Multi-objective Trajectory Planning Research Articles

Multi-objective trajectory planning and implementation of a metamorphic palletizing robot

Multi-objective trajectory planning and implementation of a metamorphic palletizing robot

A multi-objective trajectory planning approach for vibration suppression of a series–parallel hybrid flexible welding manipulator

Although the series–parallel hybrid welding manipulator has advantages over the traditional series manipulator, its must run continuously and smoothly according to a specific trajectory at the rated velocity. Considering a flexible manipulator with a complex series–parallel hybrid structure as the research object, this paper proposes a multi-objective approach to indirectly suppress the vibration. In view of the complex flexible mechanism with a multi-kinematic pair arrangement and a multi-motor drive, a system comprehensive elastodynamics model is established, and the effectiveness of the model is verified through the hammer test method. To achieve synchronous and coordinated planning of the end position and attitude, the spatial arc welding trajectory is planned on the basis of the synchronous planning controller and the dual-S velocity profile interpolation function. Then, a multi-objective optimization model considering the travel time, energy consumption and terminal amplitude fluctuations is proposed, the trajectory planning problem is transformed into a parameter optimization problem in the interpolation function, and then the elite non-dominated sorting genetic algorithm (NSGA-II) is employed to determine the optimal trajectory. The optimal trajectory thus obtained effectively suppresses the vibration of the system. Finally, compared with the classic fifth-degree polynomial trajectory planning method, the system vibration suppression effect is significant, which verifies the effectiveness and feasibility of the proposed method and provides a theoretical basis for further realizing real-time control.

Multi-objective trajectory planning for segment assembly robots using a B-spline interpolation- and infeasible-updating non-dominated sorting-based method

The rapid and smooth functioning of segment assembly robots, which is always conflicting, is critical to improving efficiency and ensuring safety during tunneling construction, particularly for the series-actuated robots employed in non-circular shield machines. However, the trade-off between the aforementioned goals has not been explored for trajectory planning in joint space. Less is known about how to acquire superior trade-off Pareto solutions for this constrained multi-objective optimization problem. To fill this gap, this paper proposes a B-spline interpolation- and infeasible-updating non-dominated sorting-based method for multi-objective trajectory planning of shield machine segment assembly robots. In particular, a multi-objective optimization model is detailed in terms of time, acceleration, and jerk of joint trajectories while accounting for operational efficiency and motion smoothness. The given objective functions can be determined using B-spline interpolation and time information based on the known via-points of hydraulic joints. Meanwhile, the constraints are transformed into a limited number of control point-derived forms. Following that, the infeasible-updating non-dominated sorting-based evolutionary algorithm (INSEA) is introduced to solve this problem and find Pareto-optimal solutions. The main improvement is that the multi-objective function information of infeasible solutions is utilized so as to update the non-dominated sorting process, which adaptively applies population division and individual replacement. The findings indicate that the proposed method is capable of executing multi-objective trajectory planning during different stages of the assembly procedure, and the computed metrics are all greater than serval advanced algorithms. Furthermore, on the basis of the proposed INSEA, multi-degree B-spline interpolation provides lower acceleration peaks and smoother global trajectories than common cubic spline curves throughout the process. Therefore, this method can provide researchers with a wide range of alternatives to achieve the optimum trade-off for multi-objective trajectory planning.

Multi-objective trajectory planning in the multiple strata drilling process:A bi-directional constrained co-evolutionary optimizer with Pareto front learning

Trajectory planning is essential to ensure the safety and efficiency of the drilling process within varying downhole geological conditions. However, numerous constraints and dispersed objectives make this task challenging, resulting in a broken constrained Pareto front (PF) in the objective space. To address this issue, we present a novel multi-objective optimization algorithm (MOEA), the Bi-directional Constrained Co-evolutionary Optimizer (BCCO), for reducing the friction torque of the drilling string system and maintaining the wellbore stability of the directional drilling process in multiple changeable strata. Inspired by dual-population co-evolutionary mechanics, BCCO is thoughtfully developed to enhance complex constraints handling. An ESOINN is introduced to guide the population in exploring the irregular PF and adaptively approximating to it. In addition, a flexible constraint dominance principle is devised to filter out non-inferior infeasible solutions that fully balance feasibility, diversity, and convergence by combining constraint violation, minimum vector angle, and angle-penalized distance. Moreover, we adopt a minimum Manhattan distance (MMD) decision-making method to select the final reference solution for trajectory tracking control. To verify the effectiveness of BCCO, we compared it with seven state-of-the-art constrained MOEAs, four latest published MOEAs used in drilling trajectory planning (DTP) applications, and three ablation MOEAs revised from original BCCO on real-world constrained test instances and four different types of designed standard benchmarks. Extensive testing confirmed adaptability to diverse constrained PFs. BCCO displayed strong convergence and diversity when applied to real-world engineering problems while maintaining feasibility. To evaluate BCCO’s DTP performance, we built a wellbore stability model on actual geological formations and empirically tested it with both composite natural curves and third-order Bézier curves in various drilling trajectory scenarios. We established a comprehensive cloud-based DTP test system with the on-site Programmable Logic Controller (PLC) and the workstation via Data Transfer Unit (DTU) communication. Actual DTP cases confirmed the feasibility of BCCO’s Pareto solutions, with MMD-selected trajectories ensuring a harmonized drilling process.

Multi-objective time-energy-impact optimization for robotic excavator trajectory planning

Single-objective optimal trajectory cannot adapt to the complex requirements of excavator construction. A comprehensive optimal trajectory planning method is proposed to optimize the working time, energy consumption, and operational impact of robotic excavators. Without fusing any performance indexes, a normalized multi-objective function and an improved particle swarm optimization algorithm are established to achieve a comprehensive optimization of multiple objectives, while considering joint angle, velocity, acceleration, and quadratic acceleration constraints. Typical deep pit excavation simulation and experimental results show that the multi-objective optimization method is feasible, can balance multi-objective constraints, and can avoid falling into extremely long working times or large impacts. This method offers a more efficient and effective solution for multi-objective trajectory planning and provides a method for planning excavation trajectories based on different operating scenarios and objectives.

Multi-objective reward shaping for global and local trajectory planning of wing-in-ground crafts based on deep reinforcement learning

AbstractThe control of a wing-in-ground craft (WIG) usually allows for many needs, like cruising, speed, survival and stealth. Various degrees of emphasis on these requirements result in different trajectories, but there has not been a way of integrating and quantifying them yet. Moreover, most previous studies on other vehicles’ multi-objective trajectory is planned globally, lacking for local planning. For the multi-objective trajectory planning of WIGs, this paper proposes a multi-objective function in a polynomial form, in which each item represents an independent requirement and is adjusted by a linear or exponential weight. It uses the magnitude of weights to demonstrate how much attention is paid relatively to the corresponding demand. Trajectories of a virtual WIG model above the wave trough terrain are planned using reward shaping based on the introduced multi-objective function and deep reinforcement learning (DRL). Two conditions are considered globally and locally: a single scheme of weights is assigned to the whole environment, and two different schemes of weights are assigned to the two parts of the environment. Effectiveness of the multi-object reward function is analysed from the local and global perspectives. The reward function provides WIGs with a universal framework for adjusting the magnitude of weights, to meet different degrees of requirements on cruising, speed, stealth and survival, and helps WIGs guide an expected trajectory in engineering.

Knowledge Database-Based Multiobjective Trajectory Planning of 7-DOF Manipulator With Rapid and Continuous Response to Uncertain Fast-Flying Objects

The problems of a 7-degree of freedom (DOF) manipulator with rapid and continuous response to uncertain fast-flying objects are addressed: 1) how to effectively solve trajectory planning of the 7-DOF manipulator with multiple criteria; and 2) how to make the 7-DOF manipulator realize the rapid and continuous response to uncertain fast-flying objects. In the proposed approach, based on the trajectory parameterization of the 7-DOF manipulator, a multiobjective teaching-learning-based optimization (MOTLBO) algorithm is adopted to find a close representation of the Pareto optimal set rather than a single solution. As such, an optimal solution can be chosen as digital knowledge information. A new methodology based on a knowledge base representing and learning the operation environment, that is, skill digitization, is presented, which enables the 7-DOF manipulator to realize the rapid and continuous response skill. Simulation and practical testing results of a ping-pong robot validate the feasibility and effectiveness of the proposed approach, in which the online trajectory generation spends only around 1 ms.

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.

A multi-objective approach for the trajectory planning of a 7-DOF serial-parallel hybrid humanoid arm

Humanoid robots are an elusive long-term goal in robotics, and a humanoid arm is an essential actuator. Inspired by the motion characteristics of the human arm, a seven-degree-of-freedom (DOF) serial-parallel hybrid humanoid robotic arm is proposed. With the mechanism as an example, a solution of multi-objective trajectory planning is addressed using an indirect method to execute a point-to-point mission with faster time, lower energy and higher stability. First, to avoid abrupt changes of the joint angle, the path with a better joint-rate distribution is gained based on normalized Jacobian condition number. On the basis of this path, a multi-optimization model considering travelling time, energy consumption and torque fluctuation is formulated to plan the trajectory interpolated by quintic B-splines. The elitist non-dominated sorting genetic algorithm (NSGA-II) is used to address the model, and the optimal solution is determined by defining the weight value of the objective. Then, the complete dynamic model is obtained by combining equilibrium and deformation coordination equations. Finally, compared with another important trajectory planning methodology, the feasibility and effectiveness of the proposed methodology are validated through numerical simulations.

Multi-objective trajectory planning of humanoid robot using hybrid controller for multi-target problem in complex terrain

Humanoid robotics is an emerging area of interest in the current engineering research scenario, owing to its ability to impersonate human deportment and emulate various jobs. The given article emphasizes the development and implementation of a hybrid navigational controller to optimize the path length, energy demand, and time spent for accomplishing assigned tasks. The proposed navigational controller is developed by hybridizing the metaheuristic Improved Spider Monkey Optimization (ISMO) approach and the Regression Analysis (RA) approach. Various input parameters like obstacle and target locations are fed to the RA approach that implements a proper navigational direction selection. And it forwards to the SMO approach that is improved using piecewise B-Spline path smoother, which exercises further refinement of the output turning angle and smoothness of path around obstacles. Simulations and real-time experiments are undertaken using different controllers involving single robot systems, which shows the proposed controller’s superiority. An average improvement of 13.72% and 13.94% in path length against RA in simulation and experiment, respectively, and an average improvement of 7.59% and 7.5% in path length against ISMO in simulation and experiment, respectively, is obtained. It is further evaluated for navigation by implementing in a single robot having a multi-target problem. Multiple robot navigation has to deal with the self-collision situations that are solved by prioritizing the specified robot using the dining philosopher controller. It is implemented in the proposed controller for navigation of multiple robots to solve the conflict. Both scenarios are tested in the simulation environment and ratified in the experimental environment. Average deviation under 5% for path length and time spent for single robot navigation and multiple robot navigation is obtained, which shows a good agreement with each other. Energy efficiency test has been performed in contrast to default controller of NAO for various joints, and an average improvement of 8.16%, 5.9% and 20.57%, has been recorded in torque for ankle, knee and hip, respectively. Comparison is carried with an established navigational controller in a similar environmental setup shows an improvement of 8.6% and 10.365%, respectively, in path length and time spent. The results obtained from these setups prove the proposed hybrid controller to be robust, efficient and superior while performing path planning.

Multi-objective optimization of gearshift trajectory planning for multi-speed electric vehicles

Multi-speed transmissions can enhance the comprehensive performance of electric vehicles (EVs), while exhibiting potential to further improve their shift quality. In this study, a gearshift control architecture combined with multi-objective trajectory planning was proposed for EVs with two-speed transmission. Three indices, namely shifting duration, jerk and friction work, were selected as optimization objectives. Numerous iterations of multi-objective optimization were conducted using the Legendre pseudospectral method, which is an optimization algorithm with high convergence speed and low sensitivity to initial values. Optimization results were presented through a Pareto solution set which was then used as a reference by the control architecture for optimal trajectory selection in the transmission control unit. In a hardware-in-the-loop experiment, the control architecture was applied in a passenger car to run the New European Driving Cycle, demonstrating the effectiveness and feasibility of the developed multi-objective trajectory planning and gearshift control architecture.

Control system of 4-DOF palletizing robot based on improved R control multi-objective trajectory planning

To realize efficient palletizing robot trajectory planning and ensure ultimate robot control system universality and extensibility, the B-spline trajectory planning algorithm is used to establish a palletizing robot control system and the system is tested and analyzed. Simultaneously, to improve trajectory planning speeds, R control trajectory planning is used. Through improved algorithm design, a trajectory interpolation algorithm is established. The robot control system is based on R-dominated multi-objective trajectory planning. System stack function testing and system accuracy testing are conducted in a production environment. During palletizing function testing, the system’s single-step code packet time is stable at approximately 5.8 s and the average evolutionary algebra for each layer ranges between 32.49 and 45.66, which can save trajectory planning time. During system accuracy testing, the palletizing robot system’s repeated positioning accuracy is tested. The repeated positioning accuracy error is currently 10−1 mm and is mainly caused by friction and the machining process. By studying the control system of a four-degrees-of-freedom (4-DOF) palletizing robot based on the trajectory planning algorithm, the design predictions and effects are realized, thus providing a reference for more efficient future palletizing robot design. Although the working process still has some shortcomings, the research has major practical significance.

Multiobjective preimpact trajectory planning of space manipulator for self-assembling a heavy payload

To assemble a heavy payload to the spacecraft (free-floating base), the present study proposes a scheme of multiobjective trajectory planning for preimpact motion of redundant space manipulator (mounted on the base). Force impulse for self-assembly is derived as the function of joint angles/velocities, base pose, and impact direction. The trajectory planning problem is formulated as multiobjective optimization to minimize force impulse, base attitude disturbance, and energy consumption in the load-carrying process. A two-stage trajectory planning algorithm is proposed. To be specific, at the first stage, multiple desired configurations at the contact point are generated by position-level inverse kinematics with Newton–Raphson iterative method. At the second stage, joint trajectories satisfying joint angle limits and desired motion of the payload are parameterized by coefficients of sinusoidal polynomial functions. Multiobjective particle swarm optimization algorithm is adopted to solve the problem of multiobjective trajectory planning, and screening process is conducted to reserve nondominated solutions in limits of joint torques. The algorithm is implemented to a seven degrees of freedom space manipulator, and the effectiveness of the proposed method is verified by simulation results.

Minimum-time Trajectory Planning for Residual Vibration Suppression of Flexible Manipulator Carrying a Payload

For the purpose of eliminating residual vibration of a two-link flexible manipulator as well as minimizing time consumption, a scheme of multi-objective trajectory planning in joint space is proposed in this paper. Piecewise polynomial is applied to generate a smooth joint trajectory. Lagrangian approach and the assumed modes method is used to derive motion equations of FMs. Finally, Multi-objective particle swarm optimization (MOPSO) algorithm is implemented to solve time of each polynomial. The effectiveness of proposed algorithm is demonstrated by simulation results.

Self-adaptive MRPBIL-DE for 6D robot multiobjective trajectory planning

This work presents self-adaptive multiobjective real-code population-based incremental learning hybridised with differential evolution (MRPBIL-DE) for solving a 6D robot trajectory planning multiobjective optimisation problem. The objective functions are assigned to minimise travelling time and minimise maximum jerk taking place during motion while the constraints are velocity, acceleration and jerk constraints. A five order polynomial function is used to represent a motion equation while the motion path is divided into two sub-paths; from initial to intermediate positions and from intermediate to final positions. The optimiser is used to find a set of design variables including joint positions, velocities and accelerations at intermediate positions, moving time from the initial to intermediate positions, and that from the intermediate to final positions. Several multiobjective meta-heuristics (MOMHs) along with the proposed algorithm are used to solve the trajectory optimisation problem of robot manipulators while their performances are investigated. The results indicated that the proposed algorithm is effective and efficient for multiobjective robot trajectory planning optimisation problem. The results obtained from such a method are set as the baseline for further study of robot trajectory planning optimisation.

Method of Multi-objective Trajectory Planning of Parallel Mechanism Based on the Kinematics

Method of Multi-objective Trajectory Planning of Parallel Mechanism Based on the Kinematics

Data-driven multi-stage multi-objective motion planning of mobile robots, application to near minimum power fuzzy parking

In this paper, the problem of multi-objective trajectory planning is studied for a wheeled mobile robot (WMR) in a crowded environment using a hybrid data-driven neuro-fuzzy system. This approach is composed of two basic stages involving a hard computing through a state space detailed modeling of the system and then a data driven evolutionary neuro-fuzzy system is used for online planning. Typically, a first pre-processing step involves an offline planning generating a large dataset of multi-objective trajectories, optimizing a time-power criterion while including robot, task, and workspace constraints. The discrete augmented Lagrangian is implemented on a decoupled form of the robot dynamics to solve for the resulting non-linear multi-objective optimal control problem. The final state constraint is satisfied with a gradient projection technique. The outcomes of this pre-processing step allow building a genetic neuro-fuzzy inference system to learn and capture the robot multi-objective dynamic behavior. Once this system is trained and optimized, it is used in a generalization phase to achieve online planning. The approach was also applied to the near optimal power fuzzy parking problem. Simulation results showing the effectiveness of the proposal are presented and discussed.

Multi-Objective Trajectory Planning of FFSM Carrying a Heavy Payload

Aiming at carrying a heavy payload to a desired pose (including position and orientation), a multi-objective optimization-based approach for maximum-payload trajectory planning of free-floating space manipulators (FFSM) is proposed in this paper. The presented approach corresponds to two typical applications: (i) the manipulator joints attain the desired states; (ii) the inertial pose of the end-effector (pose with respect to the inertial frame) attains the desired values, for which a novel two-stage method is presented. Firstly, for the purpose of reducing computational complexity, dynamics equations are derived using a spatial operator algebra (SOA) method. Secondly, objective functions are defined according to the improvement of load-carrying capacity and pose requirements of the end-effector. Then, the joint trajectories are specified using sinusoidal polynomial functions. Finally, a multi-objective particle optimization (MOPSO) algorithm is employed to obtain a non-dominated solution set, during which process particles that do not satisfy the constraints are eliminated. Simulations are performed for a 7-DOF FFSM, considering three and five objectives for optimization in the two applications, respectively. The results demonstrate that the proposed approach can provide satisfactory joint trajectories and improve load-carrying capacity effectively.

2P1-L02 多目的軌道計画器を用いたロボットアームの舞踊動作の生成と実機評価(動作計画と制御の新展開)

2P1-L02 多目的軌道計画器を用いたロボットアームの舞踊動作の生成と実機評価(動作計画と制御の新展開)

Mobile Parallel Manipulators, Modelling and Data-Driven Motion Planning

This paper provides a kinematic and dynamic analysis of mobile parallel manipulators (MPM). The study is conducted on a composed multi-degree of freedom (DOF) parallel robot carried by a wheeled mobile platform. Both positional and differential kinematics problems for the hybrid structure are solved, and the redundancy problem is solved using joint limit secondary criterion-based generalized-pseudo-inverse. A minimum time trajectory parameterization is obtained via cycloidal profile to initialize multi-objective trajectory planning of the MPM. Considered objectives include time energy minimization redundancy resolution and singularity avoidance. Simulation results illustrating the effectiveness of the proposed approach are presented and discussed.