Neuromorphic path generation in real-time

<div>In this dissertation, methods for real-time trajectory generation and autonomous obstacle avoidance for fixed-wing and quad-rotor unmanned aerial vehicles (UAV) are studied. A key challenge for such trajectory generation is the high computation time required to plan a new path to safely maneuver around obstacles instantaneously. Therefore, methods for rapid generation of obstacle avoidance trajectory are explored. The high computation time is a result of the computationally intensive algorithms used to generate trajectories for real-time object avoidance. Recent studies have shown that custom solvers have been developed that are able to solve the problem with a lower computation time however these designs are limited to small sized problems or are proprietary. Additionally, for a swarm problem, which is an area of high interest, as the number of agents increases the problem size increases and in turn creates further computational challenges. A solution to these challenges will allow for UAVs to be used in autonomous missions robust to environmental uncertainties.</div><div><br></div><div>In this study, a trajectory generation problem posed as an optimal control problem is solved using a sequential convex programming approach; a nonlinear programming algorithm, for which custom solver is used. First, a method for feasible trajectory generation for fast-paced obstacle-rich environments is presented for the case of fixed-wing UAVs. Next, a problem of trajectory generation for fixed-wing and quad-rotor UAVs is defined such that starting from an initial state a UAV moves forward along the direction of flight while avoiding obstacles and remaining close to a reference path. The problem is solved within the framework of finite-horizon model predictive control. Finally, the problem of trajectory generation is extended to a swarm of quad-rotors where each UAV in a swarm has a reference path to fly along. Utilizing a centralized approach, a swarm scenario with moving targets is studied in two different cases in an attempt to lower the solution time; the first, solve the entire swarm problem at once, and the second, solve iteratively for a UAV in the swarm while considering trajectories of other UAVs as fixed.</div><div><br></div><div>Results show that a feasible trajectory for a fixed-wing UAV can be obtained within tens of milliseconds. Moreover, the obtained feasible trajectories can be used as initial guesses to the optimal solvers to speed up the solution of optimal trajectories. The methods explored demonstrated the ability for rapid feasible trajectory generation allowing for safe obstacle avoidance, which may be used in the case an optimal trajectory solution is not available. A comparative study between a dynamic and a kinematic model shows that the dynamic model provides better trajectories including aggressive trajectories around obstacles compared to the kinematic counterpart for fixed-wing UAVs, despite having approximately the same computational demands. Whereas, for the case of quad-rotor UAVs, the kinematic model takes almost half the solution time than with a reduced dynamic model, despite having approximately the similar range of values for the cost function. When extended to a swarm, solving the problem for each UAV is four to seven times computationally cheaper than solving the swarm as a whole. With the improved computation time for trajectory generation for a swarm of quad-rotors using centralized approach, the problem is now reasonably scalable, which opens up the possibility to increase the number of agents in a swarm using high-end computing machines for real-time applications. Overall, a custom solver jointly with a sequential convex programming approach solves an optimization problem in a low computation time.</div>

This paper considers the problem of real-time trajectory generation and tracking for nonlinear control systems. We employ a two-degree-of-freedom approach that separates the nonlinear tracking problem into real-time trajectory generation followed by local (gain-scheduled) stabilization. The central problem which we consider is how to generate, possibly with some delay, a feasible state space and input trajectory in real time from an output trajectory that is given online. We propose two algorithms that solve the real-time trajectory generation problem for differentially flat systems with (possibly non-minimum phase) zero dynamics. One is based on receding horizon point to point steering, the other allows additional minimization of a cost function. Both algorithms explicitly address the tradeoff between stability and performance and we prove convergence of the algorithms for a reasonable class of output trajectories. To illustrate the application of these techniques to physical systems, we present experimental results using a vectored thrust flight control experiment built at Caltech. A brief introduction to differentially flat systems and its relationship with feedback linearization is also included. © 1998 John Wiley & Sons, Ltd.

Neural dynamics change over time and with physiologic state. Modeling of neural dynamics can thus be understood at two levels: (i) identifying the latent process that governs how and when states change, and (ii) identifying the generative circuit mechanisms within each state. Here, we develop a data-driven modeling method that tackles these two levels simultaneously. We formulate a parametric network model of neural dynamics that embeds state-dependent modulation. The modulation itself is controlled by a latent switching process, modeled as a Hidden Markov Model (HMM). A key challenge is that the model itself has internal states that must be estimated from observed data. This leads to a triune optimization problem, consisting of model parameterization of the HMM and neural dynamics, alongside state estimation. Our method brings together several optimization frameworks alongside estimation-theoretic constructs to solve this problem efficiently, enabling blind identification of state transitions and neural dynamics. We validate this methodology on ground-truth data with known parameters, and find that it accurately infers the transitions in latent state and the dynamics of each state. We demonstrate its capability of inferring changes in brain dynamics from electrophysiological data by testing it on electroencephalography recordings with labeled state transitions. While similar methods exist to infer switches and dynamics on the level of individual neurons, there is no directly comparable method available for mesoscale modeling of neural circuits. Our methodology enables blind modeling of changing neural dynamics allowing for inference of modulatory circuit mechanisms.

This thesis will present various methods of trajectory generation for various types of mobile robots. Then it will progress to evaluating Robot Operating Systems (ROS’s) that can be used to control and simulate mobile robots, and it will explain why Player/Stage was chosen as the ROS for this thesis. It will then discuss Nonlinear Trajectory Generation as the main method for producing a path for mobile robots with dynamic and kinematic constraints. Finally, it will combine Player, Stage, and NTG into a system that produces a trajectory in real-time for a mobile robot and simulates a differential drive robot being driven from the initial state to the goal state in the presence of obstacles. Experiments will include the following: Blobfinding for physical and simulated camera systems, position control of physical and simulated differential drive robots, wall following using simulated range sensors, trajectory generation for omnidirectional and differential drive robots, and a combination of blobfinding, position control, and trajectory generation. Each experiment was a success, to varying degrees. The culmination of the thesis will present a real-time trajectory generation and position control method for a differential drive robot in the presence of obstacles.

Flight management systems have greatly reduced cockpit workloads, but are not capable of calculating new flight plans in real time when flight characteristics vary or when flight trajectories become nonstationary. This paper presents a real-time flight trajectory generator (R-FTG) applicable to emergency landing approaches. First, the R-FTG calculates a preliminary flight path, which consists of an initial turn, a straight-line flight, and a terminal turn. The R-FTG then optimizes the preliminary flight path by using a direct collocation method. In order to give the direct collocation method real-time performance, an idea called stage division is incorporated. Combining the direct collocation and stage division enables real-time generation of near optimal flight trajectories. Additionally, wind effects are considered in the generating process. The R-FTG is evaluated by numerical simulations; calculation results of the R-FTG are compared with those of an offline optimization method, and the calculation results under different bank angle constraints are examined. The calculations for the wind effects are also studied. These results show the effectiveness of the proposed real-time flight trajectory generator.

This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm (without pre-assigned terminal positions). The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the swarm assignment and trajectory optimization (SATO) algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm.

The separate design of vision algorithms and motion control algorithms in existing vision servo systems limits their application in high-speed and high-precision industrial scenarios. To address this problem, a vision-motion codesign method is proposed for integrating visual servo systems with motion controllers via real-time Ethernet connections. During the engineering design phase of our proposal, we developed a control kernel architecture to clarify the system design logic. Then, we proposed a runtime module for real-time trajectory generation to facilitate the unified deployment of different planning methods in the kernel. On this basis, we implemented a self-adaptive trajectory generation synthesis method capable of dynamically adjusting the motion resources for real-time interpolation. The experimental results demonstrate that in visual servo static tracking experiments with the SCARA robot, our proposed method has a faster response time and smaller impact than other mainstream trajectory generation methods in 1 ms real-time interpolation cycles.

This paper designs an algorithm to generate time-optimal and energy-efficient trajectory for manipulators along a predefined geometric path. The path is first parameterized by cubic spline, then the trajectory generation problem is transformed into a nonlinear optimization problem with single state variable. After discretization, Sequence quadratic programming(SQP) method is applied for optimal solution. Finally, applications to a 6-DoF manipulator along different paths demonstrates the feasibility of the proposed method.

A neural dynamics model for structural optimization—Theory

This article proposes a piece of trajectory generator according to flight dynamics for strapdown inertial navigation system. First, this article uses the launch-centered earth-fixed (LCEF) frame as the reference coordinate system to introduce a high-precision flight dynamics model with six degrees of freedom. The trajectory generator proposed in this paper can output specific force, angular velocity, vehicle position, speed, attitude, angle of attack and sideslipping from the LCEF frame and local horizontal frame. The relationship between the 6DoF model and the trajectory generator was examined, and the differences were presented in comparison with traditional trajectory generation. The navigation information from the LCEF frame was converted into a local-level (LL) frame, which provided more information for the trajectory generator. Digital simulation demonstrated that total position error was less than 1 m on the generated 1100 s trajectory data. The hardware-in-the-loop (HWIL) simulation results revealed the accuracy in terms of positioning was below 10 m, and meanwhile, the speed precision was below 0.2 m/s. This proposed trajectory generator coordinated the combined systems of flight control system, the SINS, and 6DoF model. This integrated navigation simulation platform of hypersonic vehicle was designed with the input of the model. At the same time, the platform can simulate the pulse output of IMU and obtain the relevant information of satellite positioning.KeywordsTrajectory generatorHypersonic vehicleFlight dynamicsHardware-in-the-loop simulationStrapdown inertial navigation system

Unmanned aerial vehicles (UAVs), equipped with navigation systems and video capability, are currently being deployed for intelligence, reconnaissance and surveillance mission. In this paper, we present a systematic approach for the generation of UAV trajectory using a video image matching system based on SURF (Speeded up Robust Feature) and Preemptive RANSAC (Random Sample Consensus). Video image matching to find matching points is one of the most important steps for the accurate generation of UAV trajectory (sequence of poses in 3D space). We used the SURF algorithm to find the matching points between video image sequences, and removed mismatching by using the Preemptive RANSAC which divides all matching points to outliers and inliers. The inliers are only used to determine the epipolar geometry for estimating the relative pose (rotation and translation) between image sequences. Experimental results from simulated video image sequences showed that our approach has a good potential to be applied to the automatic geo-localization of the UAVs system

Vision systems in drones, specifically Unmanned Aerial Vehicles (UAV) are currently used for retrieving real-time video of the area to fly over, nevertheless commercially there are no identification nor control applications for this type of aircrafts. Some existing technologies for trajectory generation are based on cubic polynomials and Bezier curves [5] but this paper presents the implementation of an optical flow algorithm that assures to track and control the trajectory in a quadrotor drone in real time, determining the distance between the drone and a certain objective as well as the speed calculation and its displacement direction by the means of the implementation of the Lucas-Kanade (LK) algorithm. The core purpose of this paper is to achieve a low-cost and faster (due to the UAV's dynamics) solution besides the implementation of a Global Positioning System (GPS) using an Inertial Navigation System (INS) to generate an aerial trajectory, therefore it can be generated in real time converting the UAV into a semi-autonomous aircraft. The aerial robot's dynamic model was obtained by the Euler-Lagrange method, the image processing is based on the pin-hole model of a camera and optical flow. The main advantages and results obtained through the experimentation was first to correctly detect the line, and by LK implementation on OpenCV the line was correctly tracked by the drone achieving this with a low computational cost and with the possibility of indoor use covering the applications where the GPS is not able to work.

Aiming at the problem that the traditional vehicle’s trajectory generation method takes a long time and is difficult to calculate in real time, a variable step and multi-constraint trajectory generation algorithm based on a deep deterministic policy gradient (DDPG) network is proposed. Firstly, the dynamic model and constraint conditions of the vehicle are analyzed. On this basis, the reinforcement learning training model is constructed based on DDPG, and the state, action, and reward design of the training model are defined. At the same time, the variable step is introduced into the action model to improve the generated trajectory’s navigation precision. Finally, the proposed method is verified under different cases, and according to the results, the proposed method can realize quick generation of multi-constraint guidance trajectories.

Guidance algorithms for the return flight of suborbital spaceplanes must generate a variety of guidance trajectories that satisfy terminal conditions even in unexpected abort operations. To tackle this issue, a trajectory optimization method that combines convex quadratic programming and a global derivative-free optimization technique in a nested structure has been recently studied by the authors. This hybrid method efficiently explores the three-dimensional Bezier trajectories and associated guidance commands that exactly fulfill the equality terminal conditions and command continuity. In this paper, Monte-Carlo simulations are performed to investigate the applicability of this guidance method to the realistic scenario of unpowered return flight. Six stochastic evolutionary algorithms, a Bayesian optimization method, and three deterministic search algorithms are implemented and tested as global optimizers. They are compared in terms of computational and implementational complexities, robustness, and diversity of solutions obtained. The results show that reliable and real-time trajectory generation is possible, when an optimizer and its settings are properly chosen. It also reveals that diverse trajectories between initial and terminal conditions are successfully generated.KeywordsGuidanceTrajectory optimizationGlobal optimizationReal-time optimizationSuborbital spaceplane

A major objective of next generation reusable launch vehicle (RLV) programs includes significant improvements in vehicle safety, reliability, and operational costs. In this paper, trajectory generation on approach/ landing (A&L) for RLVs using motion primitives (MPs) and neighboring optimal control (NOC) is discussed. The proposed trajectory generation approach at A&L phase is based on an MP scheme which consists of trims and maneuvers. From an initial point to a given touchdown point, all feasible trajectories that satisfy certain constraints are generated and saved into a trajectory database. An optimal trajectory can then be found off-line by using Dijkstra's algorithm. After perturbations are imposed on the initial states of the off-line optimal trajectory, it is reshaped into a neighboring feasible trajectory on-line by using NOC approach. At this point, a neighboring feasible trajectory existence theorem (NFTET) is investigated and its proof is provided as well. The results show that the vehicle with stuck effectors can be recovered from failures in real time. Finally, robustness issues on NOC approach are briefly discussed.