Trajectory Planning Framework Research Articles

Unified framework for geometric error compensation and shape-adaptive scanning in five-axis metrology systems

In response to the escalating demand for precise shape metrology of complex optical surfaces, this study unveils a unified geometric error compensation and trajectory planning framework tailored for high-accuracy five-axis scanning metrology systems, which remains a notably underexplored field compared to error compensation in machine tools. Founded on a unified geometric model, the proposed framework seamlessly integrates a versatile shape-adaptive trajectory planning strategy, a thorough global error sensitivity analysis approach, and an exhaustive geometric error compensation scheme. Leveraging inverse kinematics, an innovative shape-adaptive scanning trajectory generation strategy is mathematically formulated, thereby facilitating adaptable measurement trajectory generation for diverse surface geometries. Employing forward kinematics, an exhaustive geometric error model is established to extensively address the 53 distinct geometric errors in the metrology system. This proposed error model fundamentally augments conventional geometric error models in machine tool by managing not only the geometric errors from the motion system, but also those from the probe and workpiece. To streamline the error compensation procedure, a novel global error sensitivity analysis approach is introduced, identifying both system-oriented and process-oriented sensitive geometric errors for targeted compensation. Experimental validation using a standard ball, which achieved an exceptional 89.35% reduction in the root mean square of the measurement errors, further confirms the feasibility and effectiveness of the proposed framework. By offering an universal trajectory planning, sensitivity analysis and error compensation trinity for five-axis scanning metrology systems, this study sets the stage for precision advancements and design optimization across diverse configurations of metrology systems.

Trajectory planning at a signalized road section in a mixed traffic environment considering lane-changing of CAVs and stochasticity of HDVs

Connected and automated vehicles (CAVs) are projected to bring significant benefits to traffic efficiency and driving comfort. However, the realization of full CAV penetration rate will take a long time. In this paper, a framework is proposed for planning the trajectories of vehicles at a signalized road section in a mixed traffic environment consisting of CAVs, human-driven vehicles (HDVs) and connected and automated buses (CABs). In the proposed trajectory planning framework (TPF), both the lane-changing (LC) behavior of CAVs and the stochasticity of HDVs are considered. The whole TPF is composed of a planning module, a running module, and a switching module. In the planning module, the mixed integer programming (MIP) models for trajectory planning with/without LCs are formulated to optimize the trajectories of CAVs/CABs. A parsimonious algorithm is designed to determine a suitable planning time horizon for the MIP models. The running module and the switching module are designed to ensure the driving safety of vehicles. To consider the stochasticity of HDVs, the concept of α-trajectory is employed in simulations to produce predicted trajectories of HDVs, while the actual trajectories of HDVs are generated by a stochastic car-following model. Here, α is a parameter between 0 and 1 related to one randomly changing parameter of HDVs, and α-trajectory is a series of predicted trajectories generated for HDVs based on the value of α. A rolling time horizon scheme is applied for TPF to account for the time-varying traffic situations. Numerical experiments under different traffic states and market penetration rates (MPRs) of CAVs/CABs are conducted to validate the performance of the proposed TPF. The average improvement in travel time and fuel consumption can reach up to 28.9 %, 17.8 % and 52.2 %, 35.3 % under medium and heavy traffic, respectively, and the average improvement in driving comfort is over 20 % in most traffic scenarios. The comparison experiment without fixed rolling time window (FTW) shows the advantage of setting FTW in adapting to the time-varying traffic situations, especially under heavy traffic. The sensitivity analysis shows that the values of α1 and α2 associated with α-trajectory can affect the performance of the proposed TPF in varying degrees. Finally, the length of the control zone is suggested to be set to 300–500 m.

A Novel Framework for Trajectory Planning and Safe Navigation of Satellite Swarms

This paper proposes a new framework for near-optimal, collision-free navigation of a swarm of identical satellites from an initial formation to a desired final formation. The framework combines a centralized optimization problem for location assignment with collision avoidance constraints, a decentralized fuel-optimal trajectory planner, a decentralized Artificial Potential Field (APF)-based real-time controller to ensure robustness, and a Shrinking Horizon Model Predictive Control logic to prevent deadlocks and livelocks and to improve robustness. To ensure high performance and low fuel cost, a novel optimization problem is formulated to tune the APF parameters based on mission requirements. The proposed framework provides a balance between optimality and scalability while keeping computational requirements low. The effectiveness of the frame work is demonstrated using numerical simulations.

Developing a Deep Q-Learning and Neural Network Framework for Trajectory Planning

With the recent expansion in Self-Driving and Autonomy field, every vehicle is occupied with some kind or alter driver assist features in order to compensate driver comfort. Expansion further to fully Autonomy is extremely complicated since it requires planning safe paths in unstable and dynamic environments. Impression learning and other path learning techniques lack generalization and safety assurances. Selecting the model and avoiding obstacles are two difficult issues in the research of autonomous vehicles. Q-learning has evolved into a potent learning framework that can now acquire complicated strategies in high-dimensional contexts to the advent of deep feature representation. A deep Q-learning approach is proposed in this study by using experienced replay and contextual expertise to address these issues. A path planning strategy utilizing deep Q-learning on the network edge node is proposed to enhance the driving performance of autonomous vehicles in terms of energy consumption. When linked vehicles maintain the recommended speed, the suggested approach simulates the trajectory using a proportional-integral-derivative (PID) concept controller. Smooth trajectory and reduced jerk are ensured when employing the PID controller to monitor the terminals. The computational findings demonstrate that, in contrast to traditional techniques, the approach could investigate a path in an unknown situation with small iterations and a higher average payoff. It can also more quickly converge to an ideal strategic plan.

Spatio‐temporal decision‐making and trajectory planning framework with flexible constraints in closed‐loop dynamic traffic

AbstractDriving in interactive dynamic traffic is a huge challenge for autonomous vehicles, especially for motion planning. The autonomous vehicle not only needs to predict the future states of the social vehicles to avoid a collision but also realizes the comfort and continuous plan. To deal with the problem, a spatio‐temporal decision‐making and motion planning framework with flexible constraints based on previous work is proposed. Improvements can be highlighted in three aspects. First, a neural network for trajectory prediction is trained and it is integrated into the framework, which can learn the social vehicles' reactions in the negotiation better and give more accurate predictions. Second, instead of setting the fixed local targets, the flexible‐constraint mechanism is introduced to increase the success rate of continuous planning, specifically, the local planning target is determined conditioned on the situation with an elastic factor. Third, two popular simulators with randomly disposed traffic participants are exploited, where vehicles are mutually influenced, more similar to real‐world traffic. The closed‐loop tests with zero crashes and the comparative experiments with traditional models demonstrate the superior performance and practical significance of the proposed framework.

Human-Aware Robot Task Planning with Robot Execution Time Estimation

When robots work with humans for a collaborative task, they need to plan their actions while taking humans’ actions into account. The state-of-the-art optimization-based human-aware task planner plans robot actions by prioritizing the actions that are parallel to the human's actions. However, the limitation of this approach is that the robot execution time for each action, which is an important parameter for the optimization problem, is fixed. In this paper, we investigate how online robot execution time estimation can increase the time efficiency of such a human-aware task planner. We propose a direct time estimation method and an analytical time estimation method. An integrated task and trajectory planning framework is also presented. Experiments show that online robot execution time estimation increases the time efficiency of the collaborative task. Moreover, the results of the direct time estimation method are more accurate than those of the analytical method.

Trajectory Planning for Autonomous Mining Trucks Considering Terrain Constraints

There are many constraints to be considered to plan a safe and feasible trajectory for autonomous mining trucks due to the rough terrain in open-pit mines. It is difficult to handle these constraints uniformly within a trajectory planning framework. To overcome this limitation, a novel trajectory planning framework is proposed in this paper. Different from many existing studies which characterized the spatial positions of vehicles at the sampling time points as decision variables, we characterize the time points at the sampling spatial positions as decision variables to conveniently address the terrain constraints. Based on such a formulation, we further consider the kinematic constraints, engine power constraints and time window constraints. Various objectives (e.g., transport efficiency, fuel economy) can be considered in this trajectory planning framework, and the formulated trajectory planning problems can be efficiently solved. Finally, several case studies are conducted to validate the effectiveness of the proposed trajectory planning framework.

Biomechanical Motion Planning for a Wearable Robotic Forearm

Supernumerary robotic devices in the form of wearable arms enhance a user's reachable workspace and provide them with additional capabilities. However, the user may experience considerable force and moment loads on their body due to the robot's motion. In this letter, we present a simulation and trajectory planning framework that aims to minimize the load on a user's muscles while operating a Wearable Robotic Forearm (WRF). Using a high-fidelity model of the human arm, we construct a term for biomechanical costs that is subsequently added to the overall cost function for a motion planner. For evaluation, the planner is initialized with shortest paths linearly interpolated between ten start and goal state pairs in the configuration space, as well as with paths optimized for reaction moments using a local search. We find that the biomechanical planner coupled with locally-optimized initialization reduces mean human muscle fiber forces by up to 23.47% compared to the linearly interpolated trajectories.

Autonomous Driving Ethics: from Trolley Problem to Ethics of Risk

In 2017, the German ethics commission for automated and connected driving released 20 ethical guidelines for autonomous vehicles. It is now up to the research and industrial sectors to enhance the development of autonomous vehicles based on such guidelines. In the current state of the art, we find studies on how ethical theories can be integrated. To the best of the authors’ knowledge, no framework for motion planning has yet been published which allows for the true implementation of any practical ethical policies. This paper makes four contributions: Firstly, we briefly present the state of the art based on recent works concerning unavoidable accidents of autonomous vehicles (AVs) and identify further need for research. While most of the research focuses on decision strategies in moral dilemmas or crash optimization, we aim to develop an ethical trajectory planning for all situations on public roads. Secondly, we discuss several ethical theories and argue for the adoption of the theory “ethics of risk.” Thirdly, we propose a new framework for trajectory planning, with uncertainties and an assessment of risks. In this framework, we transform ethical specifications into mathematical equations and thus create the basis for the programming of an ethical trajectory. We present a risk cost function for trajectory planning that considers minimization of the overall risk, priority for the worst-off and equal treatment of people. Finally, we build a connection between the widely discussed trolley problem and our proposed framework.

Kinematics and workspace analysis of 4SPRR-SPR parallel robots.

The 4SPRR-SPR parallel robot, which has considerable potential for application in the field of machining, is a novel closed-loop mechanism with a high rigid-weight ratio. Kinematics and workspace analyses of the 4SPRR-SPR parallel robot are key requirements for its application in machining. In this study, the inverse kinematics of the 4SPRR-SPR parallel robot is analyzed using a geometric method based on the mechanism arrangement of the robot. The forward kinematics model is derived by training the vector-quantified temporal associative memory (VQTAM) network, which originates from a self-organizing map (SOM). Furthermore, an improved algorithm is obtained by combining the locally linear embedding (LLE) and VQTAM methods. A boundary extraction algorithm for the workspace analysis of the parallel robot is proposed. The performance of the boundary extraction algorithm is analyzed and compared with that of a global search algorithm; the result indicates that the novel algorithm has the same computational accuracy in addition to higher efficiency. The workspace of the 4SPRR-SPR parallel robot is analyzed using the boundary extraction algorithm. Finally, the 3D model of the 4SPRR-SPR parallel robot is simulated using the ADAMS software to verify the reliability of the proposed algorithms. The simulation results demonstrate the effectiveness of the methods proposed in this study. In addition, the robot kinematics and workspace analysis methods described herein can be extended to other serial and parallel robots. This research provides a theoretical framework for trajectory planning of mechanisms, workspace optimization of robots, and robotic control.

On-Line Learning and Updating Unmanned Tracked Vehicle Dynamics

Increasing levels of autonomy impose more pronounced performance requirements for unmanned ground vehicles (UGV). Presence of model uncertainties significantly reduces a ground vehicle performance when the vehicle is traversing an unknown terrain or the vehicle inertial parameters vary due to a mission schedule or external disturbances. A comprehensive mathematical model of a skid steering tracked vehicle is presented in this paper and used to design a control law. Analysis of the controller under model uncertainties in inertial parameters and in the vehicle-terrain interaction revealed undesirable behavior, such as controller divergence and offset from the desired trajectory. A compound identification scheme utilizing an exponential forgetting recursive least square, generalized Newton–Raphson (NR), and Unscented Kalman Filter methods is proposed to estimate the model parameters, such as the vehicle mass and inertia, as well as parameters of the vehicle-terrain interaction, such as slip, resistance coefficients, cohesion, and shear deformation modulus on-line. The proposed identification scheme facilitates adaptive capability for the control system, improves tracking performance and contributes to an adaptive path and trajectory planning framework, which is essential for future autonomous ground vehicle missions.

A real‐time quadrotor trajectory planning framework based on B‐spline and nonuniform kinodynamic search

AbstractAutonomous navigation of quadrotor is required by many application scenarios, such as exploration, search, and rescue. The trajectory planning algorithm is the core of autonomous navigation, which can undoubtedly greatly enhance the safety of flight. In this paper, a trajectory planning framework based on B‐spline and kinodynamic search is proposed. This framework can be used for a limited‐sensing quadrotor to plan safe and dynamically feasible trajectories in unknown environments, and the flight is safe and effective along with these trajectories. First, a B‐spline based nonuniform kinodynamic (BNUK) search algorithm is proposed to generate dynamically feasible trajectories efficiently. The characteristics of nonuniform search make the generated trajectories safe and reasonable time‐allocation. Then, a trajectory optimization method based on control point optimization is proposed. The trajectory generated by BNUK is further optimized by solving a quadratically constrained quadratic programming problem. The smoothness of the trajectory is improved, and the control cost is reduced. Extensive analysis and comparative simulation experiments verify the advancedness of the proposed framework. We also integrated it into a vision‐based quadrotor autonomous navigation system, and multiple outdoor flight experiments show the effectiveness of the proposed framework.

Real-Time Acceleration-Continuous Path-Constrained Trajectory Planning With Built-In Tradeoff Between Cruise and Time-Optimal Motions

In this article, a novel real-time acceleration-continuous path-constrained trajectory planning algorithm is proposed with an appealing built-in tradeoff mechanism between the cruise motion and time-optimal motion. Different from existing approaches, the proposed approach smoothens time-optimal trajectories with bang-bang input structures to generate acceleration-continuous trajectories while preserving the completeness property. More importantly, a novel built-in tradeoff mechanism is proposed and embedded into the trajectory planning framework so that the proportion of the cruise motion and time-optimal motion can be flexibly adjusted by changing a user-specified functional parameter. Thus, the user can easily apply the trajectory planning algorithm for various tasks with different requirements on motion efficiency and cruise proportion. Moreover, it is shown that feasible trajectories are computed more quickly than optimal trajectories. Rigorous mathematical analysis and proofs are presented for those aforementioned theoretical results. Comparative simulations and experimental results on an omnidirectional wheeled mobile robot demonstrate that flexible tunings between the cruise and time-optimal motions can be achieved in a higher computational efficiency manner by the proposed algorithm. Note to Practitioners —This article is motivated by the time-optimal and smooth motion planning problem for mobile robots along given paths. Existing approaches generally use the piecewise polynomial interpolations to smoothen and adjust feasible trajectories. This article proposes a novel path-constrained trajectory planning approach, which preserves properties of completeness and a high-efficient tradeoff mechanism between the optimal and cruise motions when achieving a globally optimal and acceleration-continuous trajectory. Comparative experimental results with other methods show the effectiveness of the proposed approach. In future research, we will attempt to integrate the proposed approach with typical path planning methods to achieve a complete and high-efficient motion planning framework.

Trajectory Planning Based on Spatio-Temporal Map With Collision Avoidance Guaranteed by Safety Strip

Trajectory planning for the unmanned vehicle in the complex environment has always been a challenging task. Planned trajectory with the corresponding target velocity or acceleration sequence must be collision-free guaranteed and as comfortable as possible on the premise of obeying the traffic rules and interaction with other dynamic social vehicles. To meet this requirement, this paper proposes a framework for trajectory planning based on spatio-temporal map. Due to the time layer architecture in the map, the trajectory can be generated with velocity and acceleration simultaneously, and the whole trajectory is constrained within a `safety strip', resulting in an efficient and safety guaranteed trajectory. The framework is composed of three sections: rough search, fine optimization and safety strip-based collision avoidance. For rough search, we propose an improved A* algorithm implemented in the discrete time layer to find out the suboptimal states efficiently. In fine optimization, the B-spline curve is exploited to connect the searched states into a continuous trajectory. And the optimal control points of B-spline are further grouped into several segments, forming the safety strip which is actually the distribution space of the planned trajectory. If necessary, an adjustment will be applied to keep the strip away from the collision zone, making the entire trajectory completely collision-free. Experiments on both public dataset and self-driving simulator show that the proposed framework can adapt to different kinds of complex traffic scenes well.

Trajectory Planning of Autonomous Vehicles Based on Parameterized Control Optimization in Dynamic on-Road Environments

This paper presents a trajectory planning framework to deal with the highly dynamic environments for on-road driving. The trajectory optimization problem with parameterized curvature control was formulated to reach the goal state with the vehicle model and its dynamic constraints considered. This in contrast to existing curve fitting techniques guarantees the dynamic feasibility of the planned trajectory. With generation of multiple trajectory candidates along the Frenet frame, the vehicle is reactive to other road users or obstacles encountered. Additionally, to deal with more complex driving scenarios, its seamless interaction with an upper behavior planning layer was considered by having longitudinal motion planning responsive to the desired goal state. The trajectory evaluation and selection methodologies, along with the low-level tracking control, were also developed under this framework. The potential of the proposed trajectory planning framework was demonstrated under different dynamic driving scenarios such as lane-changing or merging with surrounding vehicles with its computation efficiency proven in real-time simulations.

Control Framework for Trajectory Planning of Soft Manipulator Using Optimized RRT Algorithm

This paper proposes a model-free control framework for the path planning of the rigid and soft robotic manipulator using an intelligent algorithm called Weighted Jacobian Rapidly-exploring Random Tree (WJRRT). The optimization approach is used to model the path planning problem, which is independent of the robotic model, and then used the WJRRT algorithm to solve it. WJRRT algorithm not only explores the cartesian space for the end-effector of the robotic manipulator randomly but also directs it towards the goal-position when required. It is robust enough to tackle the uncertainties in the manipulator and make the computation of path planning more efficient. WJRRT assigned a fitness value to each node of the tree. Based on the fitness values algorithm computes the final path, which is a trade-off between efficiency and safety of the path. The simulation results of two, three, and seven degrees of freedom (DOF) robotic manipulators are presented and compared with JT-RRT, Bi-RRT, and TB-RRT algorithms. Experimental results are verified using a soft manipulator made from flexible materials, i.e., polypropylene and polychloroprene. Their flexible structure makes their control complex and creates uncertainties in the model. The simulation and experimental results demonstrate that WJRRT can efficiently and accurately control the motion of manipulators.

Trajectory planning in 3D dynamic environment with non-cooperative agents via fast marching and Bézier curve

ABSTRACTIn this paper, we propose a framework for trajectory planning in a 3D dynamic environment where other non-cooperative agents may obstruct the active quadrotor. A trajectory predictor is designed for the non-cooperative agent via least squares. In addition, based on Euclidean signed distance field (ESDF), a velocity map configuration is developed for both dynamic and static obstacles, and then utilized in fast marching method to find a feasible discrete path. The smooth and dynamic feasible trajectory generation problem is formulated as a quadratic programming (QP) problem, where a safe flight corridor generator is developed for safe constraints in a dynamic environment. Piecewise Bézier curves are used to represent the generated trajectory. With the help of flight corridor, along with the convex hull property of Bézier curve, the quadratic programming problem turns into a convex optimization problem. Simulation results show that the proposed approach is validated for collision avoidance in a dynamic environment.

A Decoupled Trajectory Planning Framework Based on the Integration of Lattice Searching and Convex Optimization

This paper presents a decoupled trajectory planning framework based on the integration of lattice searching and convex optimization for autonomous driving in structured environments. For a 3D trajectory planning problem with timestamps information, due to the presence of multiple kinds of constraints, the feasible domain is non-convex, so it is easy to fall into local optimum for trajectory planning. And the solution space of this problem is so enormous that it is difficult to identify an optimal solution in polynomial time. To address this non-convex problem, and to improve the convergence speed of an optimization process, the approach based on lattice searching is adopted in consideration of the ability to discretize driving environments and reduce the solution space. And the resulting path generated by lattice searching typically lies in the neighborhood of the global optimum. But this solution is neither spatiotemporally smooth nor globally optimal, so it is generally called the rough solution. For this reason, a subsequent nonlinear optimization process is introduced to refine the rough trajectory (combined by path and speed). The proposed framework is implemented and evaluated through simulations in various challenging scenarios in this paper. The simulation results verify that the trajectory planner can generate high-quality trajectories, and the execution time is also acceptable.

A fast trajectory planning framework with task-priority for space robot

This paper addresses trajectory planning issue for free-floating space robotic system which is designed to track a prescribed path simultaneously fulfilling imposed constraints such as collision avoidance and minimizing base attitude disturbance. Collision avoidance can be treated as inequality constraints as part of the trajectory planning. To generate smooth trajectory for robot motion, a novel local collision avoidance method considering multiple velocity damper constraints is proposed for non-strictly convex polyhedra. Moreover, we propose a task-priority handling strategy incorporated with a full-fledged Quadratic Programming(QP) procedure to solve the planning problem with sequential tasks. The proposed task-priority handling strategy enables a rapid adaptation of the space manipulators motion, which makes this strategy feasible for real-time planning. The trajectory planning framework with collision avoidance method and task-priority handling strategy were implemented and demonstrated via a kinematically redundant dual-arm space robotic system.

Hybrid Trajectory Planning for Autonomous Driving in Highly Constrained Environments

In this paper, we introduce a novel and efficient hybrid trajectory planning method for autonomous driving in highly constrained environments. The contributions of this paper are fourfold. First, we present a trajectory planning framework that is able to handle geometry constraints, nonholonomic constraints, and dynamics constraints of cars in a humanlike and layered fashion and generate curvature-continuous, kinodynamically feasible, smooth, and collision-free trajectories in real time. Second, we present a derivative-free global path modification algorithm to extract high-order state information in free space for state sampling. Third, we extend the regular state-space sampling method widely used in on-road autonomous driving systems to a multi-phase deterministic state-space sampling method that is able to approximate complex maneuvers. Fourth, we improve collision checking accuracy and efficiency by using a different car footprint approximation strategy and a two-phase collision checking routine. A range of challenging simulation experiments show that the proposed method returns high-quality trajectories in real time and outperforms existing planners, such as hybrid A* and conjugate-gradient descent path smoother in terms of path quality, efficiency, and computation resources used.