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Ground Based Laser Transmitter to Target In-flight Drones (GiBLiT)

Anonymous — Fri, 26 Apr 2024 21:00:00 +0000

Ground Based Laser Transmitter to Target In-flight Drones (GiBLiT) Anonymous (not verified) Fri, 04/26/2024 - 15:00

N. Allanqawi , A. Fitton , D. Lee , F. McDermott , S. Robertson , H. Tomerlin , M.M. Nicotra

[video:https://www.youtube.com/watch?v=QzQaNPfgkB0]

This video features the Still Compiling Team showing off their Senior Design project at the 2024 Engineering Expo. The drone is not controlled via a (boring) RF antenna, but via an optical link between a photodiode array on the drone and a laser mounted on a swiveling ground station. The team won the ECEE Most Ambitious Project Award in recognition of the fact that the road to success required a variety of very different subsystems and technologies (Computer Vision, Aiming System, Laser Transmitter, Photodiode Receiver, and Flight Controller) to work in unison. The team also won the unofficial "Most Solutions Being Investigated in Parallel Award", which is a testament to the sheer amount of trial and error that went into getting all this to work.

Special Thanks to Eric Bogatin and Gabe Altman, who guided the team throughtout the year and helped the project stay on track. The ECEE Senior Design experience would not be the same without Eric's expert leadership and Gabe's unwavering support.

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Computation of Input-Saturated Output-Admissible Sets

Anonymous — Mon, 20 Jun 2022 19:39:47 +0000

Computation of Input-Saturated Output-Admissible Sets Anonymous (not verified) Mon, 06/20/2022 - 13:39

Yaashia Gautam , Marco M. Nicotra

Maximal Output Admissible Sets (MOAS) are the set of all initial states and references such that the output response is always constraint admissible. Introduced in [1], the MOAS holds a special place in constrained control theory and is often used in strategies such as Model Predictive Control and Reference Governors to guarantee constraint satisfaction.

As desirable as it is to find the Maximal Output Admissible Set, it is often very difficult to compute it in closed form. Depending on the system and the constraints, the MOAS may not even be convex, bounded, closed, etc. For discrete-time LTI systems subject to linear state and input constraints, [1] provides an algorithm for computing the MOAS. In our latest paper [2], we show that it is possible to compute a provably larger set by treating input saturations as a nonlinearity as opposed to a constraint.

This intuition gives rise to the Input-Saturated Output-Admissible Set (ISOAS), which is the MOAS for systems with a saturated control law.

INPUT-SATURATED OUTPUT-ADMISSIBLE SETS

The traditional MOAS for an LT-DTI system is computed by using a prestabilizing linear controller. Since the MOAS depends on the prestabilizing controller, it is possible to find a larger set (ISOAS) by using a saturated control law, rather than a linear one. The computation of ISOAS is done by leveraging the piecewise affine nature of the prestabilized system. We partition the state\reference space into three regions: Non-Saturated, Upper-Saturated, and Lower-Saturated.

The above animation shows the step-by-step computation of the ISOAS for a linear system with output constraints and input saturation. The specific system is described in [2, Section VI.C]. The Non-Saturated Region is shown in green, whereas the Upper and Lower-Saturated Regions are shown in yellow. The computation process of the ISOAS is as follows:

First, the constraints are propagated within each region, causing each polyhedron to evolve independently from the others;
Second, the constraints are shared between regions, thereby causing each reagion to be affected by the others.

This process is repeated until the final ISOAS is computed.

EROSION PREVENTION

One of the difficulties in the computation of ISOAS during the constraint sharing phase of the computation algorithm is that the constraints for one region might be harmful or redundant for the other one. To solve this issue, we introduced a erosion prevention step in our algorithm, whereby sharing constraints between regions is done only after eliminating any redundant constraints.

The above animations show the difference between the computation of the ISOAS with and without erosion prevention for the example detailed in [2, Section VI.A]. The first image has erosion prevention, while the second does not. As can be seen, the first set is both bigger and faster to compute than the second set.

EMPTY SET PREVENTION

Another complication that can arise in the saturated regions is that the constraint propagation may lead to an empty set if performed incorrectly. To solve this issue, we introduce the concept of empty set prevention, whereby we omit any constraint such that the 1-step violation requirement is fully redundant with respect to the 2-step violation requirements. Below is an example of computation of the ISOAS with and without empty set prevention algorithm for the system featured in [2, Section VI.B].

The first animation shows the computation with the empty set prevention algorithm, while the second does not have that feature. It can be observed that the saturated regions in the second animation eventually reduce to an empty set and the computation of the ISOAS can not continue further. However, the first computation shows the actual ISOAS, which is a polyhedron with non-empty saturated regions.

REFERENCES

[1] E. G. Gilbert and K. T. Tan, “Linear systems with state and control constraints: The theory and application of maximal output admissible sets,” IEEE Transactions on Automatic Control, vol. 36, no. 9, pp. 1008–1020, 1991.

[2] Y. Gautam and M. M. Nicotra, "Finite-Time Computation of Polyhedral Input-Saturated Output-Admissible Sets", IEEE Transactions on Automatic Control (under review)

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Constrained Satellite Reorientation with Control Moment Gyroscope

Anonymous — Fri, 01 Apr 2022 04:09:55 +0000

Constrained Satellite Reorientation with Control Moment Gyroscope Anonymous (not verified) Thu, 03/31/2022 - 22:09

T.L. Dearing , J. Hauser , X. Chen , M.M. Nicotra , C. Petersen

This article illustrates our group's most recent progress in developing an optimal path planner for rigid-body spacecraft rotations using Control Moment Gyroscopes (CMG's). This work improves upon our previous project by incorporating fully-modelled spacecraft actuators and addressing all of the fascinating complexities they add to the optimization problem. Above is an example of a solution returned by our solver for a 180° spacecraft rotation about its z-axis using an array of CMG's. Additonally, the satellite executes this maneuver while avoiding pointing its sensitive optical equipment (indicated in green) at the sun (indicated in yellow) during the rotation.

Spacecraft Rotations using Control Moment Gyroscopes

We begin by addressing a fascinating and nontrivial question: how exactly do spacecraft rotate themselves?

When portraying spacecraft, popular media adore the exciting visuals of gas thrusters. In practice however, fuel is a finite and valuable resource once a spacecraft has launched. As such, it is rarely used for anything other than adjusting and maintaining the orbit established by the initial launch.

Spacecraft rotations on the other hand are required regularly for normal operations (pointing the solar panels at the sun) and when executing specific missions (orienting the spacecrafts cameras/sensors, docking with other spacecraft, etc). Amazingly, this common operation can actually be performed using simple electric motors and renewable electric power.

The principle behind this achievement, called Momentum Exchange, is straightforward. When applying a torque between the connected elements of a spacecraft, the total angular momentum of the entire spacecraft is conserved. That is, a motor applying torque on its shaft produces an equal and opposite reaction torque on the motor's frame. By heavily weighting the motor shaft with a dense wheel and connecting the motor frame to the spacecraft, we can rotate the entire spacecraft (albeit slowly) using this reaction torque. This device is called a Reaction Wheel and is frequently used in the design of smaller spacecraft.

However, we can go a step further. When the motor wheel is spinning, it also acts a gyroscope and produces powerful torques proportional to the speed of the wheel (also produced by momentum conservation). Torques applied to this motor assembly (via a new second motor) produce far more powerful reaction torques on the spacecraft than those from conventional reaction wheels. These devices are called Control Moment Gyroscopes (CMG's) and are used to efficiently rotate larger spacecraft such as the ISS. The diagram below shows an outline of such a device, with the (reaction) wheel spin axis highlighted in red and the secondary (or gimbal) motor axis highlighted in blue. Note that the outermost black frame of the CMG is mounted to the spacecraft frame, while the internal assembly and wheel are free to rotate via their respective motors.

Note that, by design, CMG's and reaction wheels only provide torque around a single axis. Since spacecraft are regularly required to rotate around arbitrary axes, multiple CMG's are arranged in an array combining their outputs to produce any required torque. One popular array geometery, the Rooftop Array, is shown below.

While CMG's are vastly more efficient and powerful than reaction wheels, they present an interesting and nontrivial challenge for control engineers. Specifically, the CMG's torque axis (produced by gyropscopic forces and highlighted in purple above) rotates with the CMG's wheel assembly, meaning that the available torque from that CMG at any given time is dependent on its current orientation. As such, certain torque directions may be unavailable (even for a well designed array) if the CMG's are all poorly oriented. For example, consider the the rooftop array above. In its default configuration (shown), all of the purple torque axes for the CMG's are confined to the xz plane, meaning that no combination of them can produce a torque along the y-axis. As such, any maneuver requiring the spacecraft to rotate around its y-axis using this array will require extra time for the array to reconfigure.

Thankfully, there is a way to regain the Control Authority lost in these poor configurations (rather then avoid them entirely as most approaches do). Conventionally, CMG design engineers have assumed that the (red) wheel motor is to be used only to maintain the CMG wheel's speed to allow it to function as a gyroscope. This assumption simplifies engineering design and equations of motion, but also creates the problem discussed above. In fact, using these motors as conventional reaction wheels (while also maintaining the wheel speeds during downtime) restores the lost control authority (note that the indicated red axes from the previous example point along the previously inaccessible y-axis).

By combining the torques from the (red) wheel motors and the (blue) CMG gimbal motors, we are able to ensure that our system can produce arbitrary commanded torques in any configuration. However, this doubles the number of control inputs to the system and vastly complicates the system's equations of motion. It is this problem that we aim to solve using our PRONTO optimization algorithm.

Trajectory Optimization using PRONTO

Now that we understand how spacecraft rotate, we now consider how to plan optimal spacecraft rotation maneuvers using only the CMG motor inputs. That is, we wish to determine a path in each of the system's primary states (orientation, angular rotation rate, etc.) and control (motor) inputs which:

Moves the satellite from our initial orientation to our desired orientation
Satisfies the system's equations of motion (e.g. a path we can actually follow)
Avoids pointing the onboard camera(s) at the sun (safety)
Is optimal in the mission context (e.g. least fuel used, fastest time, etc.)

In order to determine this maneuver (or trajectory) numerically, we use a technique called PRONTO to smoothly reshape a guess solution (e.g. a path that approximately satisfies (1) above) into an optimal solution which satisfies all of the requirements. The process of the algorithm reshaping this path is shown in the animation below.

Focusing first on the large sphere in the center of the figure, the blue, magenta, and red curves represent potential paths for the primary axes of the satellite to follow as it rotates. The green path represents the orientation of the onboard camera which is adjusted to sweep its vision cone away from the sun (yellow) as the solver progresses. If we were to freeze this animation, the path shown would be a viable manuever for the satellite to execute. The animation at the top of this page shows a satellite executing the (optimal) maneuver at the end of the animation.

The remaining plots illustrate how the various states, control inputs, and performance metrics of the maneuver are adapted by the solver, including:

The orientation of the satellite given by the quaternion q
The angular rotation rate of the satellite given by omega
The gimbal angles of each of the CMG's in the array delta
The angular momentum in the CMG gimbals h_g
The angular momentum in the CMG wheels h_w
The motor inputs tau_g and tau_w for the gimbal and wheel motors respectively
The CMG array's singularity index (proximity to a 'bad' configuration)
The maneuver's angular error from the target orientation

With these metrics, we can make some fascinating observations about the planned maneuver:

Even when used to improve control authority, the wheel momentum (speed) h_g is regulated to its target value by our solver
Our planned manuever improves the solution guess to get within 0.2° of the target orientation
The control inputs tau_g for the gimbal motors change from gentle and consistent torques to shorter, more intense torques. Although this is not necessarily more energy efficient, the shorter pulses indicate a more effective use of the CMG's torque amplification.
The angular velocity along the z-axis appears to saturate between 0 and 50 seconds and, during the same time frame, it appears as though the CMG array nears a singularity (See the singularity index plot). In fact, both features originate from the finite available momentum in the array. Once the CMG's are all aligned in the same direction, no more angular momentum is available in the array to rotate the satellite more quickly, causing the velocity to saturate. In this case, the singularity we approach is the array's momentum envelope, indicating we are hitting a performance bottleneck of the CMG's themselves.

The paper detailing this project is currently undergoing final revisions and will be linked here once it becomes publicly available.

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Constrained Attitude Control of a Satellite using PRONTO

Anonymous — Mon, 22 Mar 2021 06:00:00 +0000

Constrained Attitude Control of a Satellite using PRONTO Anonymous (not verified) Mon, 03/22/2021 - 00:00

T.L. Dearing , J. Hauser , X. Chen , M.M. Nicotra , C. Petersen

This visualization illustrates our recent work in developing an optimal maneuver planner for rigid-body satellite rotations. Specifically, this animation shows how our solver reshapes a 180º rotation about the satellite's z-axis to be both optimal and feasible.

In general, finding a maneuver which is optimal (e.g. uses the minimum fuel, arrives in the least time, etc.) is extremely difficult as we must search over an infinite-dimensional space of potential maneuvers connecting the initial and target orientations. This point is easy to visualize with any household object, as you can turn it upside down an infinite number of ways (e.g. rotate the top towards you, away from you, to the right or left, and any combination of those four). This difficulty is further complicated by our inability to represent a continuous curve using the finite precision and memory available to a computer. Thus, we must accurately approximate these maneuvers as we search for the optimizer.

Additionally, real satellites have implicit safety constraints on their motion to prevent stressing or wearing out onboard hardware. As a result, we can only consider maneuvers which are feasible (i.e. satisfy these constraints along the entire maneuver). Some common operational and safety constraints for satellite rotations include:

Ensuring safe (bounded) commands for the attitude thrusters (to prevent saturating them),
Ensuring a safe (bounded) angular rotation rate along each axis during the maneuver (to avoid over-stressing the structure of the satellite and improve the accuracy of onboard sensors),
Avoiding blinding an onboard sensor by pointing it near bright objects, such as the sun, moon, or other planets.

This final constraint is particularly challenging, as it cuts a hole in the space of feasible orientations that the satellite can pass through during the maneuver.

To make this problem computationally tractable for modern CPU's, we apply a Trajectory Optimization technique called PRONTO, or the Projection-Operator-based Newton's method for Trajectory Optimization. This approach uses geometric insight of the system's Trajectory Manifold (the space of maneuvers which the satellite can execute from a fixed initial condition) to identify the exact (continuous) deformations necessary to approach the optimizer. Although we will not elaborate on this technique here, these deformations are illustrated in the above animation. Note that the final solution for the above problem can be computed rapidly (within 30s) on a modern CPU.

Examining this animation in more detail, note first that the top-left panel shows the time-varying orientation (or attitude) of the satellite using a 4-parameter representation called a quaternion. This representation is highly numerically efficient but often difficult to interpret. Alternatively, the red, magenta, and blue axes inscribed on the sphere in the top-right panel show how the x,y, and z-axes of the satellite rotate during the maneuver (shown as the satellite would appear to an external observe floating in space next to it, or in the space-fixed frame). Note that the z-axis remains almost stationary during the maneuver, as the majority of the desired rotation is around this axis. Also shown on this sphere is the current direction of an onboard camera (shown in green) and the current relative direction of the sun (shown in yellow). To adhere to the 3^rd constraint above, we must then ensure that the final maneuver does not move the green camera path through the yellow viewing angle for the sun.

In addition, the applied thrust u(t) and the angular rate ω(t) along each axis of the satellite (in its own body-fixed frame) are shown in the two panels in the bottom left. Note that, as the solver progresses in the animation, the z-axis thrust and rotation rate curves push up against the 1^st and 2^nd constraints. This indicates that the optimal, feasible behavior for this maneuver is to apply max thrust for a brief time and then coast at the maximum safe velocity until the majority of the rotation has been executed. The thrusts and rotations along the other axis are then applied to swerve the camera away from the sun to adhere to the 3^rd constraint.

Finally, the bottom right panel shows the remaining rotation angle necessary to complete the maneuver (called the MRP attitude error). While this error does not converge exactly to zero at the final time (indeed, exact convergence is actually sub-optimal), it converges well within the tolerance of the native attitude controllers on the satellite, allowing them to complete the maneuver exactly.

To better understand the progress of the algorithm, note the stage indicator in the top right of the animation. PRONTO first begins with a guess for a direct rotation between the initial and final attitudes. Because this guess incorrectly orients the sensor at the sun (and so is infeasible under the specified constraints), PRONTO quickly adjusts this maneuver to satisfy all the constraints by a safe margin (the first stage). Since this solution is sub-optimal to the overall optimization problem, PRONTO then iteratively pushes closer to the constraints by lowering the parameter ε_ko (following the so-called central path for an interior point method) to reach the optimal constrained rotation maneuver (the second stage).

A unique and useful property of the PRONTO result shown above is that each curve iterate returned by the solver is a valid trajectory under the satellite's natural dynamics. That is, in the absence of noise, the satellite can follow each of the intermediate curves exactly (as opposed to tracking along them using waypoints). Additionally, each curve iterate shown after initial feasibility is obtained (i.e. after the green curve exits the gold circle) is also feasible. That is, feasibility is maintained by PRONTO once it is achieved (also not presented by conventional approaches). Thus, each curve iterate displayed above is a sub-optimal, but safe and valid potential maneuver for the satellite when fast-decision making is required. Neither of these properties are provided by classic trajectory optimization solvers, which approximate the problem as a conventional nonlinear programming problem.

The paper detailing this project is currently undergoing final revisions and will be linked here once it becomes publicly available.

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ERG for Safe Human Robot Interaction

Anonymous — Mon, 18 Jan 2021 07:00:00 +0000

ERG for Safe Human Robot Interaction Anonymous (not verified) Mon, 01/18/2021 - 00:00

K. Merckaert , B. Convens , C.-J. Wu , A. Roncone , M.M. Nicotra , B. Vanderborght

[video:https://www.youtube.com/watch?v=UzbhMzcKSbE&feature=youtu.be]

This video is represents a significant milestone in Kelly Merckaert's research on safe Human-Robot Interaction. The control laws used in these experiments were developed during Kelly's 6-month research internship at CU Boulder, although their implementation on a physical robot had to wait for her to return to the BruBotics research center in Brussels. The robot is able to operate safely thanks to the use of an Explicit Reference Governor, which guarantees constraint satisfaction while only having a computational footprint of ~1ms.

This experiment is a significant milestone for the development of computationally inexpensive strategies for the Constrained Control for Safe Human-Robot Interaction, and doubles up as a nontrivial validation of the Explicit Reference Governor framework in a highly non-convex setting.

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Multi-agent wake estimation

Anonymous — Tue, 15 Dec 2020 07:00:00 +0000

Multi-agent wake estimation Anonymous (not verified) Tue, 12/15/2020 - 00:00

J. Annoni , C.J. Bay , M.M. Nicotra , L. Pao , D.J. Pasley

[video:https://www.youtube.com/watch?v=g4st2sJFdJs&feature=youtu.be]

Our work on wind field estimation continues with a multi-agent scenawhere multiple mobile sensors communicate with each other to identify the model parameters of the incoming wind. Each agent can only take measurements in its own section of the wind farm and can only communicate with each neighbors. As time goes on, the estimates of al the agents converge to the correct value.

This proof of concept is yet another first step in the development of Autonomous Mobile Sensors for Wind Field Estimation.

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ERG for Robotic Manipulators

Anonymous — Mon, 02 Nov 2020 07:00:00 +0000

ERG for Robotic Manipulators Anonymous (not verified) Mon, 11/02/2020 - 00:00

K. Merckaert , B. Convens , I. El Makrini , G. Van der Perre , M.M. Nicotra , B. Vanderborght

[video:https://www.youtube.com/watch?v=VAYV9x25da4&feature=youtu.be]

This video, titled "The Explicit Reference Governor for Real-Time Safe Control of a Robotic Manipulator" was presented at the 2020 IROS Workshop: Bringing constraint-based robot programming to real-world applications. These experimental results showcase the interest in implementing an Explicit Reference Governor for real-time constratined control of robotic manipulators and is the first step towards Constrained Control for Safe Human-Robot Interaction.

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Distributed ERG for Crazyswarm Control

Anonymous — Fri, 28 Feb 2020 07:00:00 +0000

Distributed ERG for Crazyswarm Control Anonymous (not verified) Fri, 02/28/2020 - 00:00

B. Convens , K. Merckaert , B. Vanderborght , M.M. Nicotra

[video:https://www.youtube.com/watch?v=PsSrDJSchFM&feature=youtu.be]

This is the support video for the article "A Distributed Explicit Reference Governor for the Safe On-Board Control of a Nano-Quadrotor Swarm" submitted to IEEE Transactions on Robotics. The paper summarizes the work done by Bryan Convens during his six-month research stay at CU Boulder. These experiment represent a significant development in the formulation of on-board real-time strategies for the Formation Control of Multiple Unmanned Aerial Vehicles, and doubles up as an extension of the Explicit Reference Governor framework to distributed systems.

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Distributed ERG for Crazyswarm Control

Anonymous — Wed, 31 Jul 2019 06:00:00 +0000

Distributed ERG for Crazyswarm Control Anonymous (not verified) Wed, 07/31/2019 - 00:00

B. Convens , K. Merckaert , M.M. Nicotra , B. Vanderborght

[video:https://youtu.be/J9-RmQb_8v8]

The video is one of the final experiments performed by Bryan Convens at the end of his six-month stay at CU Boulder. During his research stay, Bryan developed a Distributed ERG add-on to the Crazyswarm framework. The addon enables crazyflies to perform real-time formation changes without requiring any form of off-line trajectory planning. The extremely limited computational footprint of the ERG ensures that the code can be implemented onboard each Crazyflie, thus enabling the swarm to reach the desired setpoint without violating constraints (e.g. actuator saturation, external obstacle avoidance, inter-agent collision avoidance).

The proposed method demonstrates the effectiveness of the ERG framework in scenarios where the controlled system has very limited computational capabilities.

This experiment is a significant milestone for the development of computationally inexpensive strategies for the Formation Control of Multiple Unmanned Aerial Vehicles, and doubles up as a nontrivial validation of the Explicit Reference Governor framework.

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Wake estimation

Anonymous — Fri, 16 Nov 2018 07:00:00 +0000

Wake estimation Anonymous (not verified) Fri, 11/16/2018 - 00:00

J. Annoni , C.J. Bay , M.M. Nicotra , L. Pao , D.J. Pasley

[video:https://youtu.be/eookRgXa5k8]

As the ASIRT seed grant draws to a close, we have successfully demonstrated that it is possible to use a single mobile sensor to estimate the airflow within a wind farm. The principle behind the proposed method is to identify the areas of the flow field that contain the highest density of information and compare the measurements in those locations with the current model output. This comparison is then used to iteratively update the model and drive the error to zero.

The proposed method relies on a turbine wake model supplied by NREL, which we used to identify the areas with the highest information density and plan a trajectory for the mobile sensor. The wind filed estimate is then updated in real-time as the mobile sensor collects data and compares the model predictions with the actual data.

This proof of concept is the first step in the development of Autonomous Mobile Sensors for Wind Field Estimation.

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