Optimal Motion Research Articles

Optimal Collaborative Motion Planning of Dual Boom Cranes for Transporting Payloads to Desired Positions and Attitudes

With the increasing demands of high-precision hoisting, a growing number of to-be-hoisted large-scale heavy payloads <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">not only</i> need accurate positioning transportation, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">but also</i> require specific attitude adjustments, which mostly relies on dual boom cranes (DBCs) in practice due to their powerful capability. To achieve effective non-horizontal payload hoisting, the two booms of DBCs should reach different positions while guaranteeing safety, high efficiency, and energy conservation, which makes coordinated boom motions particularly difficult. To this end, an optimal collaborative motion planning method for DBCs is proposed in this paper <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> any linearization, which realizes fast, accurate, and energy-saving payload transportation with swing suppression. To the best of our knowledge, the proposed method provides the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> solution for DBCs to transport payloads to the desired non-horizontal attitudes, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneously</i> achieves comprehensive optimization of multiple performance indicators, including transportation time, energy consumption, etc., on the premise of safety. On the theoretical side, novel collaborative auxiliary signal construction and parametric design guarantee the coordination of boom motions, and the solving process of optimal trajectories is simplified through elaborate convex optimization problem reformulation and analysis. At last, the effectiveness and adaptability of the proposed method are verified by hardware experiments under different working requirements.

Automatic joint motion planning of 9-DOF robot based on redundancy optimization for wheel hub polishing

Automatic joint motion planning is very important in robotic wheel hub polishing systems. Higher flexibility is achieved based on the joint configuration with multiple solutions, which means that the robot has kinematic redundancy for machining tasks. Redundant joints can be used to optimize the motion of the robot, but less research has been done on multi-dimensional redundant optimization. In this paper, a 6-axis robot with a 3-axis actuator is designed for wheel hub polishing. We propose an automatic joint motion planning method for a nine-axis industrial robot to achieve the shortest processing time. Firstly, offline programming is designed to generate paths for the complex surface of the hub. In order to reduce the machining path points on the surface of the hub, a improved Douglas-Peucker (DP) algorithm is proposed, which can take into account the change of the path point posture. Secondly, the Greedy Best First Search (GBFS) and Sine cosine algorithm (SCA) are combined to find the optimal joint motion efficiently. Moreover, we use nested SCA for comparison to test whether the combined algorithm can avoid local optima. Finally, the performance and computational efficiency of the method are validated in both simulation and real environments based on the hub surface.

Hydrodynamic performance of a penguin wing: Effect of feathering and flapping

The penguin is the fastest underwater swimmer among the wing-propelled diving birds. To figure out the mechanism for its excellent swimming, the hydrodynamic performance of a penguin wing is numerically investigated using an immersed boundary method with the incompressible flow solver. This study examines the effects of feathering, flapping, and Strouhal number (St) under preset motion. Results indicate that feathering is the primary contributor to thrust generation. The change in angle of attack (AoA) can qualitatively reflect the change in lift but not thrust. Therefore, a new variable, angle of thrust (AoT, αT), is introduced to effectively reflect the change of thrust across different kinematic parameters. Optimal feathering amplitude balances the decrease in AoA and the increase in feathering angle to achieve the highest AoT and thrust. Excessive feathering amplitude degrades the leading-edge vortex to shear layers, transforms the pressure side to the suction side, and ultimately causes negative thrust (drag). Spatial analysis of the thrust shows that the outer three-fifths of the wing are the primary source of thrust, contributing 85.4% of thrust generation at optimal feathering amplitude. Flapping amplitude has little impact on the optimal feathering amplitude. The optimal feathering amplitude increases linearly with the St number in the scope of examination, leading to larger thrust but lower swimming efficiency. Thus, a dimensionless number, Stm, is introduced to describe the optimal wing motion. This work provides new insights into the propulsion mechanism of aquatic swimmers with flapping–feathering wings and helps design novel bio-inspired aquatic vehicles.

Longitudinal wall motion during peristalsis and its effect on reflux

In this study, for the first time, we consider longitudinal motion of the walls during peristalsis in a distensible tube and how this affects backward (or retrograde) flow, i.e. peristaltic reflux. Building on the analytical model developed by Shapiro et al. (J. Fluid Mech., vol. 37, no. 4, 1969, pp. 799–825) based on lubrication theory, we model peristalsis as a two-dimensional infinite sinusoidal wavetrain. We develop an objective function with high mechanical pumping efficiency and low reflux to find optimal peristalsis conditions. We show that optimal wall longitudinal motion contributes substantially to limiting reflux during peristalsis. The results suggest that the optimal form of wall longitudinal velocity is a linear function of the wall transverse coordinate, moving forward with the wave when the tube is distended and retracting when contracted. Our results are in general agreement with clinical observations of ureteral peristalsis.

Multi-objective Optimal Motion Planning of Heavy-duty Assembly Robot for Large Spacecraft Entering Cabin

The space inside the space capsule such as the space station sky and the core module is narrow, the size of the depth is large, and the bearing points are scattered and weak, there are some difficulties in loading, large size, different shape, complicated interface, scattered position, difficult position and pose adjustment, high assembly risk, etc.. To solve these problems, a six-DOF heavy-duty assembly robot is proposed in this paper. The robot adopts the combination of linear drive and rotating joint to increase the working space and bearing capacity of the robot. The kinematics and dynamics analysis model of the robot is established, and the path planning is carried out by means of quintic non-uniform B-spline interpolation method, considering fully the space constraints of the assembled equipment, a multi-objective trajectory optimization model based on NSGA2 algorithm is established to obtain the Pareto optimal solution set with time, impact and energy consumption as optimization objectives, prove that the equipment can be efficient and smooth. Reliable installation, with less impact and less power consumption under multi-objective optimization analysis.

Subject specific optimal control of powered knee exoskeleton to assist human lifting tasks under controlled environment

AbstractWearable robots, sometimes known as exoskeletons, are incredible devices for improving human strength, reducing fatigue, and restoring impaired mobility. The control of powered exoskeletons, on the other hand, is still a challenge. This necessitates the development of a technique to simulate exoskeleton–wearer interaction. This study uses a two-dimensional human skeletal model with a powered knee exoskeleton to predict the optimal lifting motion and assistive torque. For lifting motion prediction, an inverse dynamics optimization formulation is utilized. In addition, the electromechanical dynamics of the exoskeleton DC motor are modeled in the lifting optimization formulation. The design variables are human joint angle profiles and exoskeleton motor current profiles. The human joint torque square is minimized subject to physical and lifting task constraints. Then, the lifting optimization problem is solved by the gradient-based sparse nonlinear optimizer (SNOPT). Furthermore, the optimal exoskeleton torque is implemented through a two-phase control strategy to provide optimal assistance in lifting. Experimental validations of the optimal control with 6 Nm and 16 Nm maximum assistive torque are presented. Both 6 Nm and 16 Nm maximum optimal assistance of the exoskeletons reduce the mean values of vastus lateralis, biceps femoris, and latissimus dorsi muscle activations compared to the lifting without the exoskeleton. However, the mean value of the vastus medialis activation is increased by a small amount for the exoskeleton case, although its peak value is reduced. Finally, the experimental results demonstrate that the proposed lifting optimization formulation and control strategy are promising for powered knee exoskeleton for lifting tasks.

Multi-robot motion planning for unit discs with revolving areas

We study the problem of motion planning for a collection of n labeled unit disc robots in a polygonal environment. We assume that the robots have revolving areas around their start and final positions: that each start and each final is contained in a radius 2 disc lying in the free space, not necessarily concentric with the start or final position, which is free from other start or final positions. This assumption allows a weakly-monotone motion plan, in which robots move according to an ordering as follows: during the turn of a robot R in the ordering, it moves fully from its start to final position, while other robots do not leave their revolving areas. As R passes through a revolving area, a robot R′ that is inside this area may move within the revolving area to avoid a collision. Notwithstanding the existence of a motion plan, we show that minimizing the total traveled distance in this setting, specifically even when the motion plan is restricted to be weakly-monotone, is APX-hard, ruling out any polynomial-time (1+ε)-approximation algorithm.On the positive side, we present the first constant-factor approximation algorithm for computing a feasible weakly-monotone motion plan. The total distance traveled by the robots is within an O(1) factor of that of the optimal motion plan, which need not be weakly monotone. Our algorithm extends to an online setting in which the polygonal environment is fixed but the initial and final positions of robots are specified in an online manner. Finally, we observe that the overhead in the overall cost that we add while editing the paths to avoid robot-robot collision can vary significantly depending on the ordering we chose. Finding the best ordering in this respect is known to be NP-hard, and we provide a polynomial time O(log⁡nlog⁡log⁡n)-approximation algorithm for this problem.

Toward certifiable optimal motion planning for medical steerable needles

Medical steerable needles can follow 3D curvilinear trajectories to avoid anatomical obstacles and reach clinically significant targets inside the human body. Automating steerable needle procedures can enable physicians and patients to harness the full potential of steerable needles by maximally leveraging their steerability to safely and accurately reach targets for medical procedures such as biopsies. For the automation of medical procedures to be clinically accepted, it is critical from a patient care, safety, and regulatory perspective to certify the correctness and effectiveness of the planning algorithms involved in procedure automation. In this paper, we take an important step toward creating a certifiable optimal planner for steerable needles. We present an efficient, resolution-complete motion planner for steerable needles based on a novel adaptation of multi-resolution planning. This is the first motion planner for steerable needles that guarantees to compute in finite time an obstacle-avoiding plan (or notify the user that no such plan exists), under clinically appropriate assumptions. Based on this planner, we then develop the first resolution-optimal motion planner for steerable needles that further provides theoretical guarantees on the quality of the computed motion plan, that is, global optimality, in finite time. Compared to state-of-the-art steerable needle motion planners, we demonstrate with clinically realistic simulations that our planners not only provide theoretical guarantees but also have higher success rates, have lower computation times, and result in higher quality plans.

Evaluation of the optimal ground motion intensity measure in the prediction of the seismic vulnerability of earth dams

The large majority of existing earth dams were designed with old standards, which often accounted for the effects of earthquakes in a simplified manner. As a result, seismic re-evaluation of these structures is now becoming increasingly important for dam owners. The seismic performance of earth dams can be evaluated at different levels of resolution, typically ranging from simple sliding block analysis, to the use of advanced numerical models. Seismic inputs for these models are typically chosen using code-based or site-specific probabilistic seismic hazard analysis (PSHA). In this study, we analyze the seismic vulnerability of two major earth dams located in Southern Italy, a seismically active area. The two dam systems have different geotechnical characteristics: one of them is founded on potentially liquefiable materials, whereas the other one is not susceptible to liquefaction. Our analyses are based on finite difference numerical simulations using both simplified and advanced constitutive models. Seismic vulnerability of both dams is analyzed by means of analytical fragility functions for various damage mechanisms and ground motion intensity measures (IMs). Such fragility functions are based on nonlinear deformation analyses within the multiple stripe analysis framework. We analyze efficiency and predictability of various IMs in predicting different damage levels and mechanisms. We show that the cumulative absolute velocity is overall the optimal IM in predicting vulnerability of both earth dams. We also analyze the relative importance of PSHA inputs (i.e. alternative ground motion and earthquake rupture forecast models; GMMs and ERFMs, respectively) and numerical models (simplified vs advanced) in the seismic analysis of earth dams by means of tornado diagrams. We show that the choice of GMMs and ERFMs is always more important than that of the constitutive model. However, for dams prone to liquefaction, the choice of the constitutive model has a higher importance than for non-liquefiable earth dams.

Trajectory planning for mechanical systems in the presence of dynamic obstacles

This paper deals with an optimal motion planning method for mechanical systems subjected to velocity and acceleration constraints in the presence of dynamical geometric obstacles. Using a state parametrization method based on time polynomials the trajectory planning problem is reformulated as a constrained nonlinear optimization problem which is solved using a numerical optimization toolbox. Quadrotor motion planning in the horizontal plane is considered as an illustration example.

Multi-stage warm started optimal motion planning for over-actuated mobile platforms

This work presents a computationally lightweight motion planner for over-actuated platforms. For this purpose, a general state-space model for mobile platforms with several kinematic chains is defined, which considers dynamics, nonlinearities and constraints. The proposed motion planner is based on a sequential multi-stage approach that takes advantage of the warm start on each step. Firstly, a globally optimal and smooth 2D/3D trajectory is generated using the Fast Marching Method. This trajectory is fed as a warm start to a sequential linear quadratic regulator that is able to generate an optimal motion plan without constraints for all the platform actuators. Finally, a feasible motion plan is generated considering the constraints defined in the model. In this respect, the sequential linear quadratic regulator is employed again, taking the previously generated unconstrained motion plan as a warm start. The motion planner has been deployed into the Exomars Testing Rover of the European Space Agency. This rover is an Ackermann-capable planetary exploration testbed that is equipped with a robotic arm. Several experiments were carried out demonstrating that the proposed approach speeds up the computation time and increases the success ratio for a martian sample retrieval mission, which can be considered as a representative use case of goal-constrained trajectory generation for an over-actuated mobile platform.

Control parameter optimization based trajectory design of underwater gliders executing underwater fixed-point exploration missions

Underwater gliders are well known as a type of autonomous observation platform of ocean phenomena, which can achieve space motion by low energy consumption. In this paper, we study motion trajectory design methods of underwater gliders executing underwater fixed-point exploration missions. First, performance analysis models of an underwater glider are established, including the dynamic model and the energy consumption model. Then, according to the positions of target exploration points, we divide underwater fixed-point exploration missions into three categories, namely, the short voyage range exploration mission, the moderate voyage range exploration mission, and the long voyage range exploration mission. Based on the glider motion modes of in-profile gliding and spiral gliding, two trajectory design methods are proposed for the above three categories of exploration missions. To achieve the full coverage of target exploration points, we present a net buoyancy compensation strategy of the glider carrying out the spiral motion. Based on the surrogate model technology and a multi-objective optimization algorithm, the optimization method of the glider control parameters is further proposed to design the optimal motion trajectory. Finally, the trajectory design methods are validated by numerical examples. This study can provide certain guidance for the actual application of underwater gliders.

A general motion control framework for an autonomous underwater vehicle through deep reinforcement learning and disturbance observers

This paper investigates the application of deep reinforcement learning (RL) in the motion control for an autonomous underwater vehicle (AUV), and proposes a novel general motion control framework which separates training and deployment. Firstly, the state space, action space, and reward function are customized under the condition of ensuring generality for various motion control tasks. Next, in order to efficiently learn the optimal motion control policy in the case that the AUV model is imprecise and there are unknown external disturbances, a virtual AUV model composed of the known and determined items of an actual AUV is put forward and a simulation training method is developed on this basis. Then, in the given deployment method, three independent extended state observers (ESOs) are designed to deal with the unknown items in different directions, and the final controller is obtained by compensating the estimated value of ESOs into the output of the optimal motion control policy obtained through simulation training. Finally, soft actor-critic is chosen as deep RL algorithm of the framework, and the generality and effectiveness of the proposed method are verified in four different AUV motion control tasks.

Inverse kinematics and planning/control co-design method of redundant manipulator for precision operation: Design and experiments

In this paper, we proposed two novel algorithms to improve the operating accuracy and operating efficiency of the 7-DoF redundant manipulator. Firstly, an improved adaptive particle swarm optimization (APSO) algorithm is proposed to improve the solution precision and solution speed of the inverse kinematics of the 7-DoF redundant manipulator by introducing the probability transfer mechanism and the quality evaluation criterion. Meanwhile, the velocity directional manipulability measure (VDM) is introduced as an optimization index to search for the singular-free configuration with the optimal motion performance. Then, in order to further improve the execution efficiency and stability of the 7-DoF redundant manipulator, a novel planning/control co-design (PCC) algorithm is proposed based on the Dynamic Movement Primitives (DMPs-PCC), which ensures that the motion planner and actuator of the 7-DoF redundant manipulator can work synchronously, while optimizing the velocity and acceleration profiles of each joint of the manipulator in the operating process. Finally, an experimental platform is established based on the Robot Operating System (ROS), and the effectiveness and reliability of the two novel algorithms are demonstrated by the simulations and prototype experiments.

An optimal motion path planning control of a robotic manipulator based on the hybrid PI-sliding mode controller

This paper proposes a hybrid proportional-integral (PI-sliding) mode controller to improve and adjust the point-to-point path planning of a three-link robotic arm with three degrees of freedom. The main objectives of the proposed control unit are to control the tracking process to reach the desired path handle the outgoing vibrations, and dampen them in the links of the robotic arm during its movement to ensure accuracy in completing the work. Seventh-degree polynomial paths represented the segments of locomotion connecting the first, middle, and last points at the combined space through predefined route points via minimal travel time. While not exceeding a predetermined maximum torque, without hitting any obstacle in the robot's workspace. The results showed that the proposed control design provides a robust control performance and fast response corresponding with conventional sliding mode controller (SMC) and PI controller. Then the outcomes provide the best results for the demanded mission according to the whished intakes with minimal error. The system equations are solved using the techniques available in MATLAB software then the results of the model are validated by the results of simulations.

다자유도 갠트리형 용접로봇 시스템의 최적모션 생성을 위한 벡터 방정식 알고리즘 기초 연구

This paper is a basic study for the development of a simulator algorithm to generate optimal robot motion and path planning for a multi-D.O.F(Degree of Freedom) gantry-type welding robot system. The main idea of the simulator algorithm is to utilize vector equations to define the relationship between each frame derived by forward kinematics. Eight objective functions were defined using vector equations that define the relationship between frames, and each was formulated as an optimization problem. For the optimization problem, the optimal value was derived through optimizers such as SQP (Sequential Quadratic Problem), Active-set, and fgoalattain, and motion and error range were simulated by putting the derived control variables into a forward kinematics simulator. If a specific motion can be created through various formalized optimization problems, it is expected that it can be used as a policy for reinforcement learning in the future.

Optimal synthesis of walking robot leg

Using a straight-line generating mechanism for a walking robot leg has several advantages over traditional bio-inspired leg designs including energy efficiency and simplicity of control system. As a walking robot propeller, we proposed a six-link mechanism based on our design of lambda-type mechanism, with an output link, which performs a rectilinear and translational movement. This ensures an unlimited range of foot adaptation on irregularities of the supporting surface. A new analytical method of mechanism synthesis is developed based on least square approximation, and its numerical implementation is presented. Due to minimizing the deviation directly from the desired output motion, the method does not suffer from so-called “branching defect” and allows synthesis of the mechanism with desired transmission angle. Improving the transmission angle ensures higher efficiency (therefore, lower power consumption) of the mechanism. A walking robot was developed using the optimal leg design which has high accuracy, optimum motion transfer, and step-cycle parameter which were achieved by multicriteria optimization based on the proposed synthesis method.

Energy-Efficient Resource Allocation for Dual-NOMA-UAV Assisted Internet of Things

Employing unmanned aerial vehicles (UAVs) characterized by low cost, high maneuverability, and on-demand deployment as aerial base stations (BSs) of Internet of Things (IoT) can guarantee communication performance in the absence of terrestrial BSs. However, the limited energy budget of UAV constrains its development. In this paper, a dual-UAV-assisted IoT using non-orthogonal multiple access (NOMA) is proposed to improve IoT capacity. To reduce energy consumption of the UAVs while ensuring a certain throughput, a joint resource optimization problem of communication scheduling, transmit power and motion parameters of UAVs is formulated to maximize energy efficiency of UAVs. To solve the proposed non-convex optimization problem, we present an alternating iterative optimization algorithm to alternately optimize three sub-problems: communication scheduling optimization, UAV transmit power optimization and UAV motion parameters optimization, each of which can be converted into convex optimization and solved using Lagrange multiplier method, subgradient descent method and successive convex approximation (SCA). The numerical results show that optimizing UAV motion parameters can effectively improve energy efficiency of UAVs, and the proposed dual-NOMA-UAV assisted IoT can achieve higher energy efficiency than the orthogonal multiple access (OMA)-UAV assisted IoT.

Analysis of the punch motion curve for the springback of U-shaped sheet metal

Servo presses achieve high formability by using different punch motion curves, thereby increasing their applicability in conventional processing fields. In this study, the punch motion curves of servo presses were optimized, and the effects of punch motion curves on the springback of U-shaped sheet metal were explored. Subsequently, the optimal punch motion curve was determined, and the springback effect after processing was investigated. Different punch motion curves were proposed and simulated for comparison with the results of conventional methods, and the equivalent stress values obtained using different motion curves and mold angles were analyzed. DEFORM software was used to conduct simulations to determine the differences between processing methods. In addition, the spring-go, springback, load–stroke characteristics, and stress and strain distributions of U-shaped sheet metal were investigated. The conventional motion curve resulted in springback, stress, strain, and required processing force higher than those achieved by the curves proposed in this study. The smaller the movement difference in the motion curve of the servo press was, the lower the springback, stress, and strain were. These results indicate that the punch motion curves obtained for different types of processing can serve as a reference for selecting appropriate parameter values for servo presses.

Optimal Motion of a Rolling Stock Fleet Under Traction Power System Constraints

The operators of the railway industry [i.e., traction system operator (TSO) and railway system operator (RSO)] are currently involved in a major process of energy transition. Aimed at improving both environmental sustainability and energy efficiency, technological infrastructures are being updated and new operating solutions are studied. Moreover, the business opportunities offered by the new rail market are forcing operators to search for power quality solutions. In this article, an efficiency strategy is proposed for optimally moving a fleet of trains while taking power quality indices into account. A method to relate the traction power requirements to the electrical variables of the railway infrastructure is formulated in terms of the power flow approach. Our numerical simulations focus on the real case of Metro Line 1 in the southern Italian city of Naples. The energy problem of moving the trains on the track is solved by including a set of constraints at the point of common interaction between railway market operators. Specifically, repetitive train starts and their speed profiles are optimally managed in terms of power requirements at traction power substations (TPSs) using power quality constraints. This strategy allows improvements in energy efficiency without compromising the quality of the railway service.