Time-optimal Trajectory Research Articles

Smooth and Time-Optimal Trajectory Planning for Robots Using Improved Carnivorous Plant Algorithm

To improve the safety and reliability of robotic manipulators during high-speed precision movements, this paper proposes a method for smooth and time-optimal trajectory planning incorporating kinodynamic constraints. The primary objective is to use an evolutionary algorithm to determine a trajectory by considering time and jerk within the feasible path-pseudo-velocity phase plane region. Firstly, the path parameterization theory extracted the maximum pseudo-velocity projection curve from the kinodynamic constraints. Subsequently, the feasible region in the phase plane was defined through reachability analysis of discrete linear systems. Thereafter, we constructed the trajectory function using a cubic B-spline curve, optimizing its control points with an improved carnivorous plant optimization algorithm. Finally, the effectiveness and practicality of this method were verified through simulations on a 6-DOF manipulator.

A Convex Optimization Method to Time-Optimal Trajectory Planning With Jerk Constraint for Industrial Robotic Manipulators

A Convex Optimization Method to Time-Optimal Trajectory Planning With Jerk Constraint for Industrial Robotic Manipulators

Time-optimal trajectory planning for manipulator based on an improved sparrow search algorithm

Abstract With the development of industrial automation, it is crucial to use manipulators for efficient painting. To solve the problem of inefficient trajectory planning of manipulators in the point-to-point painting process, this paper proposes a time-optimal trajectory planning method based on an improved sparrow search algorithm. Initially, the standard D-H parameter method is used to establish the kinematic model of the manipulator. To ensure the continuity of each joint in the manipulator, a 3-5-3 polynomial interpolation function is utilized to construct the motion trajectory in joint space. Subsequently, the improved sparrow search algorithm is utilized to optimize the point-to-point motion trajectory of the manipulator with a constraint on motion time. Finally, simulations carried out in MATLAB demonstrated that the manipulator, which was optimized by using the improved sparrow search algorithm, exhibited a significant increase in motion efficiency compared to its pre-optimization state. Additionally, the movements of the manipulator’s joints were smooth.

Industrial Robot Trajectory Optimization Based on Improved Sparrow Search Algorithm

This paper proposes an enhanced multi-strategy sparrow search algorithm to optimize the trajectory of a six-axis industrial robot, addressing issues of low efficiency and high vibration impact on joints during operation. Initially, the improved D-H parametric method is employed to establish both forward and inverse kinematic models of the robot. Subsequently, a 3-5-3 mixed polynomial interpolation trajectory planning approach is applied to the robot. Building upon the conventional sparrow algorithm, a two-dimensional Logistic chaotic system initializes the population. Additionally, a Levy flight strategy and nonlinear adaptive weighting are introduced to refine the discoverer position update operator, while an inverse learning strategy enhances the vigilante position update operator. These modifications boost both the local and global search capabilities of the algorithm. The improved sparrow algorithm, based on 3-5-3 hybrid polynomial trajectory planning, is then used for the time-optimal trajectory planning of the robot. This is compared with traditional sparrow search algorithm and particle swarm algorithm optimization results. The findings indicate that the proposed enhanced sparrow search algorithm outperforms both the standard sparrow algorithm and the particle swarm algorithm in terms of convergence speed and accuracy for robot trajectory optimization. This can lead to the increased work efficiency and performance of the robot.

Force and time-optimal trajectory planning for dual-arm unilateral cooperative grasping

This paper studies the dual-arm manipulation of an object by means of two collaborative robots. The latter hold the object through limited contact areas, thus applying unilateral contact constraints. This manipulation strategy increases versatility, since it does not require specific grippers depending on the object shape and size. However, to ensure grasping stability (i.e. no slipping of the object), a suitable internal force must be prescribed to ensure the fulfillment of the static-friction condition. In this work, the trend of the internal force is included among the inputs of a time-optimal trajectory planning, in order to find the minimal internal prestress that is able to both satisfy the static-friction condition and manipulate the object in minimal time. Admittance control is used to modulate the forces exerted by the robot end-effectors on the object. An extensive experimentation, on different 6-dimensional trajectories reaching linear and angular accelerations up to 4.5 m/s2 and 7.4 rad/s2, is presented and discussed.

Time-Optimal Trajectory Planning and Tracking for Autonomous Vehicles.

This article presents a hierarchical control framework for autonomous vehicle trajectory planning and tracking, addressing the challenge of accurately following high-speed, at-limit maneuvers. The proposed time-optimal trajectory planning and tracking (TOTPT) framework utilizes a hierarchical control structure, with an offline trajectory optimization (TRO) module and an online nonlinear model predictive control (NMPC) module. The TRO layer generates minimum-lap-time trajectories using a direct collocation method, which optimizes the vehicle's path, velocity, and control inputs to achieve the fastest possible lap time, while respecting the vehicle dynamics and track constraints. The NMPC layer is responsible for precisely tracking the reference trajectories generated by the TRO in real time. The NMPC also incorporates a preview algorithm that utilizes the predicted future travel distance to estimate the optimal reference speed and curvature for the next time step, thereby improving the overall tracking performance. Simulation results on the Catalunya circuit demonstrated the framework's capability to accurately follow the time-optimal raceline at an average speed of 116 km/h, with a maximum lateral error of 0.32 m. The NMPC module uses an acados solver with a real-time iteration (RTI) scheme, to achieve a millisecond-level computation time, making it possible to implement it in real time in autonomous vehicles.

Time-Optimized Robot Trajectory Based on Improved Whale Optimization Algorithm in Intelligent Manufacturing

Abstract To discuss the low convergence accuracy of whale optimization algorithm (WOA) and the problem of converging to local optima, we proposed using nonlinear convergence factors and introducing nonlinear inertia weights in the WOA. The modified WOA was used to optimize the trajectory of a six-degrees-of-freedom (6DOF) industrial robot. To improve the convergence accuracy and the local and global search ability of the WOA, we first replaced the convergence factor with a nonlinear convergence factor and added a nonlinear inertia weight. The algorithm was used along with a quintic polynomial equation to develop a time-optimal trajectory, for the robot, for use in practical application scenarios. Simulation experiment results showed that the duration of a complete loading–unloading process was reduced by 30% after robot motion trajectory optimization compared with that before optimization, indicating the effectiveness of the improved WOA and its suitability for robot trajectory optimization.

基于改进鲸鱼优化算法的多农业搬运机器人协同作业轨迹规划研究

To solve the problem that the moving trajectory and operating trajectory are relatively independent and time-consuming when robots transfer agricultural products from harvesting fields to warehouses or transport vehicles, a type of agricultural materials handling robot was designed, the optimal trajectory planning method for the collaborative operating time of agricultural materials handling robots was proposed, and the time optimal trajectory under the collaborative operation of robot operating system and traveling system was acquired. Specifically, the kinematic model and dynamic model for the collaborative operation of robots were established to perform time optimal trajectory planning for materials handling robots, the Beta distribution was then applied to the Whale Optimization Algorithm (WOA) for population initialization, and a nonlinear convergence factor was introduced to prevent local optimum in the later stage of iterations. Finally, WOA was improved combining the variable neighborhood algorithm to enhance the diversity of the neighborhood structure, and this improved algorithm was applied to model solving. The results reveal that the proposed trajectory planning method can facilitate robots to obtain a smooth and time optical moving trajectory in collaborative operations of materials grabbing and discharging and obstacle avoidance. The displacement, speed, acceleration, and force/torque curves of each joint of the robots change gently, and the double-crawler traction can meet the requirements of the robots and rapidly stabilize and track the time optical trajectory.

Energetic cost of microswimmer navigation: The role of body shape

We study the energetic efficiency of navigating microswimmers by explicitly taking into account the geometry of their body. We show that, whereas arguments based solely on propulsion efficiency lead one to conclude that needle-like swimmers are most energetically efficient, disk-like swimmers rotated by flow gradients naturally follow time-optimal trajectories. The coupling between body geometry and hydrodynamics thus leads to a generic trade-off between the energetic costs associated with propulsion and navigation, which is accompanied by the selection of a finite optimal aspect ratio. We derive from optimal control theory the steering policy ensuring overall minimum energy dissipation, and characterize how navigation performances vary with the swimmer shape. Our results highlight the important role of the swimmer geometry in realistic navigation scenarios. Published by the American Physical Society 2024

Resonance selection and path planning for noncoplanar transfers via multiple gravity assists

Trajectory optimization of orbit transfers via multiple gravity assists is studied to generate the time-optimal trajectory for a large-scale velocity change. The optimal trajectory is considered as a combination of transfers between different resonance orbits, and an efficient algorithm for checking the feasibility and evaluating the flight time between two neighboring resonance orbits is given. Then, a mixed-encoding optimization model is proposed to select the optimal resonance orbits and plan the path through them. The transfer from a zero-inclination orbit to a polar orbit in the Jupiter system is simulated and the optimal trajectories via tens of GAs are obtained. The results show the efficiency of the optimization process and the practicability for mission analysis and trajectory design when the third body is small and the velocity change via a single gravity assist is limited.

Rapid generation of time-optimal rendezvous trajectory based on convex optimisation and DNN

Abstract The minimum flight time of spacecraft rendezvous is one of the fundamental indexes for mission design. This paper proposes a rapid trajectory planning method based on convex optimisation and deep neural network (DNN). The time-optimal trajectory planning problem is reconstructed into a double-layer optimisation framework, with the inner being a convex optimisation problem and the outer being a root-finding problem. The thrust properties corresponding to time-optimal control are analysed theoretically. A DNN-based rapid planning method (DNN-RPM) is put forward to improve computational efficiency, in which the trained DNN provides a high-quality initial guess for Newton’s method. The DNN-RPM is extended to search for the optimal entering angle of natural-motion circumnavigation orbit injection problem and the minimum reconfiguration time of spacecraft swarm. Numerical simulations show that the proposed method can improve the computational efficiency while ensuring the calculation accuracy.

Real-time interpolation with low-pass filtering for five-axis hybrid machining robots

This paper proposes a new interpolation approach for five-axis hybrid robots to enhance the surface quality and efficiency of machining processes. Hybrid robots have the potential to manufacture large, complex structural parts with high flexibility and a favorable load-to-weight ratio. To interpolate G01 commands, the proposed method implements finite impulse response (FIR) filters rather than splines. These filters smoothly synchronize the motions of tool center points (TCPs) and tool orientation vectors (TOVs), and are designed for each linear segment online with geometric programming while considering joint constraints. Additionally, the adjacent linear segments are locally blended with bounded geometric errors under kinematic constraints. The proposed method generates time-optimal trajectories with jerk-limited joint motions in real-time, making it more effective than current interpolation methods. The effectiveness of the proposed method is verified through the flank milling operation on aluminum alloy.

Unactuated and Actuated States Simultaneously Constrained Optimal Trajectory Planning-Based Path-Following Control for Underactuated Robots.

For underactuated robots working in complex environments, an important objective is to drive all variables (particularly for unactuated end-effectors) to move along the specific path and restrict positions/velocities to avoid obstacles, rather than using only point-to-point control. Unfortunately, most path planning methods are only suitable to fully actuated systems or depend on linearized models. The main motivations of our work are to directly fulfill motion constraints and achieve path following for both actuated and unactuated states (e.g., payload swing of cranes) when lacking effective control inputs. To this end, this article presents a new time-optimal trajectory planning-based motion control method for general underactuated robots. By constructing auxiliary signals (in Cartesian space) to express all actuated/unactuated variables (in joint space), their position/velocity constraints are converted into some convex/nonconvex inequalities related to a to-be-optimized path parameter and its derivatives. Then, an optimization algorithm is constructed to solve the available path parameter and derive a group of time-optimal trajectories for actuated states. As we know, this is the first study to ensure path following and necessary full-state constraints for actuated/unactuated states. Then, a tradeoff among path-constrained motions, time optimization, and state constraints is achieved together. This article takes the rotary crane as an example and provides detailed analysis of calculating desired trajectories based on the proposed planning frame, whose effectiveness is also verified through hardware experiments.

Stochastic Time-Optimal Trajectory Planning for Connected and Automated Vehicles in Mixed-Traffic Merging Scenarios

Stochastic Time-Optimal Trajectory Planning for Connected and Automated Vehicles in Mixed-Traffic Merging Scenarios

Online and Scalable Motion Coordination for Multiple Robot Manipulators in Shared Workspaces

Multi-robot motion coordination is essential to make robots work safely and efficiently in a shared workspace, ensuring task completion while avoiding interference between each other’s motions. Achieving online replanning and scaling to large numbers of robots are particularly challenging. In this paper, we present a motion coordination method for multiple robot manipulators with given targets. The approach separates the problem into a global coordination stage and a local trajectory replanning stage. Online reactivity and scalability are achieved by means of coordination in a reduced space and efficient trajectory replanning. We first introduce the method for systems with two robots, then extend it to systems with an arbitrary number of robots. The method determines whether kinematically-feasible and non-interfering trajectories leading all the robots to their targets exist. The approach generates time-efficient trajectories if solutions exist, or provides information for switching targets if solutions cannot be found. We show formally and empirically that the method has low computational overhead and scales quadratically with the number of robots. Experiments are conducted with up to three real 7-DOF robots and up to ten simulated robots. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In underground mining, a key process is that of tunneling, i.e., drilling and blasting rock to excavate tunnels that lead to sources of ore. Drilling is carried out by rigs equipped with multiple robotic arms. A key factor affecting the efficiency of tunneling is the time to completion of drilling operations. In current industrial practice, these operations are carried out manually by an operator steering the arms on the drill rig. Time to completion can be drastically reduced if the arms could operate concurrently, intelligently optimizing and coordinating their motions. However, existing methods for multi-arm motion coordination are inadequate, as they fail to cater to one or more of the following real-world constraints: several robot arms work in close proximity and their workspaces are overlapping; task completion times are uncertain due to rock density and drill bit breakage; and contingencies such as unexpected delays in motion or stops sometimes happen. These constraints exist also in other industrial applications, like manufacturing and assembly. This paper proposes a framework which enables multiple high-DOF robot manipulators to safely and efficiently work in a shared workspace. The method allows to adjust robot trajectories while robots move, and is shown to scale well with the number of robots. Motions are generated and adjusted by time-optimal trajectory planning, whose computational overhead is small enough for online operation and benefits task completion efficiency, safety, and productivity. Experiments using three 7-DOF robots suggest that this approach is practically feasible, and simulations with up to 10 robots attest to its scalability.

Safety Compliant, Ergonomic and Time-Optimal Trajectory Planning for Collaborative Robotics

Safety Compliant, Ergonomic and Time-Optimal Trajectory Planning for Collaborative Robotics

Kinodynamic Motion Planning for a System with Squid Dynamics

This paper introduces a path planning algorithm for a system with squid dynamics in a cluttered environment. We capture the complex interactions of fin, arms, and body patterning by analyzing experimental data collected from observing squid motion. We extract nine motion primitives to build the control sequence for a time-optimal trajectory. This task is formulated as a mixed-integer program, and we generate the minimum-time trajectory using a sample-based approach. Numerical simulations illustrate the efficacy of this strategy and motivate ongoing and future efforts to exploration of squid motion features, improvement of the modeling, and experimental demonstrations of the motion planning strategy.

A trajectory planning method for a casting sorting robotic arm based on a nature-inspired Genghis Khan shark optimized algorithm.

In order to meet the efficiency and smooth trajectory requirements of the casting sorting robotic arm, we propose a time-optimal trajectory planning method that combines a heuristic algorithm inspired by the behavior of the Genghis Khan shark (GKS) and segmented interpolation polynomials. First, the basic model of the robotic arm was constructed based on the arm parameters, and the workspace is analyzed. A matrix was formed by combining cubic and quintic polynomials using a segmented approach to solve for 14 unknown parameters and plan the trajectory. To enhance the smoothness and efficiency of the trajectory in the joint space, a dynamic nonlinear learning factor was introduced based on the traditional Particle Swarm Optimization (PSO) algorithm. Four different biological behaviors, inspired by GKS, were simulated. Within the premise of time optimality, a target function was set to effectively optimize within the feasible space. Simulation and verification were performed after determining the working tasks of the casting sorting robotic arm. The results demonstrated that the optimized robotic arm achieved a smooth and continuous trajectory velocity, while also optimizing the overall runtime within the given constraints. A comparison was made between the traditional PSO algorithm and an improved PSO algorithm, revealing that the improved algorithm exhibited better convergence. Moreover, the planning approach based on GKS behavior showed a decreased likelihood of getting trapped in local optima, thereby confirming the effectiveness of the proposed algorithm.

Efficient and Robust Time-Optimal Trajectory Planning and Control for Agile Quadrotor Flight

Efficient and Robust Time-Optimal Trajectory Planning and Control for Agile Quadrotor Flight

Analytical Solution of Time-Optimal Trajectory for Heaving Dynamics of Hybrid Underwater Gliders

Underwater vehicles have capacity limits for control inputs, within which their time-optimal trajectories (TOTs) can be formulated. In this study, the fastest trajectory for the depth control of a hybrid underwater glider (HUG) was found using buoyancy engines and propellers individually, and the decoupled heave dynamics of the HUG were defined using quadratic hydrodynamic damping. Because buoyancy engines always run at slow speeds, the buoyancy force was formulated based on the constant force rate of the engine. It was assumed that the nominal value of the heave dynamics parameters could be estimated; therefore, the analytical solution of heave dynamics could be formulated using the thrusting saturation and constant buoyancy force rate. Then, the shortest trajectory for depth control of the HUG could be established while considering the actuator saturation. To verify the effectiveness of the TOT in HUG heave dynamics, extensive tracking control simulations following the TOT were conducted. It was found that the proposed TOT helps the HUG reach the desired depth in the shortest arrival time, and its robust depth control showed good tracking performance in the presence of external bounded disturbances.