Trajectory Optimization Method Research Articles

An Efficient Online Trajectory Generation Method Based on Kinodynamic Path Search and Trajectory Optimization for Human-Robot Interaction Safety.

With the rapid development of robot perception and planning technology, robots are gradually getting rid of fixed fences and working closely with humans in shared workspaces. The safety of human-robot coexistence has become critical. Traditional motion planning methods perform poorly in dynamic environments where obstacles motion is highly uncertain. In this paper, we propose an efficient online trajectory generation method to help manipulator autonomous planning in dynamic environments. Our approach starts with an efficient kinodynamic path search algorithm that considers the links constraints and finds a safe and feasible initial trajectory with minimal control effort and time. To increase the clearance between the trajectory and obstacles and improve the smoothness, a trajectory optimization method using the B-spline convex hull property is adopted to minimize the penalty of collision cost, smoothness, and dynamical feasibility. To avoid the collisions between the links and obstacles and the collisions of the links themselves, a constraint-relaxed links collision avoidance method is developed by solving a quadratic programming problem. Compared with the existing state-of-the-art planning method for dynamic environments and advanced trajectory optimization method, our method can generate a smoother, collision-free trajectory in less time with a higher success rate. Detailed simulation comparison experiments, as well as real-world experiments, are reported to verify the effectiveness of our method.

A Novel Resolution Scheme of Time-Energy Optimal Trajectory for Precise Acceleration Controlled Industrial Robot Using Neural Networks

The surging popularity of adopting industrial robots in smart manufacturing has led to an increasing trend in the simultaneous improvement of the energy costs and operational efficiency of motion trajectory. Motivated by this, multi-objective trajectory planning subject to kinematic and dynamic constraints at multiple levels has been considered as a promising paradigm to achieve the improvement. However, most existing model-based multi-objective optimization algorithms tend to come out with infeasible solutions, which results in non-zero initial and final acceleration. Popular commercial software toolkits applied to solve multi-objective optimization problems in actual situations are mostly based on the fussy conversion of the original objective and constraints into strict convex functions or linear functions, which could induce a failure of duality and obtain results exceeding limits. To address the problem, this paper proposes a time-energy optimization model in a phase plane based on the Riemann approximation method and a solution scheme using an iterative learning algorithm with neural networks. We present forward-substitution interpolation functions as basic functions to calculate indirect kinematic and dynamic expressions introduced in a discrete optimization model with coupled constraints. Moreover, we develop a solution scheme of the complex trajectory optimization problem based on artificial neural networks to generate candidate solutions for each iteration without any conversion into a strict convex function, until minimum optimization objectives are achieved. Experiments were carried out to verify the effectiveness of the proposed optimization solution scheme by comparing it with state-of-the-art trajectory optimization methods using Yalmip software. The proposed method was observed to improve the acceleration control performance of the solved robot trajectory by reducing accelerations exceeding values of joints 2, 3 and 5 by 3.277 rad/s2, 26.674 rad/s2, and 7.620 rad/s2, respectively.

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

For the problem of autonomous and safe landing on irregularly shaped asteroids, a real-time collision-free trajectory optimization method based on deep neural networks (DNNs) is proposed. First, in order to overcome the difficulty of solving the optimal trajectories by indirect methods caused by anti-collision path constraints and the difficulty of establishing the mapping relationship between states and initial costates by DNNs, a two-stage anti-collision trajectory optimization model is constructed, which can provide the initial costates for trajectory optimization under anti-collision constraints of each stage through the approximate analytical solution of costates. It can efficiently generate a large number of optimal trajectory samples. Second, a region division strategy is proposed for further reducing the time-consuming of DNN training. Then, the path constraints are slightly relaxed to avoid the optimal trajectories predicted by DNNs from violating the anti-collision constraints. The proposed method is applied to the scenarios of landing on asteroids 101955 Bennu and 433 Eros. The simulation results indicate that this method can estimate the initial costates efficiently and accurately, and can plan the optimal trajectories of anti-collision landing in real time.

Optimization of Geostationary Orbit Transfers via Combined Chemical–Electric Propulsion

For geostationary orbit transfers, a long duration is required using electric propulsion and a large propellant mass is needed with chemical propulsion. Hybrid transfers can achieve a balance between the fuel consumption and transfer time. In this paper, a trajectory optimization method is proposed for time-fixed minimum-fuel orbital transfer with combined chemical–electric propulsion. The necessary conditions and transversality conditions related to impulsive burns are derived theoretically with Pontryagin’s maximum principle. The long-duration geostationary orbit transfer is a many-revolution transfer, and is solved with the homotopic approach from the short-duration transfer problem. The variation in fuel consumption with transfer time is nearly linear, and the variation in the magnitude of impulsive burn is exponential. A simple model is presented for the estimation of fuel consumption and magnitude of impulsive burn with given transfer time, specific impulse of propulsion system and low-thrust magnitude.

Posture optimization in robotic machining based on comprehensive deformation index considering spindle weight and cutting force

Industrial robot has been considered to be the most promising choice to replace traditional CNC machine tool due to its low cost, high flexibility, versatility and large workspace. However, insufficient stiffness of the robot often leads to deformations and vibrations during the machining process. To improve the machining performance of robot, a posture optimization method through controlling the functional redundancy of robot is proposed. First, considering the spindle weight-induced deformation and cutting force-induced deformation simultaneously, a comprehensive deformation index is proposed to evaluate the stiffness performance of robot posture along the robot milling trajectory. Then, ideal stiffness interval at each cutter location point is calculated by minimizing the proposed deformation index in consideration of the constraints of joint and joint velocity. Next, the kinematics performance index is taken as the optimization target, and the postures of the entire milling trajectory are optimized collaboratively within the ideal stiffness intervals. In order to approximate the global optimal solution, the genetic algorithm is used to solve the optimal robot posture. Finally, a series of simulations and experiments are carried out to verify the proposed index and robot trajectory optimization method, and the results show that the machining accuracy can be efficiently improved by the proposed method.

A DNN based trajectory optimization method for intercepting non-cooperative maneuvering spacecraft

Current successes in artificial intelligence domain have revitalized interest in neural networks and demonstrated their potential in solving spacecraft trajectory optimization problems. This paper presents a data-free deep neural network (DNN) based trajectory optimization method for intercepting non-cooperative maneuvering spacecraft, in a continuous low-thrust scenario. Firstly, the problem is formulated as a standard constrained optimization problem through differential game theory and minimax principle. Secondly, a new DNN is designed to integrate interception dynamic model into the network and involve it in the process of gradient descent, which makes the network endowed with the knowledge of physical constraints and reduces the learning burden of the network. Thus, a DNN based method is proposed, which completely eliminates the demand of training datasets and improves the generalization capacity. Finally, numerical results demonstrate the feasibility and efficiency of our proposed method.

A Real-Time Trajectory Optimization Method for Hypersonic Vehicles Based on a Deep Neural Network

Considering the high-efficient trajectory planning requirements for hypersonic vehicles, this paper proposes a real-time trajectory optimization method based on a deep neural network. First, the trajectory optimization model of the hypersonic vehicle reentry phase is developed. The pseudo-spectral method is used to perform the trajectory optimization offline, and multiple optimal trajectory data are obtained. In addition, based on the inherent relationship between the state and control variables of a trajectory, a neural network is established to predict the current control outputs. The sample library of optimal trajectory data is used to train the parameters of the deep neural network to obtain an optimal neural network model. Finally, the simulation verification of the hypersonic vehicle reentry phase is performed. The simulation results show that under the condition of the initial value deviation and environmental interference, the proposed deep learning-based method can achieve a fast generation of hypersonic vehicle optimal trajectories, while achieving the advantages of high computational efficiency and reliability. Compared to traditional trajectory optimization algorithms, the proposed method has the generalization capability that satisfies the accuracy requirements and meets the demands of online real-time trajectory optimization.

Design and Implementation of Deep Neural Network-Based Control for Automatic Parking Maneuver Process.

This article focuses on the design, test, and validation of a deep neural network (DNN)-based control scheme capable of predicting optimal motion commands for autonomous ground vehicles (AGVs) during the parking maneuver process. The proposed design utilizes a multilayer structure. In the first layer, a desensitized trajectory optimization method is iteratively performed to establish a set of time-optimal parking trajectories with the consideration of noise-perturbed initial configurations. Subsequently, by using the preplanned optimal parking trajectory data set, several DNNs are trained in order to learn the functional relationship between the system state-control actions in the second layer. To obtain further improvements regarding the DNN performances, a simple yet effective data aggregation approach is designed and applied. These trained DNNs are then utilized as the motion controllers to generate feedback actions in real time. Numerical results were executed to demonstrate the effectiveness and the real-time applicability of using the proposed control scheme to plan and steer the AGV parking maneuver. Experimental results were also provided to justify the algorithm performance in real-world implementations.

HD Camera-Equipped UAV Trajectory Planning for Gantry Crane Inspection

While Unmanned Aerial Vehicles (UAVs) can be a valuable solution for the damage inspection of port machinery infrastructures, their trajectories are still prone to collision risks, trajectory non-smoothness, and large deviations. This research introduces a trajectory optimization method for inspecting vulnerable parts of a gantry crane by a UAV fitted with a high-definition (HD) camera. We first analyze the vulnerable parts of a gantry crane, then use the A* algorithm to plan a path for the UAV. The trajectory optimization process is divided into two steps, the first is a trajectory correction method and the second is an objective function that applies a minimum snap method while taking into consideration flight corridor constraints. The experimental simulation results show that, compared with previous methods, our approach can not only generate a collision-free and smooth trajectory but also shorten the trajectory length significantly while substantially reducing the maximum deviation average deviation distances. The simulation results show that this modelling approach provides a valuable solution for UAV trajectory planning for gantry crane inspection.

Projection-operator-based Newton method for the trajectory optimization of closed quantum systems

Quantum optimal control is an important technology that enables fast state preparation and gate design. In the absence of an analytic solution, most quantum optimal control methods rely on an iterative scheme to update the solution estimate. At present, the convergence rate of existing solvers is at most superlinear. This paper develops a new general purpose solver for quantum optimal control based on the PRojection Operator Newton method for Trajectory Optimization, or PRONTO. Specifically, the proposed approach uses a projection operator to incorporate the Schr\"odinger equation directly into the cost function, which is then minimized using a quasi-Newton method. At each iteration, the descent direction is obtained by computing the analytic solution to a Linear-Quadratic trajectory optimization problem. The resulting method guarantees monotonic convergence at every iteration and quadratic convergence in proximity of the solution. To highlight the potential of PRONTO, we present an numerical example that employs it to solve the optimal state-to-state mapping problem for a qubit and compares its performance to a state-of-the-art quadratic optimal control method.

A Novel Method of Trajectory Optimization for Underwater Gliders Based on Dynamic Identification

For underwater gliders (UGs), high trajectory accuracy is an important factor in improving the observation of ocean phenomena. In this paper, a novel method of trajectory optimization is proposed to increase the trajectory accuracy of UGs, which is approximately based on the nonlinear dynamic model, rather than the linearization model. Firstly, a dynamic model of UGs is established to analyze the effect of the input parameters on the trajectory error, based on some approximate models that replaced the dynamic model due to its strong nonlinearity. Then, an identification strategy for the trajectory error is proposed, and the trajectory optimization strategy is analyzed while considering gliding range loss and observation distance loss. Finally, the identification strategy and trajectory optimization strategy proposed in this paper are verified by a sea trial of Petrel-L. The dynamic model, identification strategy, and optimization strategy are appropriate for other UGs.

Multi-objective Trajectory Planning Method based on the Improved Elitist Non-dominated Sorting Genetic Algorithm

Robot manipulators perform a point-point task under kinematic and dynamic constraints. Due to multi-degree-of-freedom coupling characteristics, it is difficult to find a better desired trajectory. In this paper, a multi-objective trajectory planning approach based on an improved elitist non-dominated sorting genetic algorithm (INSGA-II) is proposed. Trajectory function is planned with a new composite polynomial that by combining of quintic polynomials with cubic Bezier curves. Then, an INSGA-II, by introducing three genetic operators: ranking group selection (RGS), direction-based crossover (DBX) and adaptive precision-controllable mutation (APCM), is developed to optimize travelling time and torque fluctuation. Inverted generational distance, hypervolume and optimizer overhead are selected to evaluate the convergence, diversity and computational effort of algorithms. The optimal solution is determined via fuzzy comprehensive evaluation to obtain the optimal trajectory. Taking a serial-parallel hybrid manipulator as instance, the velocity and acceleration profiles obtained using this composite polynomial are compared with those obtained using a quintic B-spline method. The effectiveness and practicability of the proposed method are verified by simulation results. This research proposes a trajectory optimization method which can offer a better solution with efficiency and stability for a point-to-point task of robot manipulators.

Trajectory optimisation with musculoskeletal integration features for fracture reduction orthopaedic robot.

Human body is an integrated system of bones and muscles. To date, there are insufficient studies on the effect of muscles on the trajectory planning of orthopaedic robot. To this end, based on a Stewart-Gough platform (6-UPU) fracture reduction orthopaedic robot, a musculoskeletal trajectory optimisation method was constructed for the interference of soft tissue during the reduction process. Firstly, pose description of the fracture reduction orthopaedic robot was introduced, and its working space was analysed. Secondly, an improved Hill muscle theory was used to construct the musculoskeletal system, and finite element analysis (FEA) was carried out. Thirdly, particle swarm optimisation (PSO) with variable weights was imported, and fracture reduction trajectory planning was obtained by quintic polynomial in the workspace. Then mathematical model for trajectory optimisation was presented, and targets of musculoskeletal optimisation were extracted, which include muscle energy consumption, robot-assisted repositioning time and trajectory length. In this sense, musculoskeletal integration trajectory optimisation method was put forward. Finally, comparative optimisation simulation with skeleton only and bone and muscle together were tested, and safety experiment with musculoskeletal integration was conducted. A cone shape workspace was got, whose range can be defined as 635.14mm on the X axis, 720mm on the Y axis, and 240mm on the Z axis, respectively. Besides, different FEA displacements revealed the effect of bone and muscle on the movement of the robot. Moreover, the optimal results with and without muscle had showed different movement time: the former consumed about 27s, but the latter spent about 25s. Additionally, the speed and acceleration of the drive rods can be obtained from zero to zero during the reset. The results show that the optimised trajectory obtained with this method is safe and reliable. Furthermore, the presence of muscle has great influence on the trajectory of robot, which could prolong the reduction time so as to prevent the occurrence of uneven soft and hard traction rate problem. This paper could be helpful for the future trajectory planning study of fracture reduction orthopaedic robot.

Robust optimization of control command for aerospace vehicles with aerodynamic uncertainty

To reduce the design burden of Aerospace Vehicles (ASVs) control systems, this paper proposes a multi-constrained robust trajectory optimization method, which provides a good front-end input for the control system. Differ from the conventional aircraft, some control performance of ASVs is not only related to the model parameters, but also affected by the flight status. Therefore, the robust optimization method combines this characteristic of ASVs, sets the control performance as one of the optimization objectives, and considers the influence of parameter uncertainty. In this method, the polynomial chaos expansion algorithm is used to transform the trajectory optimization problem with uncertain parameters into the equivalent deterministic robust trajectory optimization problem. Finally, compared with traditional deterministic trajectory optimization methods to illustrate the effectiveness of proposed control optimization method.

Onboard optimization of multi-arc trajectories with constraints on duration of arcs

Autonomous operation of rocket-powered vehicles is a promising technique that could significantly improve the adaptiveness of rocket-powered vehicles. However, to remedy in-flight engine failures and allow mission changes, the autonomous operation requires an onboard method to optimize the powered trajectories. While onboard methods to optimize the powered trajectories have been proposed before, none of them considered the constraints on duration of arcs in multi-arc trajectory optimization problems. The constraints on the duration of burn arcs and coast arcs often arise from the safe operating conditions of rocket engines, and violating these constraints will likely result in physically-infeasible trajectories. Determining the optimal duration of each arc while satisfying the constraints is a challenging problem for onboard trajectory optimization methods. In this paper, an onboard method to optimize multi-arc trajectories is proposed that is capable of enforcing the constraints on the duration of burn arcs and coast arcs. The proposed method employs a hybrid regularization approach to facilitate the convergence of the duration of arcs. Quadratic penalty terms and fixed-radius trust-region terms are simultaneously used to limit the change of duration of arcs between iterations. The two terms complement each other, contributing to the efficiency of the hybrid regularization approach. Moreover, we propose an optimality-based stopping criterion that certifies the optimality of optimized duration of arcs and helps reduce unnecessary iterations. Numerical results on an onboard computational platform are provided to validate the efficiency of the proposed method.

Multiobjective Optimization and Weight Selection Method for Heavy Haul Trains Trajectory

Energy-saving, punctuality and smoothness are difficult to achieve in the operation of heavy haul train. This paper proposes a multi-objective method for speed curve optimization. Firstly, a quadratic programming optimization model is established, using train kinetic energy and train force as independent variables and several goals of energy conservation, smoothness, and target speed tracking. Under the supplied weight vector, the model can realize the ideal speed curve under unbounded time. Secondly, in order to address the demand for punctuality, this paper develops a weight selection algorithm to optimal weight vector for any given trip time. Finally, a time-bounded multi-objective speed curve optimization model is proposed, which achieves energy conservation, punctuality and smoothness train operation. The simulation indicates that the proposed algorithm outperforms human driving in multi-objectives. And the designed time bounded weight selection algorithm is more efficient than the conventional linear approaching weight search method.

Research on Trajectory Optimization of Upper Limb Rehabilitation Robot

For the current wide application of robots in the field of rehabilitation, in order to improve the auxiliary rehabilitation effect of upper limb movement disorder patients in the rehabilitation period and enhance the security of patients during use, this paper proposes a method for trajectory planning and optimization of upper limb rehabilitation robot, which can achieve good and safe auxiliary rehabilitation effect by modifying the tangent offset parameters. In order to solve the problem of redundant inflection points and poor smoothness of traditional A Star Algorithm, a hierarchical progressive algorithm optimization strategy is proposed, such as collision detection algorithm and dynamic tangent smoothing algorithm with variable tangent points. By using this strategy, the technical problems such as the judgment and deletion of redundant inflection points and the excessive corner of poor convergence of planned path are solved. The accuracy of optimal path judgment is significantly improved, and the safety performance and auxiliary rehabilitation effect of upper limb rehabilitation machine are significantly improved. In this paper, the kinematics modeling of upper limb rehabilitation robot is carried out by MATLAB, and the trajectory simulation of the robot is carried out, and a trajectory optimization scheme based on A Star Algorithm is proposed. The generated path conforms to the trajectory of the rehabilitation operation, and can effectively assist the rehabilitation movement, which provides a basis for kinematics.

Hybrid trajectory optimization method for service logistics robots

The paper discusses topical problems of increasing the efficiency of logistics operations and the functioning of logistics robots, speed, movement accuracy, optimization of the trajectories of logistics robots. The considered criterion of the optimal trajectory in the working area of logistic robots when avoiding an obstacle ensures the minimum working cycle time of the robot. The aim of the work is to develop methods for optimizing the modes of movement of logistics robots in automated logistics systems. The paper presents a new hybrid method for optimizing the trajectory of movement of logistics robots in automated logistics systems. The method improves the speed and positioning accuracy of logistic robots. The developed method of trajectory optimization can be used to increase the speed and optimize the movement of various logistics robots.

Trajectory optimization method of variable pitch spiral matrix for intermediate frequency error

Trajectory optimization method of variable pitch spiral matrix for intermediate frequency error

OGI-SLAM2: A Hybrid Map SLAM Framework Grounded in Inertial-Based SLAM

Indoor localization using mobile sensors has gained momentum lately. However, indoor pedestrian localization with low-cost IMU has not been practically applied, and the main challenge is that it is difficult for low-cost IMU to obtain high-precision localization performance over a long period of time. In this paper, we propose a multi-source fusion indoor pedestrian autonomous localization framework combining landmark maps and occupancy grid maps. Combining the ideas of optimization and occupancy grid map-based inertial SLAM algorithm(OGI-SLAM), we maintain the short- and medium-term localization accuracy with OGI-SLAM, and achieve long-term localization accuracy improvement with keypoint maps. Without prior knowledge of the map, we use user motion features and environmental features to extract keypoints in the trajectory and construct keypoint descriptors. Combining the uncertainty of system location and the similarity of environmental features, we propose a keypoint extraction and association method to solve the problem of inaccurate particle filtering loop closing with low-cost IMU. In addition, a two-step trajectory optimization method is proposed, which uses bundle adjustment to correct the positioning error of keypoints and models the error correction of common points between keypoints as affine transformation, avoiding the large matrix inversion operation in the optimization process. Simulations and field trial evaluations show that the system is able to achieve a maximum positioning accuracy of 1.64 meters with low-performance IMU on board, representing a 57% maximum improvement in positioning accuracy compared to OGI-SLAM. This highlights the promise of OGI-SLAM2 as an unconventional indoor positioning method.