent reduction in tracking error may be achieved with only ten percent increase in control effort. Prequel work recommended tracking sinusoidal shaped trajectories while structurally filtering the first mode’s resonance and anti–resonance. The future research recommended in that prequel is manifest in this present work which recommends a simpler system of lower order, eliminating the notch compensation of the first resonance while no longer compensating the first anti–resonance.

The damped van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Controlling, or forcing, the behavior of a van der Pol oscillator is difficult to achieve through traditional adaptive control methods. Connecting two van der Pol oscillators together where the output of one oscillator, the driver, drives the behavior of its partner, the responder, is a proven technique for controlling the van der Pol oscillator. Deterministic artificial intelligence is a feedforward and feedback control method that leverages the known physics of the van der Pol system to learn optimal system parameters for the forcing function. We assessed the performance of deterministic artificial intelligence employing three different online parameter estimation algorithms. Our evaluation criteria include mean absolute error between the target trajectory and the response oscillator trajectory over time. Two algorithms performed better than the benchmark with necessary discussion of the conditions under which they perform best. Recursive least squares with exponential forgetting had the lowest mean absolute error overall, with a 2.46% reduction in error compared to the baseline, feedforward without deterministic artificial intelligence. While least mean squares with normalized gradient adaptation had worse initial error in the first 10% of the simulation, after that point it exhibited consistently lower error. Over the last 90% of the simulation, deterministic artificial intelligence with least mean squares with normalized gradient adaptation achieved a 48.7% reduction in mean absolute error compared to baseline.

Classical and optimal control architectures for motion mechanics in the presence of noisy sensors use different algorithms and calculations to perform and control any number of physical demands, to varying degrees of accuracy and precision in regards to the system meeting the desired end state. To circumvent the deleterious effects of noisy sensors, a variety of control architectures are suggested, and their performances are tested for the purpose of comparison through the means of a Monte Carlo simulation that simulates how different parameters might vary under noise, representing real-world imperfect sensors. We find that improvements in one figure of merit often come at a cost in the performance in the others, especially depending on the presence of noise in the system sensors. If sensor noise is negligible, open-loop optimal control performs the best. However, in the overpowering presence of sensor noise, using a control law inversion patching filter performs as the best replacement, but has significant computational strain. The control law inversion filter produces state mean accuracy matching mathematically optimal results while reducing deviation by 36%. Meanwhile, rate sensor issues were more strongly ameliorated with 500% improved mean and 30% improved deviation. Inverting the patching filter is innovative but consequently understudied and lacks well-known equations to use for tuning gains. Therefore, such a patching filter has the additional drawback of having to be tuned through trial and error.

Discretization is the process of converting a continuous function or model or equation into discrete steps. In this work, learning and adaptive techniques are implemented to control DC motors that are used for actuating control surfaces of unmanned underwater vehicles. Adaptive control is a strategy wherein the controller is designed to adapt the system with parameters that vary or are uncertain. Parameter estimation is the process of computing the parameters of a system using a model and measured data. Adaptive methods have been used in conjunction with different parameter estimation techniques. As opposed to the ubiquitous stochastic artificial intelligence approaches, very recently proposed deterministic artificial intelligence, a learning-based approach that uses the physics-defined process dynamics, is also applied to control the output of the DC motor to track a specified trajectory. This work goes further to evaluate the performance of the adaptive and learning techniques based on different discretization methods. The results are evaluated based on the absolute error mean between the output and the reference trajectory and the standard deviation of the error. The first-order hold method of discretization and surprisingly large sample time of seven-tenths of a second yields greater than sixty percent improvement over the results presented in the prequel literature.

This manuscript compares deterministic artificial intelligence to a model-following control applied to DC motor control, including an evaluation of the threshold computation rate to let unmanned underwater vehicles correctly follow the challenging discontinuous square wave command signal. The approaches presented in the main text are validated by simulations in MATLAB®, where the motor process is discretized at multiple step sizes, which is inversely proportional to the computation rate. Performance is compared to canonical benchmarks that are evaluated by the error mean and standard deviation. With a large step size, discrete deterministic artificial intelligence shows a larger error mean than the model-following self-turning regulator approach (the selected benchmark). However, the performance improves with a decreasing step size. The error mean is close to the continuous deterministic artificial intelligence when the step size is reduced to 0.2 s, which means that the computation rate and the sampling period restrict discrete deterministic artificial intelligence. In that case, continuous deterministic artificial intelligence is the most feasible and reliable selection for future applications on unmanned underwater vehicles, since it is superior to all the approaches investigated at multiple computation rates.

Teaching kinematic rotations is a daunting task for even some of the most advanced mathematical minds. However, changing the paradigm can highly simplify envisioning and explaining the three-dimensional rotations. This paradigm change allows a high school student with an understanding of geometry to develop the matrix and explain the rotations at a collegiate level. The proposed method includes the assumption of a point (P) within the initial three-dimensional frame with axes (x^i, y^i, z^i). The method then utilizes a two-dimensional rotation view (2DRV) to measure how the coordinates of point P translate after a rotation around the initial axis. The equations are used in matrix notation to develop a rotation matrix for follow-on direction cosine matrixes. The method removes the requirement to use Euler’s formula, ultimately, providing a high school student with an elementary and repeatable process to compose and explain kinematic rotations, which are critical to attitude direction control systems commonly found in vehicles.

Pre-existing surgical robotic systems are sold with electronics (sensors and controllers) that can prove difficult to retroactively improve when newly developed methods are proposed. Improvements must be somehow "imposed" upon the original robotic systems. What options are available for imposing performance from pre-existing, common systems and how do the options compare? Optimization often assumes idealized systems leading to open-loop results (lacking feedback from sensors), and this manuscript investigates utility of prefiltering, such other modern methods applied to non-idealized systems, including fusion of noisy sensors and so-called "fictional forces" associated with measurement of displacements in rotating reference frames. A dozen modern approaches are compared as the main contribution of this work. Four methods are idealized cases establishing a valid theoretical comparative benchmark. Subsequently, eight modern methods are compared against the theoretical benchmark and against the pre-existing robotic systems. The two best performing methods included one modern application of a classical approach (velocity control) and one modern approach derived using Pontryagin's methods of systems theory, including Hamiltonian minimization, adjoint equations, and terminal transversality of the endpoint Lagrangian. The key novelty presented is the best performing method called prefiltered open-loop optimal + transport decoupling, achieving 1-3 percent attitude tracking performance of the robotic instrument with a two percent reduced computational burden and without increased costs (effort).