Energy-optimal Motion Research Articles

Energy optimal path planning for wheeled mobile robots with circular obstacle

AbstractThe energy optimal motion planning algorithm for a differential drive robot with a circular obstacle in the maneuver space is introduced in this article. Rather than the traditional unicycle model, a non‐canonical state space model of the kinematics of a wheeled mobile robot is used to formulate the optimal control problem. The necessary conditions for optimality are formally derived using calculus of variations, resulting in constraints for the costates when the inequality constraint become active, revealing that the controls are required to be continuous. The optimality conditions permit decomposing the motion planning problem in two independent segments: prior to and after activation of the inequality constraints. Analytical expressions for the evolving states and control are found to be a function of Jacobi elliptic functions, permitting reducing the optimal control problem to a root‐finding problem. A comprehensive parametric study is included to demonstrate the impact on the optimal trajectories by varying the radius of the obstacle. The study shows that there are three distinct maneuver strategies with respect to the size of the obstacle. Furthermore, by including entering and exit time as optimization variables, a methodology for generalizing the development to any given motion scenario is developed and numerically illustrated.

Coordinated Ship Welding with Optimal Lazy Robot Ratio and Energy Consumption via Reinforcement Learning

Ship welding is a crucial part of ship building, requiring higher levels of robot coordination and working efficiency than ever before. To this end, this paper studies the coordinated ship-welding task, which involves multi-robot welding of multiple weld lines consisting of synchronous ones to be executed by a pair of robots and normal ones that can be executed by one robot. To evaluate working efficiency, the objectives of optimal lazy robot ratio and energy consumption were considered, which are tackled by the proposed dynamic Kuhn–Munkres-based model-free policy gradient (DKM-MFPG) reinforcement learning algorithm. In DKM-MFPG, a dynamic Kuhn–Munkres (DKM) dispatcher is designed based on weld line and co-welding robot position information obtained by the wireless sensors, such that robots always have dispatched weld lines in real-time and the lazy robot ratio is 0. Simultaneously, a model-free policy gradient (MFPG) based on reinforcement learning is designed to achieve the energy-optimal motion control for all robots. The optimal lazy robot ratio of the DKM dispatcher and the network convergence of MFPG are theoretically analyzed. Furthermore, the performance of DKM-MFPG is simulated with variant settings of welding scenarios and compared with baseline optimization methods. Compared to the four baselines, DKM-MFPG owns a slight performance advantage within 1% on energy consumption and reduces the average lazy robot ratio by 11.30%, 10.99%, 8.27%, and 10.39%.

Combining optimization and dynamic movement primitives for planning energy optimal forestry crane motions

Forestry cranes are an important tool for safe and efficient timber harvesting with forestry machines. However, their complex manual control often led to inefficiencies and excessive energy usage, due to the many joysticks and buttons that must be used in a precise sequence to perform efficient movements. To address this, the industry is increasingly turning to partial automation, making manual control more intuitive for the operator and, consequently, achieving improvements in energy efficiency. This article introduces a novel approach to energy-optimal motion planning that can be used along with a feedback control system to automate crane motions, taking over portions of the operator’s work. Our method combines dynamic movement primitives (DMPs) and an energy-optimization algorithm. DMPs is a machine learning technique for motion planning based on human demonstrations, while the optimization algorithm exploits the crane’s redundancy to find energy-optimal trajectories. Simulation results show that DMPs can replicate human-like controlled motions with a 25% reduction in energy consumption. However, our energy optimization algorithm shows improvements of over 40%, providing substantial energy savings and a promising pathway towards environmentally friendly partially automated machines.

Multimethod computing technology for searching energy-optimal motion modes of electric rolling stock of railways

The article is devoted to the problem of finding energy-optimal modes of movement of electric rolling stock of railways, considered as a set of problems of finding a global extremum of a functional defined on a set of logical-dynamic system (LDS) movement trajectories that are acceptable under operating conditions, and a structural-parametric synthesis of the LDS control strategy and optimization of its parameters based on random search methods, swarm intelligence, evolutionary algorithms and multi-agent models. A multi-method technology for optimizing the modes of train movement according to the criterion of minimum energy consumption, and software and algorithmic support based on the original multi-agent evolutionary-swarm method for synthesizing the optimal-terminal control of multi-mode moving objects developed by the author are proposed. The specified computing technology includes the following stages: formation of a set of promising control strategies; their optimization and recombination based on the evolutionary genetic algorithm; finding the global extremum of the functional using parametric optimization of the solutions identified at the previous stages using the modified particle swarm method. The computational experiments performed with the simulation model of train movement showed that when a sufficiently large number of options for control strategies are generated at the first stage, the algorithm converges to the global extremum of the functional.

Energy-optimal motion planning of underwater gliders accounting for seabed topography and ocean currents

The sawtooth gliding profile of underwater gliders can be determined by motion parameters, including yaw angles, diving depths, and pitch angles. Planning a series of motion parameters can generate a 3D gliding path that helps underwater gliders adapt to ocean currents and seabed topography. This paper presents an offline motion planning method for underwater gliders. By optimizing each gliding profile’s motion parameters, i.e., yaw angle, diving depth, and pitch angle, the seabed topography and ocean currents can be taken into account to generate an energy-optimal 3D path. To solve the motion planning problem, we propose a well-designed encoding method and a piecewise fitness function, which are used with the JADE algorithm to determine the optimal motion parameters. Experimental results on real seabed topography demonstrate that our method significantly reduces energy consumption and has better adaptability to complex ocean environments than traditional underwater glider path planning methods.

Optimal motion planning of hopping robot based on pseudospectral method during flight phase

The energy optimal motion planning of a hopping robot with three links is investigated in the flight phase. Firstly, the conservation equation of angular momentum of the hopping robot in the flight phase is established which is a nonholonomic constraint. Then the energy consumption of the robot in the flight phase is selected as the optimization goal. Given the initial and terminal positions, the Gaussian pseudospectrum method is used to solve the optimal control problem. The simulation results show that the initial angular momentum has a great influence on the performance of the hopping robot. With the zero initial angular momentum, although the flight time can be selected arbitrarily, the greater the flight time, the smaller the energy consumption, the force required by the robot is greater. Thus, it is necessary to select an appropriate value.

Energy optimal motion planning of a 14-DOF biped robot on 3D terrain using a new speed function incorporating biped dynamics and terrain geometry

AbstractIn this paper, a new method is proposed to find a feasible energy-efficient path between an initial point and goal point on uneven terrain and then to optimally traverse the path. The path is planned by integrating the geometric features of the uneven terrain and the biped robot dynamics. This integrated information of biped dynamics and associated cost (energy) for moving toward the goal point is used to define the value of a new speed function at each point on the discretized surface of the terrain. The value is stored as a matrix called the dynamic transport cost (DTC). The path is obtained by solving the Eikonal equation numerically by fast marching method (FMM) on an orthogonal grid, by using the information stored in the DTC matrix. One step of walk on uneven terrain is characterized by 10 footstep parameters (FSPs); these FSPs represent the position of swinging foot at the starting and ending time of the walk, orientation, and state (left or right) of support foot. A walking dataset was created for different walking conditions (FSPs), which the biped robot is likely to encounter when it has to walk on the uneven terrain. The corresponding energy optimal hip and foot trajectory parameters (HFTPs) are obtained by optimization using a genetic algorithm (GA). The created walk dataset is generalized by training a feedforward neural network (NN) using the scaled conjugate gradient (SCG) algorithm. The Foot placement planner gives a sequence of foot positions and orientations along the obtained path, which is followed by the biped robot by generating real-time optimal foot and hip trajectories using the learned NN. Simulation results on different types of uneven terrains validate the proposed method.

Energy-Optimal Motion Trajectory of an Omni-Directional Mecanum-Wheeled Robot via Polynomial Functions

SUMMARYThe Mecanum wheel is one of the practical omni-directional wheel designs in industry, especially for heavy-duty tasks in a confined floor. An issue with Mecanum-wheeled robots is inefficient use of energy. In this study, the robotic motion trajectories are optimized to minimize the energy consumption, where a robotic path is expressed in polynomial functions passing through a given set of via points, and a genetic algorithm is used to find the polynomial’s coefficients being decision variables. To attempt a further reduction in the energy consumption, the via points are also taken as decision variables for the optimization. Both simulations and experiments are conducted, and the results show that the optimized trajectories result in a significant reduction in energy consumption, which can be further lowered when the via points become decision variables. It is also found that the higher the order of the polynomials the larger the reduction in the energy consumption.

Energy Modeling and Experimental Validation of Four-Wheel Mecanum Mobile Robots for Energy-Optimal Motion Control

Four-wheel Mecanum mobile robots (FWMRs) are widely used in transportation because of their omnidirectional mobility. However, the FWMR trades off energy efficiency for flexibility. To efficiently predict the energy consumption of the robot movement processes, this paper proposes a power consumption model for the omnidirectional movement of an FWMR. A power consumption model is of great significance for reducing the power consumption, motion control, and path planning of robots. However, FWMRs are highly maneuverable, meaning their control is complicated and their energy modeling is extremely complex. The speed, distance, path, and power consumption of the robot can vary greatly depending on the control method. This energy model was mathematically implemented in MATLAB and validated by our laboratory’s Mecanum wheel robot. The prediction accuracy of the model was over 95% through simulation and experimental verification.

Simulation-based comparison between two crane-bunk systems for loading work when considering energy-optimal motion planning

ABSTRACTPerforming work for extended periods of time while using the lowest amount of resources is an important aspect for productivity in many industries. In forestry, the productivity of a forwarder is seen as the volume of material it can extract to a roadside landing in a certain amount of time, where the process of loading and unloading logs represents a large part of the work. During this process, the esnergy consumed by the machine is directly related to the speed of the crane. Thus, increasing productivity implies increasing the operating velocity of cranes. But according to current design of forestry cranes, this conversely leads to an undesired increase in consumption of resources (e.g. fuel). A second method is to alter the machine’s design, such as rotating the log bunk. This article considers both methods through a simulation-based comparison aiming to evaluate the energy consumption of two crane-bunk systems when loading. The first simulation system considers a forestry crane with a fixed log bunk (forwarder-like crane). The second simulation system takes into account a forestry crane and a rotating log bunk (harwarder-like crane). The analysis presented considers the fundamental mathematics required to analyze the dynamics of forestry cranes and the principles required to plan energy-optimal motions. The simulation results show that energy savings of 43% to 61% can be obtained by determining energy-optimal motions and using a harwarder-like crane architecture.

Optimization of the energy consumption of industrial robots for automatic code generation

At present, energy consumption strongly affects the financial payback period of industrial robots, as well as the related manufacturing process sustainability. Henceforth, during both design and manufacturing management stages, it becomes crucial to assess and optimize the overall energy efficiency of a robotic cell by means of digital manufacturing tools. In practice, robotic plant designers and managers should be able to provide accurate decisions also aimed at the energy optimization of the robotic processes. The strong scientific and industrial relevance of the topic has led to the development of many solutions but, unfortunately, state of the art industrial manipulators are equipped with closed controllers, which heavily limit the feasibility and performance of most of the proposed approaches. In light of the aforementioned considerations, the present paper presents a novel simulation tool, seamlessly interfaced with current robot offline programming tools used in industrial practices, which allows to automatically compute energy-optimal motion parameters, thus reducing the robot energy consumption, while also keeping the same productivity and manufacturing quality. The main advantage of this method, as compared to other optimization routines that are not conceived for direct integration with commercial industrial manipulators, is that the computed parameters are the same ones settable in the robot control codes, so that the results can automatically generate ready-to-use energy-optimal robot code. Experimental tests, performed on a KUKA Quantec KR210 R2700 prime industrial robot, have confirmed the effectiveness of the method and engineering tool.

Energy-Optimal Collision-Free Motion Planning for Multiaxis Motion Systems: An Alternating Quadratic Programming Approach

This work investigates energy-optimal motion planning for a class of multiaxis motion systems where the system dynamics are linear time-invariant and decoupled in each axis. Solving the problem in a reliable and efficient manner remains challenging owing to the presence of various constraints on control and states, nonconvexity in its cost function, and obstacles. This paper shows how the cost function can be convexified by considering the system dynamics, while decomposing decision variables to obtain a convex representation of collision avoidance constraints. With the convexified cost function and constraints, the original problem is decomposed into two quadratic programming (QP) problems. An alternating quadratic programming (AQP) algorithm is proposed to solve both the QP problems alternatingly and iteratively till convergence. Requiring an initial feasible trajectory as a guess, AQP necessarily converges to an energy-efficient solution that is homotopic to the initial guess. Under certain circumstances, AQP is guaranteed to produce a local optimum. Simulation demonstrates that AQP is computationally efficient and reliable while claiming comparable energy saving as the mixed-integer QP approach. Note to Practitioners —This paper presents an energy-optimal motion planning algorithm that can be easily implemented on a class of multiaxis motion systems. Main advantages of the proposed algorithm are: 1) it produces a trajectory resulting in lower but comparable energy efficiency as the global optimum; 2) it is guaranteed to provide an energy-efficient and constraint-compliant trajectory, and thus is reliable; 3) it requires a low computational load and can be deployed on a wide range of applications; and 4) its implementation is straightforward to any engineer with basic knowledge of numerical methods.

Energy-optimal motion planning of a biped pole-climbing robot with kinodynamic constraints

PurposeApplications of robotic systems in agriculture, forestry and high-altitude work will enter a new and huge stage in the near future. For these application fields, climbing robots have attracted much attention and have become one central topic in robotic research. The purpose of this paper is to propose an energy-optimal motion planning method for climbing robots that are applied in an outdoor environment.Design/methodology/approachFirst, a self-designed climbing robot named Climbot is briefly introduced. Then, an energy-optimal motion planning method is proposed for Climbot with simultaneous consideration of kinematic constraints and dynamic constraints. To decrease computing complexity, an acceleration continuous trajectory planner and a path planner based on spatial continuous curve are designed. Simulation and experimental results indicate that this method can search an energy-optimal path effectively.FindingsClimbot can evidently reduce energy consumption when it moves along the energy-optimal path derived by the method used in this paper.Research limitations/implicationsOnly one step climbing motion planning is considered in this method.Practical implicationsWith the proposed motion planning method, climbing robots applied in an outdoor environment can commit more missions with limit power supply. In addition, it is also proved that this motion planning method is effective in a complicated obstacle environment with collision-free constraint.Originality/valueThe main contribution of this paper is that it establishes a two-planner system to solve the complex motion planning problem with kinodynamic constraints.

Methods to Decrease Power Consumption in Industrial Robotics

This paper shows the possibilities and methods of decreasing power consumption in industrial robotic systems.The authors characterize different mechanical procedures to reduce the consumption by using alternative types of robots. In this context, one of the approaches not requiring changes in the existing hardware (such as robots or transporters) is to program the parameters of a robot with an energy optimal motion or trajectory. This option can be employed only in point-to-point movements and is not applicable in all types of production.The robot idling and homing times depend on the actual process; however, simple speed and acceleration adjustment can minimize the idling time and lower the energy consumption. Multiple programs are available for simulating robot behavior, but only a small portion of these can provide energy consumption data to the programmer. Yet, if this function is implemented, it usually remains unused. The present article outlines the operational potential of these simulators in applications designed to project robot parameters ensuring optimal energy consumption. A significant part of industrial robots or robotic systems perform only lift-and-drop tasks; here, the energy generated during a downward motion can cover the peaks occurring when, for example, a robot accelerates with a heavy object. Thus, there is a viable possibility of recuperating the discussed type of energy.

A novel model-based heuristic for energy-optimal motion planning for automated driving

Predictive motion planning is the key to achieve energy-efficient driving, which is one of the main benefits of automated driving. Researchers have been studying the planning of velocity trajectories, a simpler form of motion planning, for over a decade now and many different methods are available. Dynamic programming has shown to be the most common choice due to its numerical background and ability to include nonlinear constraints and models. Although planning of an optimal trajectory is done in a systematic way, dynamic programming does not use any knowledge about the considered problem to guide the exploration and therefore explores all possible trajectories.A⁎ is a search algorithm which enables using knowledge about the problem to guide the exploration to the most promising solutions first. Knowledge has to be represented in a form of a heuristic function, which gives an optimistic estimate of cost for transitioning to the final state, which is not a straightforward task. This paper presents a novel heuristics incorporating air drag and auxiliary power as well as operational costs of the vehicle, besides kinetic and potential energy and rolling resistance known in the literature. Furthermore, optimal cruising velocity, which depends on vehicle aerodynamic properties and auxiliary power, is derived. Results are compared for different variants of heuristic functions and dynamic programming as well.

A Simulation Tool for Computing Energy Optimal Motion Parameters of Industrial Robots

This paper presents a novel robot simulation tool, fully interfaced with a common Robot Offline Programming software (i.e. Delmia Robotics), which allows to automatically compute energy-optimal motion parameters, for a given end-effector path, by tuning the joint speed/acceleration during point-to-point motions whenever allowed by the manufacturing constraints. The main advantage of this method, as compared to other optimization routines that are not conceived for a seamless integration with commercial industrial manipulators, is that the computed parameters are the same required by the robot controls, so that the results can generate ready-to-use energy-optimal robot code.

Energy-optimal motions for Servo-Systems: A comparison of spline interpolants and performance indexes using a CAD-based approach

Position-controlled Servo-Systems (SeSs) may be envisaged as a key technology to keep the manufacturing industry at the leading edge. Unfortunately, based on the current state-of-the-art, these mechatronic devices are well performing but intrinsically energy intensive, thus compromising the overall system sustainability. Therefore, traditional design and optimization paradigms, previously focused on productivity and quality improvement, should be critically reviewed so as to introduce energy efficiency as an optimality criterion alongside with the global production rate. In particular, focusing on mono-actuator systems with one degree-of-freedom, among the several design factors that can influence the SeS overall performance, the end-effector motion law can be easily modified without either hardware substitution or further investments. In this context, the purpose of the present paper is twofold. On one side, an effective method for the quick set-up of an energy-predictive CAD-based virtual prototype is discussed. In parallel, an energy comparison of some commonly employed Point-To-Point motions and optimization cost functions is provided. For what concerns the trajectory interpolation scheme, a standard optimization problem based on the aforementioned virtual model is solved by means of either algebraic or trigonometric splines. For what concerns the optimality criterion, either the system energy consumption or the root-means square value of the actuator torque are taken into account. In general, torque-based approaches, which may be preferred since they do not require a full knowledge of the SeS electrical parameters, can be effectively employed only when friction effects are negligible as compared to purely inertial loads. In parallel, cubic algebraic splines outperform other types of trajectories, although losing continuity of the resulting jerk profile. HighlightsDescription of a CAD-based modeling approach for Position-Controlled Servomechanism.Comparison of various techniques for trajectory planning.Torque-based methods compared to energy-based methods.Results on a simulation case study: a slider crank mechanism connected to a PMSM.

Energy-Optimal Motion Planning for Multiple Robotic Vehicles With Collision Avoidance

We propose a numerical algorithm for multiple-vehicle motion planning that explicitly takes into account the vehicle dynamics, temporal and spatial specifications, and energy-related requirements. As a motivating example, we consider the case where a group of vehicles is tasked to reach a number of target points at the same time ( simultaneous arrival problem ) without colliding among themselves and with obstacles, subject to the requirement that the overall energy required for vehicle motion be minimized. With the theoretical setup adopted, the vehicle dynamics are explicitly taken into account at the planning level. This paper formulates the problem of multiple-vehicle motion planning in a rigorous mathematical setting, describes the optimization algorithm used to solve it, and discusses the key implementation details. The efficacy of the method is illustrated through numerical examples for the simultaneous arrival problem. The initial guess to start the optimization procedure is obtained from simple geometrical considerations, e.g., by joining the desired initial and final positions of the vehicles via straight lines. Even though the initial trajectories thus obtained may result in intervehicle and vehicle/obstacle collisions, we show that the optimization procedure that we employ in this paper will generate collision-free trajectories that also minimize the overall energy spent by each vehicle and meet the required temporal and spatial constraints. The method developed applies to a very general class of vehicles; however, for clarity of exposition, we adopt as an illustrative example the case of wheeled robots.

Sensory Agreement Guides Kinetic Energy Optimization of Arm Movements during Object Manipulation.

The laws of physics establish the energetic efficiency of our movements. In some cases, like locomotion, the mechanics of the body dominate in determining the energetically optimal course of action. In other tasks, such as manipulation, energetic costs depend critically upon the variable properties of objects in the environment. Can the brain identify and follow energy-optimal motions when these motions require moving along unfamiliar trajectories? What feedback information is required for such optimal behavior to occur? To answer these questions, we asked participants to move their dominant hand between different positions while holding a virtual mechanical system with complex dynamics (a planar double pendulum). In this task, trajectories of minimum kinetic energy were along curvilinear paths. Our findings demonstrate that participants were capable of finding the energy-optimal paths, but only when provided with veridical visual and haptic information pertaining to the object, lacking which the trajectories were executed along rectilinear paths.

The energy-optimal motion of a vibration-driven robot in a medium with a inherited law of resistance

The rectilinear motion of a two-mass system consisting of a spherical body and a movable internal mass in a liquid is considered. In addition to quadratic in velocity viscous forces, resistance forces also include those dependent on the history of the motion of Basset forces and inertial forces of added mass. The task is to find the periodic law of motion of the internal mass that minimizes the work of the resistance forces during the period of motion of the system for a fixed period of oscillations and the given average velocity of the shell. The dependence of the optimal modes of the dimensionless oscillation period that characterizes the ratio of Basset forces to viscous forces is investigated.