Trajectory Optimization Method Research Articles

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.

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.

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.

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

AbstractSpacecraft 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.

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.

Optimization of multi-target continuous dynamic trajectory for unmanned aerial vehicles

In the problem of trajectory optimization for unmanned aerial vehicles (UAVs) passing through multiple target points, continuous velocity and acceleration in the process of optimization are essential for maintaining a feasible trajectory. This paper proposes a multi-segment holistic Bezier shaping method (MHBSM) for dynamic trajectory optimization. The MHBSM not only achieves holistic optimization of UAVs passing through a multi-target trajectory but also ensures high-order continuity at the junctions of trajectory segments. Unlike methods that generate non-dynamic trajectories by connecting arcs and straight lines (such as Dubins curves) without considering speed changes, MHBSM optimizes the trajectory while taking into account the dynamics of UAVs. The method optimizes the differential flat output space of a fixed-wing UAV dynamic model and transforms the dynamic optimization problem into a three-dimensional position optimization problem. The problem is then further transformed into an optimization of control points using the Bezier curve. The resulting trajectory satisfies the dynamic constraints. In comparison to the Gaussian pseudospectral method (GPM), MHBSM achieves similar optimization results with only a 2.58% difference, while requiring approximately 1.36% of the computational time on average. The MHBSM demonstrates excellent convergence performance while satisfying the constraints of continuous acceleration and obstacle avoidance.

Design and Practical Implementation of a High Efficiency Two-Layer Trajectory Planning Method for AGV

This paper proposes a two-layer trajectory optimization method for the autonomous ground vehicle (AGV). This twolayer strategy includes an efficient path planning layer and a fast trajectory planning layer. In the first layer, a novel target area adaptive rapidly exploring random tree algorithm (TAA-RRT*) is proposed to search the shortest path. This layer mainly includes a preprocessing and a sampling planning process. In the preprocessing process, the generalized voronoi diagram (GVD) is used to construct the environment information and find the initial path. Then, the sampled target area (TA) is constructed based on this initial path to provide non-uniform sampling. In the sampling planning process, the improved adaptive RRT* algorithm is used to carry out sampling planning in the TA, and the direct connection strategy (DCS) is combined to quickly locate the optimal solution. In the trajectory planning layer, combined with the constraints of the unmanned vehicle and the path constraints obtained in the first layer, the speed planning and the trajectory optimization are addressed by solving the optimal control problem (OCP). After performing a large number of experiments, the feasibility and effectiveness of the proposed method is verified.

DTC: Deep Tracking Control.

Legged locomotion is a complex control problem that requires both accuracy and robustness to cope with real-world challenges. Legged systems have traditionally been controlled using trajectory optimization with inverse dynamics. Such hierarchical model-based methods are appealing because of intuitive cost function tuning, accurate planning, generalization, and, most importantly, the insightful understanding gained from more than one decade of extensive research. However, model mismatch and violation of assumptions are common sources of faulty operation. Simulation-based reinforcement learning, on the other hand, results in locomotion policies with unprecedented robustness and recovery skills. Yet, all learning algorithms struggle with sparse rewards emerging from environments where valid footholds are rare, such as gaps or stepping stones. In this work, we propose a hybrid control architecture that combines the advantages of both worlds to simultaneously achieve greater robustness, foot-placement accuracy, and terrain generalization. Our approach uses a model-based planner to roll out a reference motion during training. A deep neural network policy is trained in simulation, aiming to track the optimized footholds. We evaluated the accuracy of our locomotion pipeline on sparse terrains, where pure data-driven methods are prone to fail. Furthermore, we demonstrate superior robustness in the presence of slippery or deformable ground when compared with model-based counterparts. Last, we show that our proposed tracking controller generalizes across different trajectory optimization methods not seen during training. In conclusion, our work unites the predictive capabilities and optimality guarantees of online planning with the inherent robustness attributed to offline learning.

Hypersonic vehicle terminal velocity improvement considering ramjet safety boundary constraint

The air-breathing ramjet is an essential power plant to improve the terminal velocity of hypersonic vehicles. The high-performance requirement of ramjet makes it operate close to the safety boundary, and the optimization of the terminal velocity of vehicle is faced with challenges. An integrated flight/ propulsion model considering thrust and safety performance is constructed, and the trajectory optimization method for the whole flight phase operating process of hypersonic vehicles with multiple performance optimization indicators and complex safety constraints is studied. Moreover, the trajectory optimization results of the whole flight phase for CAV-H and X-43A (powered/unpowered) plans are compared and analyzed, and the dive-acceleration-climb strategy can improve the maneuverability of the vehicle in the ramjet operating phase. Furthermore, the terminal flight velocity of the vehicle in the powered plan is increased from 363.60 m/s to 943.57 m/s under the effect of ramjet. In addition, the trajectory optimization results of vehicle with different geometrical configurations of the ramjet are compared under safety constraints. The results show that the variable geometry ramjet enables the vehicle to increase its terminal velocity by up to 9.73 % with respect to the fixed geometry engine. Hypersonic vehicle terminal velocity is effectively improved by considering ramjet variable geometry adjustment.

Rapid ascent trajectory optimization of rocket-based combined cycle hypersonic vehicle

The ascent trajectory design of a rocket-based combined cycle (RBCC) hypersonic vehicle has many typical characteristics, including the complex working mode of the RBCC power system, strong coupling between thrust and flight state, strong nonlinear model and many complex constraints etc. This paper proposes a rapid trajectory optimization method based on sequential convex optimization to optimize the complex ascent trajectory with the RBCC power system. Firstly, a mathematical model for optimizing the ascent trajectory of the RBCC hypersonic vehicle is established to describe the angle of attack control system with and without the second-order lag. Then, the optimization model is made convex and discretized based on the convex optimization theory, and a trajectory optimization strategy is improved. Finally, taking the maximum terminal mechanical energy as optimization objective, the ascent trajectory optimization is simulated in cases with and without the second-order lag in the angle of attack control system. The simulation results show that the proposed mathematical model and the ascent trajectory optimization method are rapid and reliable and that the optimization results meet the characteristics of the RBCC power system and provide reference for the application of a RBCC power system and the design of an angle of attack control system.

On the Performance of Different Smoothing Methods for Indirect Low-Thrust Trajectory Optimization

On the Performance of Different Smoothing Methods for Indirect Low-Thrust Trajectory Optimization

Runtime optimization of acquisition trajectories for x-ray computed tomography with a robotic sample holder

Tomographic imaging systems are expected to work with a wide range of samples that house complex structures and challenging material compositions, which can influence image quality in a bad way. Complex samples increase total measurement duration and may introduce beam-hardening artifacts that lead to poor reconstruction image quality. This work presents an online trajectory optimization method for an x-ray computed tomography system with a robotic sample holder. The proposed method reduces measurement time and increases reconstruction image quality by generating an optimized spherical trajectory for the given sample without prior knowledge. The trajectory is generated successively at runtime based on intermediate sample measurements. We present experimental results with the robotic sample holder where two sample measurements using an optimized spherical trajectory achieve improved reconstruction quality compared to a conventional spherical trajectory. Our results demonstrate the ability of our system to increase reconstruction image quality and avoid artifacts at runtime when no prior information about the sample is provided.

A coordinated optimization method of energy management and trajectory optimization for hybrid electric UAVs with PV/Fuel Cell/Battery

There are complex coupling relationships between flight motion and energy management for hybrid electric fixed wing UAVs with photovoltaic/fuel cell/battery. Aiming at realizing high-energy-efficiency long endurance autonomous flight, this paper proposes a coordinated optimization method of trajectory optimization and energy management for hybrid electric UAVs. Numerical simulation and experiment are carried out. Separated by surplus demand energy except that produced by PV, this method includes an optimal energy flight trajectory optimization layer and an energy management layer. For the former, fuzzy neural network sequential convex optimization (FNNSCP) is proposed to handle the flight trajectory optimization problem for maximizing utilization solar energy. For the latter, an online energy management strategy based on convex quadratic programming MPC (CQPMPC) is proposed to realize the power allocation. Numerical simulation results show that FNNSCP reduced 2% energy requirement compared with Radau pseudo-spectral method (RPM) from flight trajectory optimization level. From energy management level, CQPMPC saves hydrogen consumption by 3.1% and 16.3% compared with nonlinear model predictive control (NMPC) and fuzzy logic state machine (FLSM), respectively. In the experiment, less hydrogen fuel is consumed by proposed method by 5.2% and 15.6% compared with NMPC and FLSM, respectively. Experimental results show that the proposed method has better energy-saving performance and excellent real time performance. It indicates that optimizing flight trajectory and improving energy management efficiency can realize the high-energy-efficiency flight of hybrid electric UAVs. This method is conducive to promoting the application of hydrogen energy in the field of UAVs.

Trajectory optimization for collaborative recovery of parafoil systems using unmanned vessel

Traditional trajectory optimization methods for the parafoil system set fixed-point landing as the objective. However, in recent payload fairing recovery missions, the recovery system comprising two parafoils is collaboratively recovered by a mobile vehicle, posing new challenges to the current trajectory optimization technique. In order to recover two parafoil systems autonomously with an unmanned surface vessel, this paper presents a trajectory optimization framework composed of three following component processes consecutively. Firstly, a feasibility judgment algorithm based on reachable boundary estimation is designed to determine the possibility of recovering two parafoil systems. Secondly, the decoupled-then-simultaneous strategy is proposed to enhance the convergence of solving the collaborative recovery problem. Thirdly, the finite-element collocation approach is utilized to convert the formulated trajectory optimization problems into nonlinear programming (NLP) problems, which are solved by a highly efficient NLP solver. Simulation results show that the proposed trajectory optimization framework can efficiently generate the optimal trajectory for recovering two parafoil systems with a vessel.

Multi-objective Velocity Trajectory Optimization Method for Autonomous Mining Vehicles

Multi-objective Velocity Trajectory Optimization Method for Autonomous Mining Vehicles