Real-time trajectory optimization for collision-free asteroid landing based on deep neural networks

This paper presents a systematic method for generating optimal helicopter flight trajectories in real time for cockpit display. Helicopter flights in the event of a single engine failure are critical, and display of optimal flight paths on-board is desirable. Due to the large number of states and constraints, however, numerical solutions on a mainframe computer can take a long tune. In this paper, optimal solutions are first obtained off-line using a ground computer. For a given set of initial helicopter states and flight parameters, optimal solutions are fitted by a Fourier series. The coefficients of the Fourier approximations are then interpolated as functions of initial flight states and parameters. The approximate optimal trajectories can be quickly generated on-board using the proposed method. Introduction Engine failure is a major safety issue for all helicopters, especially during takeoff and landing operations. Due to the complexity of the situation and the dependence of safety on many parameters, optimal flight trajectories can provide useful guidance for pilot operation. In particular, on-board display of optimal trajectories is desirable. This paper presents a method for generating optimal flight trajectories in real-tune that can be used for on-board display. Depending on its capability and performance during an engine failure, a transport helicopter can be certified as Category A or Category B. The Federal Aviation Administration (FAA) grants Category B certification to a single or multi-engine helicopter with gross weight less than 20,000 Ib and capable of landing safely in case of one or all engine failures. Category A certification, on the other hand, is granted to multi-engine helicopters with independent engine systems. Category A helicopters must be able to either land safely or continue flight in case of One Engine Inoperation (OEI). This makes Category A helicopters uniquely suited for remote places where emergency landing sites are not available. I Ph.D. Candidate, Center for Control Sciences, Member AIAA * Assistant Professor, Dept. of Aerospace Eng. and Mechanics, Member AIAA + Civil Rotorcraft Group Leader, Rotorcraft and Powered Lift Branch The decision to continue the flight or to land represents an energy management problem. It has been shown''' that this decision depends on initial conditions at the time of failure as well as flight parameters. Due to the numerous initial variables involved in this decision, a method to communicate all this information to the pilot instantaneously, at engine failure, is needed. This method must keep the emergency procedure simple and manageable. In particular, on-board cockpit display of optimal flight trajectories is useful. This requires a reliable real-tune solution of optimal trajectories, on board, with limited time, limited computing power, and limited memory available. If possible, an analytical solution of optimal trajectories is desirable. Unfortunately, this can only be achieved for systems of low order and where the equations of motion and the cost function are simple. Therefore, for a complex system, an open-loop numerical procedure becomes necessary. Research efforts were made to solve optimal control problems in real-time. Schultz et al. used calculus of variation and energy state method to generate optimal trajectories on-board for the National Aerospace Plane (NASP). In his study, the equations of motion of the NASP are less complex than those of the helicopter, and an interval of time of few minutes is allowed. Bryson used neighboring control theory to generate near-optimal solutions that could be used in real-time. This method is elegant but requires a large amount of memory to store the needed perturbation matrices. Also, it is valid on a relatively small neighborhood of the nominal trajectory. Perturbation methods and table lookups are often used if only few parameters are involved. In the current problem, the equations of motion of the helicopter are complex and too many path equality and inequality constraints are present. Also, limitations on tune, computing power, and memory available make all the above methods unsuitable for this problem. This paper proposes a technique of real-time optimal trajectory generation based on approximation and

Real-time trajectory optimization for powered planetary landings based on analytical shooting equations

This paper presents a practical optimization framework for improving trajectory feasibility in constrained nonlinear optimal control problems for agile unmanned aerial vehicles (UAVs). The proposed method addresses trajectory optimization problems with non-convex geometric constraints, where gradient-based solvers often fail to converge to feasible solutions. The framework combines Model Predictive Path Integral (MPPI) control and the Augmented Lagrangian iterative Linear Quadratic Regulator (AL-iLQR). MPPI is employed as a fast sampling-based guidance mechanism to explore feasible regions of the trajectory space, while AL-iLQR is used to efficiently refine locally optimal solutions with high numerical accuracy. By decoupling feasibility exploration from local optimal refinement, the proposed method mitigates the sensitivity of gradient-based trajectory optimization to initialization in highly constrained environments. Numerical simulations involving both simplified two-dimensional dynamics and full quadrotor models demonstrate that the proposed approach significantly improves the probability of converging to feasible and dynamically consistent trajectories compared with AL-iLQR alone. The proposed method does not aim to provide theoretical guarantees of global optimality; instead, it offers a practical and computationally efficient strategy for enhancing feasibility and robustness in real-time UAV trajectory optimization.

In this paper, a real-time optimizing controller is developed to steer a differentially flat nonlinear control system to closed-loop trajectories that optimize a cost functional of interest. An interior point optimization method with penalty function is used to formulate a real-time optimization scheme. The problem is posed as a real-time optimal trajectory generaction problem in which the optimal trajectories are computed using an adaptive extremum-seeking approach. A fed-batch bioreactor simulation example is used to demonstrate the application of the technique to a finite time dynamic optimization problems that arise in batch process control.

Real-time dynamic optimization of nonlinear systems: A flatness-based approach

This study focuses on the key challenge of achieving high-precision guidance for spacecraft: real-time trajectory optimization. The highly efficient sequential convex programming (SCP) is a potential method to address this issue, but its convergence is difficult to guarantee. To enhance the convergence performance of SCP, this paper proposes a high-dimensional merit-function-based SCP method. The main contribution of this paper is threefold. Firstly, the traditional one-dimensional penalty function used to ensure the convergence of SCP is extended to a high-dimensional merit function, which avoids using the penalty parameter that is difficult to determine in advance. Secondly, to match the high-dimensional merit function, a feasibility-then-optimality convergence strategy is proposed, which is essentially an application of the iterative direction descent property in higher dimensions. Finally, based on the high-dimensional merit function and the feasibility-then-optimality strategy, an iterative algorithm is developed, and its convergence analysis is provided under certain assumptions. In numerical simulations, the effectiveness and robustness of the proposed algorithm are validated using the reentry trajectory optimization problem of a lunar capsule.

<div>Taking advantage of communication and sensing technology, trajectory optimization at signalized intersection (i.e., Eco-Approach and Departure) based on information from vehicle-to-infrastructure (V2I) communications has been proven to be effective to improve vehicle energy efficiency while guaranteeing safety and mobility. However, existing approaches are either rule-based models or optimization models, which cannot achieve optimality and computational efficiency at the same time. In this article, we propose and test a novel learning-based approach, machine learning trajectory planning algorithm (MLTPA), to achieve real-time optimization by training a machine learning model to approximate the solution from a previously developed optimization-based method named graph-based trajectory planning algorithm (GBTPA). Five types of machine learning techniques, including linear regression, <i>k</i>-nearest neighbors, decision tree, random forest, and multilayer perceptron (MLP) neural network, are compared in terms of the prediction accuracy, and the random forest method is finally selected. The proposed MLTPA reduces computation time from tens of seconds to a few milliseconds. Simulation results illustrate that MLTPA can achieve median 5.0%-6.20% improvement on energy savings over multiple simulation runs. The proposed method also has the potential to approximate other trajectory planning algorithms to achieve real-time performance while ensuring optimality.</div>

The main aim of future mobile networks is to provide secure, reliable, intelligent, and seamless connectivity. It also enables mobile network operators to ensure their customer’s a better quality of service (QoS). Nowadays, Unmanned Aerial Vehicles (UAVs) are a significant part of the mobile network due to their continuously growing use in various applications. For better coverage, cost-effective, and seamless service connectivity and provisioning, UAVs have emerged as the best choice for telco operators. UAVs can be used as flying base stations, edge servers, and relay nodes in mobile networks. On the other side, Multi-access Edge Computing (MEC) technology also emerged in the 5G network to provide a better quality of experience (QoE) to users with different QoS requirements. However, UAVs in a mobile network for coverage enhancement and better QoS face several challenges such as trajectory designing, path planning, optimization, QoS assurance, mobility management, etc. The efficient and proactive path planning and optimization in a highly dynamic environment containing buildings and obstacles are challenging. So, an automated Artificial Intelligence (AI) enabled QoS-aware solution is needed for trajectory planning and optimization. Therefore, this work introduces a well-designed AI and MEC-enabled architecture for a UAVs-assisted future network. It has an efficient Deep Reinforcement Learning (DRL) algorithm for real-time and proactive trajectory planning and optimization. It also fulfills QoS-aware service provisioning. A greedy-policy approach is used to maximize the long-term reward for serving more users with QoS. Simulation results reveal the superiority of the proposed DRL mechanism for energy-efficient and QoS-aware trajectory planning over the existing models.

The aim of this study was to develop trajectory planning that would allow an autonomous racing car to be driven as close as possible to what a driver would do, defining the most appropriate inputs for the current scenario. The search for the optimal trajectory in terms of lap time reduction involves the modeling of all the non-linearities of the vehicle dynamics with the disadvantage of being a time-consuming problem and not being able to be implemented in real-time. However, to improve the vehicle performances, the trajectory needs to be optimized online with the knowledge of the actual vehicle dynamics and path conditions. Therefore, this study involved the development of an architecture that allows an autonomous racing car to have an optimal online trajectory planning and path tracking ensuring professional driver performances. The real-time trajectory optimization can also ensure a possible future implementation in the urban area where obstacles and dynamic scenarios could be faced. It was chosen to implement a local trajectory planning based on the Model Predictive Control(MPC) logic and solved as Linear Programming (LP) by Sequential Convex Programming (SCP). The idea was to achieve a computational cost, 0.1 s, using a point mass vehicle model constrained by experimental definition and approximation of the car’s GG-V, and developing an optimum model-based path tracking to define the driver model that allows A car to follow the trajectory defined by the planner ensuring a signal input every 0.001 s. To validate the algorithm, two types of tests were carried out: a Matlab-Simulink, Vi-Grade co-simulation test, comparing the proposed algorithm with the performance of an offline motion planning, and a real-time simulator test, comparing the proposed algorithm with the performance of a professional driver. The results obtained showed that the computational cost of the optimization algorithm developed is below the limit of 0.1 s, and the architecture showed a reduction of the lap time of about 1 s compared to the offline optimizer and reproducibility of the performance obtained by the driver.

ABSTRACTAn efficient trajectory optimisation approach combining the classical control variable parameterisation (CVP) with a novel smooth technology and two penalty strategies is developed to solve the trajectory optimal control problems. Since it is difficult to deal with path constraints in CVP method, the novel smooth technology is firstly employed to transform the complex constraints into one smooth constraint. Then, two penalty strategies are proposed to tackle the converted path and terminal constraints to decrease the computational complexity and improve the constraints satisfaction. Finally, a nonlinear programming problem, which approximates the original trajectory optimisation problem, is obtained. Error analysis shows that the proposed method has good convergence property. A general hypersonic cruise vehicle trajectory optimisation example is employed to test the performance of the proposed method. Numerical results show that the path and terminal conditions are well satisfied and better trajectory profiles are obtained, showing the effectiveness of the proposed method.

In this paper, a real-time collision-free path planning of the rust removal robot in a ship environment is proposed, which is based on an improved biologically inspired neural network algorithm. This improved algorithm is based on the biologically inspired neural network and modified with obstacle detection sensors and kinematic state templates, and is implemented in a ship rust removal robot planning system for dynamic trajectory generation. The real-time optimal trajectory is generated by the biologically inspired neural network, and the moving obstacle detection process of a ship robot working on the wall is simulated with the obstacle detection sensors models. The local real-time trajectory can be re-planned by the updated local map information, where the obstacle detection sensors are used to inspect partial environment information and update the robot nearby information in real time in the original neural network algorithm. At the same time, the method of the kinematic state templates matching and searching is used to solve the pipes’ influence of the rust removal robot climbing on the wall, which can not only provide a smooth path, but also can judge the motion direction and turning angle of the robot. Comparison of the proposed approach with the simulation shows that the improved algorithm is capable of planning a real-time collision-free path with achieving the local environmental information and judging the rust removal robot’s motion direction and turning angle. This proposed algorithm can be good used in the ship rust removal robot.

The objective of this paper is to investigate a reliable method to generate optimal ascent trajectory for hypersonic air-breathing vehicles. When solving optimal trajectories in endo-atmospheric flight, most of traditional indirect methods suffer from difficulties in finding an appropriate initial guess and getting a convergent solution for the two point boundary value problem (TPBVP). With improvements on on-board computer performance, direct methods such as pseudospectral method show promising potential for real-time optimal guidance. It removes the need for computing analytical gradients of aerodynamic coefficients, and remains high accurate solution similar to indirect methods. In this work, optimal ascent trajectory generation problem was formulated as a fuel-optimal control problem. Gauss pseudospectral method (GPM) was presented to generate the optimal ascent trajectories. Optimal solutions from GPM were compared with an indirect method based on finite difference method (FDM). Numerical simulations were studied with various initial conditions to investigate the optimal trajectory characteristics for hypersonic air-breathing vehicles. The results verified the validity and accuracy of GPM for ascent trajectory optimization.

Reinforcement learning can be modeled as markov decision process mathematically. In consequence, the interaction samples as well as the connection relation between them are two main types of information for learning. However, most of recent works on deep reinforcement learning treat samples independently either in their own episode or between episodes. In this paper, in order to utilize more sample information, we propose another learning system based on directed associative graph (DAG). The DAG is built on all trajectories in real time, which includes the whole connection relation of all samples among all episodes. Through planning with directed edges on DAG, we offer another perspective to estimate state-action pair, especially for the unknowns to deep neural network (DNN) as well as episodic memory (EM). Mixed loss function is generated by the three learning systems (DNN, EM and DAG) to improve the efficiency of the parameter update in the proposed algorithm. We show that our algorithm is significantly better than the state-of-the-art algorithm in performance and sample efficiency on testing environments. Furthermore, the convergence of our algorithm is proved in the appendix and its long-term performance as well as the effects of DAG are verified.

This article primarily focuses on the design, testing, and validation of a deep neural network (DNN)-based control scheme for predicting multi-stage trajectory optimization in autonomous ground vehicles (AGVs) used in material transportation systems. The proposed design employs a multilayer structure. In the first layer, a desensitized trajectory optimization method is iteratively applied to establish a set of time-optimal multi-stage trajectories, taking into account noise-perturbed initial configurations. Subsequently, DNNs are trained using the preplanned optimal transportation trajectory dataset to learn the functional relationship between the system’s state and control actions in the second layer. To further enhance DNN performance, a simple yet effective data aggregation approach is designed and implemented. These trained DNNs are then utilized as motion controllers to generate real-time feedback actions. Numerical experiments are conducted to showcase the effectiveness and real-time applicability of the proposed control scheme in planning the multi-stage AGV transportation process.

In this article, we focus on safe and effective completion of a rendezvous and docking task by looking at planning approaches and control with fuel-optimal rendezvous for a target spacecraft running on a near-circular reference orbit. A variety of existent practical path constraints are considered, including the constraints of field of view, impulses, and passive safety. A rendezvous approach is calculated by using a hybrid genetic algorithm with those constraints. Furthermore, a control method of trajectory tracking is adopted to overcome the external disturbances. Based on Clohessy–Wiltshire equations, we first construct the mathematical model of optimal planning approaches of multiple impulses with path constraints. Second, we introduce the principle of hybrid genetic algorithm with both stronger global searching ability and local searching ability. We additionally explain the application of this algorithm in the problem of trajectory planning. Then, we give three-impulse simulation examples to acquire an optimal rendezvous trajectory with the path constraints presented in this article. The effectiveness and applicability of the tracking control method are verified with the optimal trajectory above as control objective through the numerical simulation.