Optimal Trajectory Planning Research Articles

Corrections to “Optimal Trajectory Planning of Connected and Automated Vehicles at On-Ramp Merging Area” [early access DOI:10.1109/TITS.2021.3116666

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Optimal Trajectory Planning of Connected and Automated Vehicles at On-Ramp Merging Area

Cooperative Adaptive Cruise Control (CACC) systems can significantly improve traffic safety and roadway capacity utilizing short following gaps of vehicles enabled by inter-vehicle communications. However, due to merging processes occurring at freeway merging areas, existing CACC operation approaches are generally not applicable and the operation will have to revert back to Adaptive Cruise Control (ACC) or human-driven mode, which in turn will result in a capacity drop. This paper proposes an optimal trajectory optimization strategy for Connected and Automated Vehicles (CAVs) to cooperatively carry out mainline platooning and on-ramp merging. Firstly, a control framework of the CACC is adopted for a longitudinal control of CAVs, which helps individual CAVs to join platoons and to maintain platoon operations. Secondly, to ensure smooth lane-changing executions while achieving stable platoons, an optimal controller that considers lane-changing motivation of merging vehicles and impact of merging on platoons, is proposed. Third, a Legendre pseudo-spectral algorithm is applied to transform the controller into a simpler nonlinear programming problem and to efficiently solve it. Simulation assessments of the proposed method are conducted at both individual vehicle level and traffic-flow level. At the individual vehicle level, the proposed method has the potential to improve the traffic safety without compromising fuel consumption and emissions compared with unoptimized feasible schemes. At a traffic-flow level, an online evaluation platform is implemented, and a typical freeway on-ramp area is studied. The simulation results have demonstrated that the proposed controller provides significant improvements in terms of efficiencies in traffic operations.

A Fast and Close-to-Optimal Receding Horizon Control for Trajectory Generation in Dynamic Environments

This paper presents a new approach for the optimal trajectory planning of nonlinear systems in a dynamic environment. Given the start and end goals with an objective function, the problem is to find an optimal trajectory from start to end that minimizes the objective while taking into account the changes in the environment. One of the main challenges here is that the optimal control sequence needs to be computed in a limited amount of time and needs to be adapted on-the-fly. The control method presented in this work has two stages: the first-order gradient algorithm is used at the beginning to compute an initial guess of the control sequence that satisfies the constraints but is not yet optimal; then, sequential action control is used to optimize only the portion of the control sequence that will be applied on the system in the next iteration. This helps to reduce the computational effort while still being optimal with regard to the objective; thus, the proposed approach is more applicable for online computation as well as dealing with dynamic environments. We also show that under mild conditions, the proposed controller is asymptotically stable. Different simulated results demonstrate the capability of the controller in terms of solving various tracking problems for different systems under the existence of dynamic obstacles. The proposed method is also compared to the related indirect optimal control approach and sequential action control in terms of cost and computation time to evaluate the improvement of the proposed method.

Fast trajectory planning and control of a lab-scale 3D gantry crane for a moving target in an environment with obstacles

In this work, the real-time optimal trajectory planning, together with a cascaded tracking controller, is presented for a three-dimensional (3D) gantry crane in an environment with static obstacles and a dynamically moving target considering dynamic constraints and control input limits. State-of-the-art trajectory optimization-based approaches require long computation times and cannot quickly respond to changes in the target state. The focus of this paper lies on a novel trajectory planning algorithm, which consists of two steps. First, an offline trajectory planner is implemented to compute a time-optimal, collision-free, and dynamically feasible trajectory database that connects all possible initial states of the gantry crane from a predefined starting subspace to the target states in a target subspace. Second, based on linear constrained quadratic programming, the online trajectory replanner makes use of this trajectory database to generate an optimal trajectory in real time that accounts for all changes in the target state. Additionally, a trajectory tracking controller is developed to take into account the dynamic constraints of the gantry crane and to compensate for possible model inaccuracies, disturbances, and other non-modeled effects. Both simulation and experimental results are presented to demonstrate the performance of the proposed trajectory (re)planning algorithm and the control concept.

Multi-objective optimal trajectory planning of customized industrial robot based on reliable dynamic identification for improving control accuracy

PurposeThe purpose of this paper is to enhance control accuracy, energy efficiency and productivity of customized industrial robots by the proposed multi-objective trajectory optimization approach. To obtain accurate dynamic matching torques of the robot joints with optimal motion, an improved dynamic model built by a novel parameter identification method has been proposed.Design/methodology/approachThis paper proposes a novel multi-objective optimal approach to minimize the time and energy consumption of robot trajectory. First, the authors develop a reliable dynamic parameters identification method to obtain joint torques for formulating the normalized energy optimization function and dynamic constraints. Then, optimal trajectory variables are solved by converting the objective function into relaxation constraints based on second-order cone programming and Runge–Kutta discrete method to reduce the solving complexity.FindingsExtensive experiments via simulation and in real customized robots are conducted. The results of this paper illustrate that the accuracy of joint torque predicted by the proposed model increases by 28.79% to 79.05% over the simplified models used in existing optimization studies. Meanwhile, under the same solving efficiency, the proposed optimization trajectory consumes a shorter time and less energy compared with the existing optimization ones and the polynomial trajectory.Originality/valueA novel time-energy consumption optimal trajectory planning method based on dynamic identification is proposed. Most existing optimization methods neglect the effect of dynamic model reliability on energy efficiency optimization. A novel parameter identification approach and a complete dynamic torque model are proposed. Experimental results of dynamic matching torques verify that the control accuracy of optimal robot motion can be significantly improved by the proposed model.

Stability-constrained mobile manipulation planning on rough terrain

AbstractThis paper presents a hierarchical framework that allows online point-to-point dynamic-stability-constrained optimal trajectory planning of a mobile manipulator robot working on rough terrain. First, the kinematics model of a mobile manipulator robot and the zero moment point stability measure are presented as theoretical background. Then, a sampling-based quasi-static planning algorithm modified for stability guarantee and traction optimization in continuous dynamic motion is presented along with a mathematical proof. The robot’s quasi-static path is then used as an initial guess to warm start a nonlinear optimal control solver which may otherwise have difficulties finding a solution to the stability-constrained formulation efficiently. The performance and computational efficiency of the framework are demonstrated through an application to a simulated timber harvesting mobile manipulator machine working on varying terrain. The results demonstrate feasibility of online trajectory planning on varying terrain while satisfying the dynamic stability constraint. Qualitative and quantitative comparisons with existing methods are also presented.

Trajectory planning and control of multiple mobile robot using hybrid MKH-fuzzy logic controller

AbstractRobotics with artificial intelligence techniques have been the center of attraction among researchers as it is well equipped in the area of human intervention. Here, the krill herd (KH) optimization algorithm is modified and hybridized with a fuzzy logic controller to frame an intelligent controller for optimal trajectory planning and control of mobile robots in obscure environments. The controller is demonstrated for single and multiple robot’s trajectory planning. A Petri-net controller has also been added to avoid conflict situations in multi-robot navigation. MATLAB and V-REP software are used to simulate the work, backed with real-time experiments under laboratory conditions. The robots efficiently achieved the goals by tracing an optimal path without any collision. Trajectory length and time spent during navigation are recorded, and a good agreement between the results is observed. The proposed technique is compared against existing research techniques, and an improvement of 14.26% is noted in terms of path length.

Time-Jerk optimal Trajectory Planning of Industrial Robots Based on a Hybrid WOA-GA Algorithm

An optimal and smooth trajectory for industrial robots has a positive impact on reducing the execution time in an operation and the vibration in their joints. In this paper, a methodology for the time-optimal and jerk-continuous trajectory planning of industrial robots is proposed. The entire trajectory is interpolated in the joint space utilizing fifth-order B-splines and then optimized by a hybrid whale optimization algorithm and genetic algorithm (WOA-GA). Two objective functions, including the integral of the squared jerk along the entire trajectory and the total execution time, are minimized to obtain the optimal entire trajectory. A fifth-order B-spline interpolation technique enables the achievement of a jerk-continuous trajectory, while respecting the kinematic limits of jerk, acceleration and velocity. WOA-GA is utilized to solve the time-jerk optimal trajectory planning problem with nonlinear constraints. The proposed hybrid optimization algorithm yielded good results and achieved the time-jerk optimal trajectory better under kinematic constraints compared to the genetic algorithm, whale optimization algorithm, improved whale optimization algorithm with particle swarm optimization and adaptive cuckoo search algorithm. The numerical results show the competent performances of the proposed methodology to generate trajectories with high smooth curves and short total execution time.

Optimal trajectory planning strategy for underactuated overhead crane with pendulum-sloshing dynamics and full-state constraints

Optimal trajectory planning strategy for underactuated overhead crane with pendulum-sloshing dynamics and full-state constraints

Deep Reinforcement Learning Based Trajectory Planning Under Uncertain Constraints.

With the advance in algorithms, deep reinforcement learning (DRL) offers solutions to trajectory planning under uncertain environments. Different from traditional trajectory planning which requires lots of effort to tackle complicated high-dimensional problems, the recently proposed DRL enables the robot manipulator to autonomously learn and discover optimal trajectory planning by interacting with the environment. In this article, we present state-of-the-art DRL-based collision-avoidance trajectory planning for uncertain environments such as a safe human coexistent environment. Since the robot manipulator operates in high dimensional continuous state-action spaces, model-free, policy gradient-based soft actor-critic (SAC), and deep deterministic policy gradient (DDPG) framework are adapted to our scenario for comparison. In order to assess our proposal, we simulate a 7-DOF Panda (Franka Emika) robot manipulator in the PyBullet physics engine and then evaluate its trajectory planning with reward, loss, safe rate, and accuracy. Finally, our final report shows the effectiveness of state-of-the-art DRL algorithms for trajectory planning under uncertain environments with zero collision after 5,000 episodes of training.

Mobile Robot Path Planning Optimization Based on Integration of Firefly Algorithm and Cubic Polynomial Equation

Mobile Robot is an extremely essential technology in the industrial world. Optimal path planning is essential for the navigation of mobile robots. The firefly algorithm is a very promising tool of Swarm Intelligence, which is used in various optimization areas. This study used the firefly algorithm to solve the mobile robot path-planning problem and achieve optimal trajectory planning. The objective of the proposed method is to find the free-collision-free points in the mobile robot environment and then generate the optimal path based on the firefly algorithm. It uses the A∗ algorithm to find the shortest path. The essential function of use the firefly algorithm is applied to specify the optimal control points for the corresponding shortest smooth trajectory of the mobile robot. Cubic Polynomial equation is applied to generate a smooth path from the initial point to the goal point during a specified period. The results of computer simulation demonstrate the efficiency of the firefly algorithm in generating optimal trajectory of mobile robot in a variable degree of mobile robot environment complexity.

Time-optimal trajectory generation in joint space for 6R industrial serial robots using Cuckoo search algorithm

The trajectory planning problem in industrial robotic applications has recently attracted the great attention of many researchers. In this paper, an optimal trajectory planning approach is proposed based on optimal time by utilizing the interpolation spline method. The method including a combination of cubic spline and 7th order polynomial is used for generating the trajectory in joint space for robot manipulators. Cuckoo Search (CS) optimization algorithm is chosen to optimize the joint trajectories based on objective, including minimizing total traveling time along the whole trajectory. The spline method has been applied to the PUMA robot for optimizing the joint trajectories with the CS algorithm based on the objective. With the trajectory planning method, the joint velocities, accelerations, and jerks along the whole trajectory optimized by CS meet the requirements of the kinematic constraints in the case of the objective. Simulation results validated that the used trajectory planning method based on the proposed algorithm is very effective in comparison with the same methods based on the algorithms proposed by earlier authors. Keywords: CS; industrial robots; interpolation; spline methods; trajectory planning.

Q-Free Walk Ant Hybrid Architecture for Mobile Robot Path Planning in Dynamic Environment

This work provides a novel hybrid system for the trajectory planning of an autonomous mobile robot named Q-Free Walk Ant Hybrid Architecture (Q-FWAHA). The proposed approach combines two layers: a deliberative layer (global planning) and a reactive one (local planning), it is adapted to partially unknown environments (dynamic). It includes both reactive planning methods based on the Perception &amp; Action principle (Sense &amp; Act) and deliberative methods based on the Perception-Planning &amp; Action principle (Sense-Plan &amp; Act). The deliberative layer consists of a global planning algorithm and a model (a map) based on current knowledge of the environment. It is based on a method inspired by nature called Ant Colony Optimization (ACO) for optimal trajectory planning in known environments. The next layer is the reactive layer, it allows the robot to avoid collisions with dynamic obstacles by directly using sensory data. The reactive planning method used is a reinforcement learning approach for planning in dynamic environments; The Q-learning method. The deliberative layer is compared alone with an existing system for path planning, results show that the final path produced by our system is more efficient in terms of safety and energy saving. Simulations and experimental results to validate the proposed hybrid system are presented.

Multi-objective excavation trajectory optimization for unmanned electric shovels based on pseudospectral method

With the proposal of intelligent mines, unmanned electric shovels have become a research hotspot in recent years. In the field of autonomous mining, optimal excavation trajectory planning is a key issue since it has a considerable influence on production efficiency and energy consumption. In this paper, a multi-objective trajectory optimization framework based on pseudospectral method is proposed for excavation trajectory planning in autonomous mining scenarios. First, the machinery-ore coupling dynamics of electric shovel is modeled based on the Lagrange method and a multi-objective optimization model is established. Then, the trajectory optimization model is considered as a continuous Optimal Control Problem (OCP) with multiple constraints, a Radau pseudospectral method is developed to discretize the constraints, states and control variables of the dynamics model at the Legendre-Gauss-Radau collocation points, and the shovel dynamics and objective function are converted to algebraic forms. Finally, the associated Non-Linear Programming (NLP) is solved to obtain the optimal excavation trajectory and optimal control variables. In addition, the mapping relationship between the co-states of the OCP and KKT multipliers of the NLP is derived to assess the optimality of the solutions. The results confirm the effectiveness of applying the proposed framework to produce optimal excavation trajectories for unmanned electric shovels by performing a number of simulation and experimental studies. Moreover, the proposed framework tends to be more capable in terms of excavation time and energy consumption compared with other common approaches.

Robotic Manipulation Planning for Automatic Peeling of Glass Substrate Based on Online Learning Model Predictive Path Integral.

Autonomous planning robotic contact-rich manipulation has long been a challenging problem. Automatic peeling of glass substrates of LCD flat panel displays is a typical contact-rich manipulation task, which requires extremely high safe handling through the manipulation process. To this end of peeling glass substrates automatically, the system model is established from data and is used for the online planning of the robot motion in this paper. A simulation environment is designed to pretrain the process model with deep learning-based neural network structure to avoid expensive and time-consuming collection of real-time data. Then, an online learning algorithm is introduced to tune the pretrained model according to the real-time data from the peeling process experiments to cover the uncertainties of the real process. Finally, an Online Learning Model Predictive Path Integral (OL-MPPI) algorithm is proposed for the optimal trajectory planning of the robot. The performance of our algorithm was validated through glass substrate peeling tasks of experiments.

Research on trajectory planning and control system of general mobile platform for Mountain Orchard

To solve the problems of agricultural machinery simplification, lack of universality and uneven land in mountain orchards, a light self-propelled universal mobile platform for mountain orchards is studied in this paper. A light crawler chassis, an electric drive system and a multi-sensor control system are designed. Through the kinematics and dynamics modelling of the general platform, the prediction model of the motion system of the general mobile platform is determined. Then the observation model of the system motion is determined based on the multi-sensor fusion, and the multi-sensor fusion navigation control system is established. Based on the energy consumption model of mobile platform, the energy consumption optimal trajectory planning is carried out. The energy consumption optimal trajectory radius is 2.5 m and the deflection angle is 36.9°, and the optimal trajectory radius of energy consumption is 1.9 m. Orchard experiments show that the maximum lateral displacement deviation of the universal mobile platform is less than 0.1 m, which can basically achieve the expected trajectory autonomous walking function.

Dynamic Modelling and Control of Flexible Link Manipulators: Methods and Scope - Part 2

Objectives: This paper addresses two key issues in the area of flexible robotics. The issues are vibration control of flexible links and trajectory control of flexible robots. A brief, yet, significant review is provided that addresses these two issues. Methods: For vibration control of flexible links, possibilities of the use of passive and active damping methods are explored in the literature. After that, the effect of proper trajectory planning to ensure positional accuracy at the end-effector is studied. Findings: After a review of 181 research papers from the year 1970 to 2021, it has been found that the vibration suppression of flexible links can be achieved through the application of viscoelastic materials, piezoelectric materials, and optimum trajectory planning. Recent trends in research in the area of flexible manipulators show that an optimal trajectory can significantly help in reduction of link vibrations and achievement of positional accuracy simultaneously. Novelty: The novelty of the present work lies in exploring the possible application of passive and active damping control methods for vibration suppression of flexible link manipulators. Besides that, the survey also highlights how well planned trajectory may help achieve accurate tip positioning of flexible robots. Keywords: Flexible manipulator; viscoelastic damping; active vibration control; trajectory planning and control

Efficient Trajectory Optimization for Constrained Spacecraft Attitude Maneuvers

This paper introduces an optimal trajectory planner for spacecraft rest-to-rest attitude transfers subject to input saturation, angular velocity, and nonconvex exclusion cone constraints. The proposed solution adapts the Projection-Operator-Based Newton’s Method for Trajectory Optimization (PRONTO) to address the nonlinearity of the unit quaternion manifold. The system constraints are then handled using a modified interior point method designed to remain applicable when an intermediate solution estimate is infeasible. Through an extensive numerical study, the proposed solution is compared with a state-of-the-art commercial solver, its computational efficiency is demonstrated, and its unique ability to provide feasible intermediate solutions is highlighted. These results strongly indicate PRONTO as a suitable real-time optimal maneuver planner for spacecraft attitude control.

EDTP: Energy and Delay Optimized Trajectory Planning for UAV-IoT Environment

In modern days, UAV (Unmanned Aerial Vehicle) are being extensively used in various fields like military, healtcare, security, government sectors, supervision, home delivery agents, etc. They significantly enhance the potential of IoT devices by processing their data. However, issues like efficient trajectory planning, security and privacy protection, task scheduling, a delegation of tasks from one UAV to another in multi-UAV systems, etc., require rigorous research and analysis. In this paper, we consider a multi-UAV multi-IoT network, which is divided into certain hexagonal cells. Each cell consists of some IoT devices and a UAV to process the data those IoT devices collect from the environment. IoT devices in each cell are grouped into clusters so that UAVs hover only above cluster heads and midpoints of cell boundaries to collect and delegate tasks whenever required. Provision of both single and multi-hop task delegation exists in our system. The schedule is formed based on the UAV’s next intended arrival time as computed by cluster heads in the cell using the Auto-Regressive Moving Average (ARMA) model. Timestamps of visiting midpoints of cell boundaries are fitted between predicted next arrival times of visiting cluster heads. Energy consumption and time of transition from one hovering point to another can be optimized. However, the most energy-efficient solution may not necessarily be the most delay efficient. A multi-objective optimization technique is applied to identify the Pareto-optimal front and select the best possible solution. Simulation results show that compared to other trajectory planning algorithms viz. Dijkstra’s and HEA, our proposed technique saves much more energy (approx 78% over the other two) and time (42% over the other two).

Optimal Trajectory Planning of the Variable-Stiffness Flexible Manipulator Based on CADE Algorithm for Vibration Reduction Control.

Robotic manipulators are widely used for precise operation in the medical field. Vibration suppression control of robotic manipulators has become a key issue affecting work stability and safety. In this paper an optimal trajectory planning control method to suppress the vibration of a variable-stiffness flexible manipulator considering the rigid-flexible coupling is proposed. Through analyzing the elastic deformation of the variable-stiffness flexible manipulator, a distributed dynamic physical model of the flexible manipulator is constructed based on the Hamilton theory. Based on the mathematical model of the system, the design of the vibration damping controller of the flexible manipulator is proposed, and the control system with nonlinear input is considered for numerical analysis. According to the boundary conditions, the vibration suppression effect of the conventional and the variable-stiffness flexible manipulator is compared. The motion trajectory of the variable-stiffness flexible manipulator and compare the vibration response from different trajectories. Then, with minimum vibration displacement, minimum energy consumption and minimum trajectory tracking deviation as performance goals, the trajectory planning of the variable-stiffness flexible manipulator movement is carried out based on the cloud adaptive differential evolution (CADE) optimization algorithm. The validity of the proposed trajectory planning method is verified by numerical simulation.