Trajectory Optimization Method Research Articles

Optimization of paddle trajectory for fin-wheel underwater robot

Purpose The purpose of this paper is to investigate the oscillating trajectory of the paddle of a fin-wheel underwater robot to enhance its propulsion efficiency in water. This robot can be used for underwater detection and military operations. Design/methodology/approach By studying the propulsion mode of underwater fin-based robots, it is found that such robots periodically generate a large reverse thrust during the swing process, resulting in low propulsion efficiency. Therefore, according to the propulsion characteristics of the oscillating paddle in the underwater environment, the hydrodynamic model and physical constraints of the oscillating paddle are established. Then, the oscillating gait trajectory of the paddle is optimized by the trajectory optimization method. The performance of the optimized trajectory was tested in the simulation environment and the actual underwater environment. Findings The prototype of the robot was built and tested in a small swimming pool. The research results confirm that the propulsion efficiency of the optimized trajectory is higher than that of the traditional trajectory under the condition of the same amplitude and period. Specifically, the maximum speed of the robot can reach 0.24 m/s when using the optimized trajectory, which is about 50% higher than that before optimization. Originality/value The optimized trajectory with the generated impulse as the optimization target is applied to the paddle oscillation, which can improve the thrust impulse generated by the fin-wheel underwater robot during underwater motion, thereby greatly improving the underwater propulsion efficiency and moving speed.

A trajectory optimization method for CAVs at intersections considering energy-efficiency balance

With the development of vehicle-to-everything (V2X) technology, connected automated vehicles (CAVs) will be an important part of urban road transportation. However, frequent acceleration, deceleration, and rapid stopping within intersections lead to increased energy consumption, reduced driving efficiency and balanced benefits. The study proposes an optimal control method for vehicle trajectories that considers energy-efficiency balance (OCM-EEB) based on the characteristics of V2X technology. The method first develops a vehicle trajectory control model based on the Intelligent Driver Model (IDM) by accounting for the features of V2X technology, and further, introduces the idea of balanced optimization, considering energy-efficiency balance, a vehicle trajectory optimal control model (OCM) is proposed. The proposed model was solved by design algorithms based on the non-dominated sorting genetic algorithm-II (NSGA-II). The experimental results showed that the vehicle trajectory optimization control method could increase the balanced driving efficiency of the vehicle within intersection, which is conducive to improving the robustness of the vehicle’s trajectory state, and then prove the effectiveness of the method proposed in this study. The method also provides an important technical basis for the vehicle trajectory optimization experiments under a real V2X environment in the future.

A train trajectory optimization method based on the safety reinforcement learning with a relaxed dynamic reward

Train trajectory optimization (TTO) is an effective way to address energy consumption in rail transit. Reinforcement learning (RL), an excellent optimization method, has been used to solve TTO problems. Although traditional RL algorithms use penalty functions to restrict the random exploration behavior of agents, they cannot fully guarantee the safety of the process and results. This paper proposes a proximal policy optimization based safety reinforcement learning framework (S-PPO) for the train trajectory optimization, including a safe action rechoosing mechanism (SARM) and a relaxed dynamic reward mechanism (RDRM) combining a relaxed sparse reward and a dynamic dense reward. SARM guarantees that the new states generated by the agent consistently adhere to the environmental security constraints, thereby enhancing sampling efficiency and facilitating algorithm convergence. RDRM makes it easier for agents to obtain successful samples by relaxing time constraints, which also offers a better balance between exploration and exploitation. The experimental results show that S-PPO can significantly improve performance and obtain better train operation trajectories than soft constraint methods, and the convergence process is smoother. Finally, it was demonstrated that S-PPO exhibits good adaptability across various speed limit tracks.

Research on real-time trajectory optimization methods for stratospheric airships based on deep learning

Research on real-time trajectory optimization methods for stratospheric airships based on deep learning

Research on the Optimal Trajectory Planning Method for the Dual-Attitude Adjustment Mechanism Based on an Improved Multi-Objective Salp Swarm Algorithm

In this study, an optimization method for the motion trajectory of attitude actuators was investigated in order to improve assembly efficiency in the automatic docking process of large components. The self-developed dual-attitude adjustment mechanism (2-PPPR) is used as the research object, and the structure is symmetrical. Based on the modified Denavit–Hartenberg (MDH) parameter description method, a kinematic model of the attitude mechanism is established, and its end trajectory is parametrically expressed using a five-order B-spline curve. Based on the constraints of the dynamics and kinematics of the dual-posture mechanism, the total posturing time, the degree of urgency of each joint, and the degree of difficulty of the mechanism’s posturing are selected as the optimization objectives. The Lévy flight and Cauchy variation algorithms are introduced into the salp swarm algorithm (SSA) to solve the parameters of the multi-objective trajectory optimization model. By combining the evaluation method of the multi-objective average optimal solution, the optimal trajectory of the dual-tuning mechanism and the motion trajectory of each joint are obtained. The simulation and experiment results show that the trajectory planning method proposed in this paper is effective and feasible and can ensure that the large-part dual-posture mechanism can complete the automatic docking task smoothly and efficiently.

Research on time-energy optimal trajectory planning of articulated heavy-duty robot

Articulated heavy-duty robots are more and more widely used in the construction environment. Aiming at the problems of low working efficiency and high energy consumption of this kind of robot, a multi-objective adaptive trajectory planning method combining path optimization and trajectory optimization is proposed to improve the working efficiency of the robot and reduce energy consumption. Firstly, based on kinematics and dynamic analysis considering friction, the energy consumption model of robot trajectory is constructed. Then, according to the posture of the key points in the known workspace, the optimal path points in the joint space are obtained by a path point solution method considering the joint load characteristics. On this basis, a multi-objective model considering running time and energy consumption is established to plan the interpolation trajectory of the joint space of the quintic B-spline curve. Finally, constrained by the velocity, acceleration and torque of the joint of the manipulator, the optimal solution is obtained by using the elite non-dominated sorting genetic algorithm (NSGA-II), and the optimal weight factor is selected by a multi-objective adaptive optimization method to obtain the optimal position-time series. The experimental results show that compared with the quintic polynomial trajectory optimization method, the energy consumption of the proposed method is reduced by 10.90% under the same working efficiency. The research results of this paper provide a new optimization idea for other target trajectory planning.

Convex Approach to Real-Time Multiphase Trajectory Optimization for Urban Air Mobility

Electric vertical takeoff and landing technology has emerged as a promising solution to alleviate ground transportation congestion. However, the limited capacity of onboard batteries enforces hard time constraints for vehicle operations in a complex urban environment. Therefore, a constrained, real-time trajectory optimization method is necessary to enable safe and energy-efficient vehicle flight. Unfortunately, most existing trajectory optimization methods suffer from low computational efficiency, unpredictable convergence processes, and strong dependence on a good initial trajectory. In this paper, we employ a successive convex programming approach to solve the multiphase minimum-energy-cost electric vertical takeoff and landing vehicle trajectory optimization problem for urban air mobility applications. The main contribution is the development and validation of two novel convexification methods that find approximate optimal solutions to the multiphase nonlinear trajectory optimization problem in real time by solving a sequence of convex subproblems. Specifically, the first method transforms the original nonlinear problem into a sequence of second-order cone programming problems through a convenient change of variables and lossless convexification, while the second approach achieves a similar goal without the need for control convexification. The resulting convex subproblems can be solved reliably in real time by advanced interior point methods. The proposed methods are demonstrated through numerical simulations of two different urban air mobility scenarios and compared with the solution obtained from GPOPS-II, a state-of-the-art general-purpose optimal control solver. Our proposed sequential convex programming methods can obtain near-optimal solutions with faster computational speed than GPOPS-II.

Improved Data-Driven Trajectory Optimization Method Utilizing Deep Trajectory Generation

The imbalance between air traffic capacity and demand, especially in the terminal maneuvering area, constrains the development of the civil aviation industry. To enhance the capacity, providing aircraft with optimal trajectories is the way forward. The key challenge of building a trajectory optimization model lies in embedding air traffic controllers’ operation experience into the optimization process. Previous efforts proposed a data-driven trajectory optimization method to learn operation experience from historical data for trajectory optimization use, which is limited by the issues of insufficient quantity and diversity of trajectory data. To solve those issues, an improved model is proposed to further improve the trajectory optimization performance. Firstly, this paper exploited a connecting-based trajectory generation model to generate massive synthetic trajectories. Then, this paper used a data-mining-based valuable trajectory identification technique to find valuable trajectories that can be used to enrich its operation experience. A case study on Guangzhou Baiyun International Airport was conducted to verify the proposed method. The results show that the proposed model successfully incorporates more operation experience during the optimization process. Compared with the benchmark model, the proposed model can adapt to more complex air traffic and provide optimal trajectories for more incoming aircraft.

Time‐energy consumption optimal path‐constrained trajectory planning of excavator robotics

AbstractReasonable operation of each excavator joint under path constraints directly affects operation efficiency and energy consumption. Efficiency and energy consumption are considerably important performance indicators, particularly for large equipment, such as excavators. Therefore, we propose a quadratic trajectory optimization method based on time–energy consumption. With the pseudo‐path velocity, acceleration, and equivalent convex jerk as constraints, the interior‐point method was used to obtain the time–energy consumption optimal trajectory of an excavator. The time and energy consumption values for different weight coefficients were obtained, and the optimal trajectory planning of the excavator was achieved. Furthermore, the simulation results of the proposed method for lifting 70 kg of materials for a weight coefficient of 0.5 were compared with the result of second‐order cone programming. Experimental results showed that using proposed method to plan the motion of each joint reasonably and effectively reduced the pseudo‐path jerk, acceleration, and velocity peaks by 40.67%, 25.03%, and 12.54%, respectively, ensuring smooth excavator movement. It also improved the working efficiency of the excavator; reduced unnecessary energy consumption; and improved the stability, efficiency, and energy saving of the autonomous operation of the excavator.

Predictive control method for mode transition process of multi-mode turbine engine based on onboard adaptive composite model

In order to achieve precise control of thrust and flow during the mode transition(MT) process of multi-mode turbine engine(MMTE) within the switching envelope and under the condition of engine performance degradation, research on multi-mode model predictive control method is conducted. A mode transition trajectory optimization method based on SQP is explored, and a small range of adjustable parameters that ensure the continuous thrust and flow is obtained. Based on this, a multi-mode onboard modeling approach based on the directional adjustment law scheduling of the variable geometry adjustment mechanism is proposed. Furthermore, an investigation into a predictive control method for MT process based on onboard adaptive composite model is conducted. The simulation results demonstrate that the proposed method exhibits a maximum thrust fluctuation of less than 0.66 % during MT process, under both normal and degraded engine component performance conditions, which is significantly superior to the conventional PID control of 2.8 %. Compared to the average single step calculation time of 7.24 ms using the SQP optimization method, the proposed approach only requires 0.204 ms. The methodology presented takes into consideration of control accuracy and computing efficiency, thereby offering promising prospects for engineering applications in MMTE MT control system design.

Fall prediction, control, and recovery of quadruped robots

When legged robots perform complex tasks in unstructured environments, falls are inevitable due to unknown external disturbances. However, current research mainly focuses on the locomotion control of legged robots without falling. This paper proposes a comprehensive decision-making and control framework to address the falling over of quadruped robots. First, a capturability-based fall prediction algorithm is derived for planar single-contact and 3D multi-contact locomotion with a predefined gait sequence. For safe fall control, a novel contact-implicit trajectory optimization method is proposed to generate both state and input trajectories and contact mode sequences. Specifically, incorporating uncertainty into the system and terrain models enables mitigating the non-smoothness of contact dynamics while improving the robustness of the resulting trajectories. Furthermore, a model-free deep reinforcement learning-based approach is presented to achieve fall recovery after the robot completes a fall. Experimental results demonstrate that the proposed fall prediction algorithm accurately predicts robot falls with up to 95% accuracy approximately 395ms in advance. Compared to classical locomotion controllers, which often struggle to maintain balance under significant pushes or terrain perturbations, the presented framework can autonomously switch to the fall controller approximately 0.06s after the perturbation, effectively preventing falls or achieving recovery with a threefold reduction in touchdown impact velocity. These findings highlight the effectiveness of the proposed framework in enhancing the stability and safety of legged robots in unstructured environments.

Single Sequential Trajectory Optimization with Centroidal Dynamics and Whole-Body Kinematics for Vertical Jump of Humanoid Robot.

High vertical jumping motion, which enables a humanoid robot to leap over obstacles, is a direct reflection of its extreme motion capabilities. This article proposes a single sequential kino-dynamic trajectory optimization method to solve the whole-body motion trajectory for high vertical jumping motion. The trajectory optimization process is decomposed into two sequential optimization parts: optimization computation of centroidal dynamics and coherent whole-body kinematics. Both optimization problems converge on the common variables (the center of mass, momentum, and foot position) using cost functions while allowing for some tolerance in the consistency of the foot position. Additionally, complementarity conditions and a pre-defined contact sequence are implemented to constrain the contact force and foot position during the launching and flight phases. The whole-body trajectory, including the launching and flight phases, can be efficiently solved by a single sequential optimization, which is an efficient solution for the vertical jumping motion. Finally, the whole-body trajectory generated by the proposed optimized method is demonstrated on a real humanoid robot platform, and a vertical jumping motion of 0.5 m in height (foot lifting distance) is achieved.

State-dependent trust region for successive convex programming for autonomous spacecraft

Spacecraft trajectory optimization is essential for all the different phases of a space mission, from its launch to end-of-life disposal. Due to the increase in the number of satellites and future space missions beyond our planet, increasing the level of autonomy of spacecraft is a key technical challenge. In this context, traditional trajectory optimization methods, like direct and indirect methods are not suited for autonomous or on-board operations due to the lack of guaranteed convergence or the high demand for computational power. Heuristic control laws represent an alternative in terms of computational power and convergence but they usually result in sub-optimal solutions. Successive convex programming (SCVX) enables to extend the application of convex optimization to non-linear optimal control problems. The definition of a good value of the trust region size plays a key role in the convergence of SCVX algorithms, and there is no systematic procedure to define it. This work presents an improved trust region based on the information given by the nonlinearities of the constraints which is unique for each optimization variable. In addition, differential algebra is adopted to automatize the transcription process required for SCVX algorithms. This new technique is first tested on a simple 2D problem as a benchmark of its performance and then applied to solve complex astrodynamics problems while providing a comparison with indirect, direct, and standard SCVX solutions.

Numerical simulation of postlaunching behaviors for a “balloon-borne UAV system”

PurposeThis paper aims to present numerical simulations for a series of flight processes for the postlaunching stage of the “balloon-borne UAV system.” It includes the balloon further ascent motion after airborne launching. In terms of unmanned aerial vehicles (UAVs), the tailspin state and the charge-out process with an anti-tailspin parachute-assisted suspending are analyzed. Then, the authors conduct trajectory optimization simulations for the long-distance gliding process.Design/methodology/approachThe balloon kinematics model and the parachute Kane multibody dynamic model are established. Using steady-state tailspin to reduced-order analysis and achieving change-out simulation by parachute suspension dynamic model. A reentry optimization control problem is developed and the Radau pseudo-spectral method is used to calculate the glide trajectory.FindingsThe established dynamic model and trajectory optimization method can effectively simulate the motion process of balloons and UAVs. The system mass reduction for launching UAVs will not cause damage to the balloon structure. The anti-tailspin parachute can reduce the UAV attack angles effectively. The UAV can glide to the designated target position by adjusting the attack angle and sideslip angle. The farthest flight distance after launching from 20 km height is 94 km and the gliding time is 40 min, which demonstrates the potential application advantage of high-altitude launching.Practical implicationsThe research content and related conclusions of this article achieve a closed-loop analysis of the flight mission chain for the “balloon-borne UAV system,” which provides simulation references for relevant balloon launching experiments.Originality/valueThis paper establishes a complete set of numerical simulation models and can effectively analyze various postlaunching behaviors.

Flight analysis and optimization design of vectored thrust eVTOL based on cooperative flight/propulsion control

The rise of electric vertical take-off and landing (eVTOL) aircraft has sparked research interest, but attention to modeling and evaluation methods, particularly for vectored thrust eVTOL, lags behind. The intricate flight/propulsion coupling and structure/control complexity contribute to the gap. Moreover, integrated modeling and evaluation processes for vectored thrust eVTOL should fully account for the tilting characteristics of the fan/propeller. This paper proposes a flight/propulsion cooperative control modeling and evaluation method for vectored thrust eVTOL. The methodology uses the Gaussian pseudospectral trajectory optimization method to obtain the overall characteristics and cooperative control strategy of flight/propulsion under strict take-off and landing trajectory constraints. Besides, this paper yielded the parameterized analysis and matching optimization design of the propulsion system. Results indicated that for an aircraft with a take-off weight of 1.8 tons, equipped with four 1.6 m diameter tilting ducted fans and a single discharge rate 5C battery, its cruising range is 135.1 km based on the selected technical parameters. The power consumption accounts for merely 12.6% of the total battery capacity during the take-off phase with high-power demand but short duration. By employing a pack of high-power-density and high-energy-density batteries to drive the ducted fans jointly, the aircraft's cruising range, fan size, and payload can be optimized. The 20C+2C battery scheme can either increase the cruising range by 27.3% without changing the fan diameter or increase the cruising range by 6.1% when the fan diameter is reduced to 1.1 m. Wherein without changing the fan diameter, the battery mass can be reduced from 720 kg to 571 kg while satisfying the takeoff and cruising requirements. The results demonstrated the effectiveness of improving the cruising range and optimizing the fan size and payload.

Correction: Chen et al. Online Trajectory Optimization Method for Large Attitude Flip Vertical Landing of the Starship-like Vehicle. Mathematics 2023, 11, 288

Additional Notes on Article [...]

Optimal time-invariant distributed formation tracking for second-order multi-agent systems

This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton’s method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies.

Trajectory optimization for automated tape placement on triangular mesh surfaces considering gap requirements

Abstract Automated tape placement (ATP) is an important automated process adopted for the fabrication of large composite components. Trajectory planning is the key link of ATP, which directly affects the precision and efficiency of the layup process, and the quality of final products. Presently, most existing trajectory optimization methods for ATP focus on smooth surfaces. Nevertheless, as commercial CAD/CAM software generally uses NURBS (Non-uniform Rational B-Splines) for modelling, the difficulty of finding the solution and the low efficiency associated with the calculation process are inevitable. The discrete methods provide alternatives for designing layup trajectories, whereas their accuracy is seldom analyzed. Furthermore, a path optimization algorithm for eliminating gap problems while preventing wrinkles on discrete models is rarely reported. In this paper, the adjustment of layup trajectories for ATP is considered on triangular meshes. Firstly, the triangular mesh is reconstructed as a Nagata patch to recover the original geometry with good accuracy. Then, a numerical method for tracing desired paths on the Nagata patch set is provided, and the computation efficiency is validated. Next, two optimization methodologies are proposed to improve the layup of composite tapes while avoiding wrinkles. Finally, the presented two strategies are examined on a discrete hyperbolic surface and a discrete freeform surface, and some of the results are delivered.

Optimizing the traversal time for gantry trajectories for proton arc therapy treatment plans

Background. Proton arc therapy (PAT) is an emerging radiation therapy technique where either the gantry or the patient continuously rotates during the irradiation treatment. One of the perceived advantages of PAT is the reduced treatment time, but it is still unclear exactly how long these treatment times will be, given that no machine capable of its delivery is available on the market at the time of writing. Objective. We introduce the algorithm arc trajectory optimization method (ATOM), which aims to determine an efficient velocity profile for the gantry for rapid delivery of a given proton arc treatment plan. This algorithm could be used to minimize the delivery time of a proton arc plan without changing the plan or updating the machine. Approach. ATOM computes the trajectory with the shortest delivery time while ensuring there is enough time to deliver all spots in each energy layer and switch energy between layers. The feasibility of the dynamic gantry movement was assured by enforcing maximum and minimum limits for velocity, acceleration, and jerk. This was achieved by discretizing the gantry velocity and combining the A* algorithm with the open-source motion generation library Ruckig. The algorithm was tested on a synthetic data set as well as a liver case, a prostate case and a head and neck case. Main results. Arc trajectories for plans with 360 energy layers were calculated in under a second using 256 discrete velocities. The delivery time of the liver case, the prostate case and the head and neck case were 284 s, 288 s and 309 s respectively, for 180 energy layers. Significance. ATOM is an open-source C++ library with a Python interface that rapidly generates velocity profiles, making it a highly efficient tool for determining proton arc delivery times, which could be integrated into the treatment planning process.

SVPTO: Safe Visibility-Guided Perception-Aware Trajectory Optimization for Aerial Tracking

In this article, we propose a safe visibility-guided perception-aware trajectory optimization method for aerial tracking, which can handle occlusion and collision in complex environments simultaneously. Different from the existing methods, the key idea of the proposed method is to actively adjust the relative distance and angle between the quadrotor and the target to avoid occlusion and collision with obstacles. Specifically, a novel field of view (FOV) based metric is proposed to avoid the occlusion of the target from obstacles. On this basis, the complexity of the environment is also introduced to adjust the relative distance between the quadrotor and the target to further reduce the probability of occlusion. Then, a critical relative angle is proposed to enhance the obstacle perception in the quadrotor motion direction. In addition, a time optimization method is proposed to improve the smoothness of quadrotor flight. Finally, comparative simulation and real-world experiments are conducted to verify the superior performance including both the visibility and safety of the proposed method.