Optimal Velocity Profile Research Articles

A novel methodology for the selection of the optimal velocity profile for planned point-to-point trajectories in 1-DoF manipulators

In this work, an approach based on velocity profile selection is developed and validated to decrease forces, acceleration, velocity, mechanical power, and energy consumption in 1 DOF Cartesian manipulators. Initially, a mathematical modeling of the kinematic and kinetic variables rising in linear, exponential, parabolic, sinusoidal, and s-curve ramp velocity profiles is proposed for different load conditions and saturation values of the velocity profiles, focusing on generic Cartesian manipulators moving a constant inertia load and not equipped with regenerative devices. Lastly, a summary table outlining the benefits and drawbacks of each velocity profile in relation to the relevant variables is given to the reader, along with a set of recommendations for selecting the best velocity profile in accordance with the load conditions and optimization goals. It was shown that, depending on the load conditions, the inappropriate choice of one type of speed profile can increase the required forces by up to 400%, the required maximum power by more than 88%, and the energy consumption by up to 77% with respect to the optimal speed profile.

Integral solution method of the laminar conjugated natural convection heat transfer from a hollow cylinder

The laminar conjugated natural convection heat transfer from a hollow cylinder is a common problem in engineering. The accurate calculation of the hot-spot temperature helps to monitor and evaluate the operating status of the equipment. In this paper, first, a mathematical model of the conjugated natural convection from a hollow cylinder is established. The boundary layer integral equations under arbitrary heat flux distribution on the surface are derived, and the optimal velocity and temperature profiles corresponding to different Prandtl numbers are determined. By combining the integral equations and the thermal network model, the hot-spot temperature and the average surface temperature of a hollow cylinder are solved iteratively. Subsequently, a computational fluid dynamic (CFD) simulation based on finite volume method is carried out to verify the accuracy of the integral solution method. The maximum relative error of the computed results of the two methods is 1.35%. The integral solution method performs much better in computation speed, increasing by 90 times. It is also found that as the thermal conductivity of solid materials decreases, although the hot-spot temperature increases, the average surface temperature remains basically unchanged. Finally, based on the lumped thermal equivalent circuit, the correlation of the Nusselt number corresponding to the hot-spot temperature is predicted. The parameters in the correlation are estimated by regression orthogonal design. The results show that under a wide range of solid thermal conductivity and fluid Prandtl numbers, the maximum error of the correlation is 6.02%. Therefore, this novel method is feasible and significant for calculating hot-spot temperature.

The Effect of Employing an Optimal Web Velocity Profile on Transverse Vibrations in Roll-to-Roll Manufacturing

The Effect of Employing an Optimal Web Velocity Profile on Transverse Vibrations in Roll-to-Roll Manufacturing

Energy Economization Using Connectivity-Based Eco-Routing and Driving for Fleet of Battery Electric Vehicles

Energy economizing using Connectivity-based eco-Routing and Driving (CeRD) is a key to conserve the resources of a fleet. This work takes maximum advantage by advising optimal energy consumption based route and velocity. Product delivery to several universities by group of Battery Electric Vehicles (BEVs), is considered. Problem contains certain constraints i.e., BEV load capacity, time window, resources restriction, speed bounds, battery charging/discharging limits and traffic. Simulation of Urban Mobility (SUMO) is used for the estimation of traffic and routes. Selection of route is based on energy consumption of traffic’s velocity. Once the traffic based energy consumptions are available, Dijkstra’s algorithm is then applied to select the route with least energy consumption. Clarke and Wright (C&W) algorithm is then applied to find the optimal sequence of visiting universities. Pontryagin’s Minimum Principle (PMP) is then applied to find the optimal velocity profiles for BEVs on the optimized routes. Results have shown 60-70% reduction in energy consumption along with improvement in charging rates as compared to the vehicles without CeRD assistance in different scenarios. Furthermore, results are validated for distance and time using online route planner, for energy efficiency using electric vehicles database and for energy consumptions using driver model based forward simulator.

Hierarchical Velocity Optimization for Connected Automated Vehicles With Cellular Vehicle-to-Everything Communication at Continuous Signalized Intersections

The rapid development of intelligent connected technologies and cellular vehicle-to-everything communication (C-V2X) provide new opportunities to solve the connected automated vehicle (CAV) traffic problem for eco-driving at continuous signalized intersections. With C-V2X, a hierarchical velocity optimization design based on hybrid model predictive control technique (HVO-HMPC) is presented to reduce the fuel consumption and pollution emission. First, a distance–domain velocity optimization problem, with distance as the independent variable, was constructed. Second, a hybrid MPC scheme was developed by combining the multiple shooting method and MPC technique to calculate the optimal velocity profile of a high-level controller, which acts as the reference velocity in a low-level controller. Then, a car-following model was built, the low-level controller tracked the reference velocity with the predictive control as the backbone, and the optimal velocity was calculated while ensuring that the safety velocity constraint is satisfied. Next, the proposed HVO-HMPC was tested in Prescan, and the effect comparisons with different control methods in terms of fuel consumption, pollution emission, braking time, and number of braking applications were studied under different driving scenarios. Results show that once the maximal speed is limited to 40 km/h under short-period signals and 20 km/h under long-period signals, the HVO-HMPC effectively reduces fuel consumption by 27.21%, 25.89%, and pollution emissions by 25.3%, 25.97%, respectively, while achieving best performance. Finally, an experimental prototype is built to confirm the validity of the HVO-HMPC.

An eco-driving strategy for autonomous electric vehicles crossing continuous speed-limit signalized intersections

The rapid advancement of Vehicle-to-Everything communication (V2X) technology presents opportunities for enhancing traffic energy efficiency. With V2X, this paper introduces an eco-driving strategy for autonomous electric vehicles to navigate continuous signalized intersections. This strategy incorporates the realistic powertrain's working efficiency and constraints into the vehicle motion optimization. In the domain of the global path, we formulate a co-optimization problem of vehicle motion and powertrain operation to tap the vehicle energy-saving potential and derive an optimal velocity profile, considering constraints related to queue release and limit speed in intersections. In the short rolling time domain, we propose a predictive control approach for vehicle speed tracking and real-time powertrain control. Simulation results under various scenarios show the advantages of the proposed method in terms of energy consumption compared to the baseline and existing methods.

Path-Constrained Time-Optimal Motion Planning for Robot Manipulators With Third-Order Constraints

Planning time-optimal motions of robot manipulators is important for maximizing productivity in industry and has attracted much attention in academia. Time-optimal time scaling (TOTS) of specified paths subject to second-order constraints is a well-studied problem in robotics. However, there is still a lack of effective approaches for computing TOTS with higher order constraints. This article proposes a novel method for TOTS subject to third-order constraints. The proposed method formulates the third-order TOTS as a four-stage optimization involving only linear programming by exploiting the special structure of the problem. The proposed method first performs a backward pass and a forward pass to generate the second-order optimal velocity profile. Then, the points violating the third-order constraints are identified, and the constraint violations are eliminated through numerical integration around the violating points. A bisection search algorithm is proposed to quickly determine the switching points at which the elimination process begins. The proposed method is verified through numerical examples and experimental tests. The results indicate that the proposed method outperforms the state-of-the-art approaches in terms of solution quality and computation time.

Optimization of Fuel Economy and Emissions Through Coordinated Energy Management for Connected Diesel Vehicles

This paper presents a comprehensive study of fuel economy and emissions optimization regarding both offline analysis and online strategies. A control-oriented model of the diesel vehicle is built concerning fuel economics, NOx emission, and vehicle dynamics, based on which OCPs covering several distinct scenarios are provided and serve as guidelines for online energy- and emission-aware control. Moreover, the optimized velocity profile and the corresponding performance improving rate are analyzed in different control weights, driving styles, and prediction horizons. Notably, a novel predictive eco-driving strategy with long-term connected information is proposed to realize much lower idling time, combining predictive cruise control (car-following scenario) and long-term eco-driving without preceding cars. The traffic signal is transferred into the constraints in the online control through a detailed case judgment. Based on the connected data collected in real-world traffic scenarios, the effectiveness of the proposed controller is verified, and the result shows 6.1% and 17.7% improvement in the economic and emission performances.

Hierarchical Velocity Control Considering Traffic Signal Timings for Connected Vehicles

Velocity profile optimization using upcoming signal information of urban vehicles is one of the main eco-driving techniques, which can significantly enhance the capability of reducing idling fuel loss and trip time. This paper proposes a hierarchical velocity control system considering different drive preferences for connected and automated vehicles to improve overall efficiency under the vehicle-to-X (V2X) environment. Two major contributions are (i) control-oriented formulation of task planning in multiple road segments, which is amiable to numerical computation and can consider different drive preferences; and (ii) solving the nonlinear velocity trajectory optimization to realize real-time control in the lower level. Simulation results indicate that energy-saving and computational efficiency are improved using the proposed control system. The solution algorithm is further demonstrated under a hardware-in-the-loop simulation.

Eco-Friendly On-Ramp Merging Strategy for Connected and Automated Vehicles in Heterogeneous Traffic

The on-ramp area usually produces congestion, high energy consumption, and high emission. In order to improve the efficiency of multi-lane heterogeneous on-ramp traffic composed of vehicles with different dynamic characteristics, we propose an eco-friendly on-ramp merging strategy for connected and automated vehicles in heterogeneous traffic. Firstly, the optimal lane decision method is proposed via the conditional proximal policy optimization algorithm to optimize the traffic flow of each lane and avoid local congestion in heterogeneous traffic. Then, considering travel time, energy consumption, and emission, the eco-friendly merging optimization problem is established to optimize vehicles' longitudinal velocity. According to the optimal lane and the optimal longitudinal velocity profile, the lateral end-point and longitudinal end-point of the local trajectory are solved for planning the local trajectory of the vehicles. Each vehicle tracks its local trajectory, realizing eco-friendly on-ramp merging. Compared with two existing ramp merging methods, results show that the proposed algorithm can mitigate local congestion effectively, and has superiority in traffic efficiency, energy economy, and eco-friendliness.

An integrated two‐dimensional merging trajectory optimization model for automated vehicles considering mixed traffic flow

Recently, automated vehicles have been recognized as a promising tool to address the problem of on-ramp merging. However, the complexity of the problem includes ignorance of the vehicle's lateral dynamics, the limitation of the fixed merging point, the mismatch problem caused by the sequential optimization scheme, and the fixed terminal states assumption. These factors make it intractable in practical driving scenarios. This paper proposed an integrated optimization model for on-ramp automated vehicles, which can guide the vehicle to complete the merging behaviour from the ramp lane to the main lane safely and efficiently. A merging path is first constructed in the two-dimensional plane with two critical parameters recommended by a neural network predictor, enabling it to incorporate both longitudinal and lateral dynamics. Then, an integrated Mixed Integer Quadratic Program (MIQP) model is built to determine the optimal velocity profiles and merging gap simultaneously while considering the safety and efficiency factors. Specifically, with the introduction of discretization and linearization techniques, linear collision avoidance constraints and smooth transition constraints can be built, which can address the challenging computational problem. The effectiveness of the proposed model is validated through the microscopic and macroscopic numerical results under different levels of mixed traffic.

Hierarchical Energy-Efficient Control for CAVs at Multiple Signalized Intersections Considering Queue Effects

The rapid development of connected vehicles (CVs) has offered novel opportunities for eco-driving control. Considering inherent spatial and temporal constraints from the preceding vehicle, multiple signalized intersections, and queues, this paper proposes a hierarchical energy-efficient control strategy (HCS) in different domains to reduce fuel consumption and travel time. Considering both traffic lights and queue information, the concept of virtual traffic lights is proposed based on queue estimation. In the higher-level controller, a distance-based energy-economy velocity optimization problem is formulated to treat spatial constraints from virtual traffic lights and queues. The optimal velocity profile is solved by the direct multiple shooting algorithm in a model predictive control (MPC) framework, which is used as a reference by the lower-level controller. To treat temporal constraints of safe inter-vehicular time, a predictive cruise control (PCC) in the time domain is introduced in the lower-level controller to ensure safe inter-vehicle distances and improve fuel efficiency while tracking the reference speed. Comparative simulation results show that the proposed strategy can significantly reduce fuel consumption and travel time.

Convex Performance Envelope for Minimum Lap Time Energy Management of Race Cars

The optimization of the energy management of modern hybrid-electric or fully electric race cars for minimum lap time requires a description of the vehicle dynamics performance envelope, that is, of the tires’ grip limit in corners, braking zones and during acceleration. In this paper, we present a computationally efficient performance envelope model in the form of convex constraints on the achievable longitudinal and lateral acceleration, on the assumption that the path on the track is given. The proposed acceleration limits are modeled velocity-dependent to take into account the effect of aerodynamic downforce present in many circuit race cars. The formulation as linear equality, inequality and second-order cone constraints allows to embed the model in a convex energy management optimization framework. To showcase the approach, we identify the model with data obtained from a state-of-the-art hybrid-electric Formula 1 car and present results for the Silverstone and Spa-Francorchamps circuits. The optimal energy management strategies can be evaluated with a computational time of less than 1 s. The optimal velocity profile subject to the performance envelope constraints is close to the measured one. The good agreement between the optimal solution and the measurement data shows that the proposed model captures the vehicle dynamics accurately enough for the purposes of energy management optimization.

An efficient multi-objective hierarchical energy management strategy for plug-in hybrid electric vehicle in connected scenario

Nowadays, the comprehensive performance of plug-in hybrid electric vehicle (PHEV) is expected to be further improved with development of connected vehicle technology. However, the strong coupling and traffic flow uncertainty characteristics of connected scenario pose formidable challenge to existing energy management strategies (EMSs) in terms of optimization effect and computational efficiency. For comprehensively improving connected PHEV performances including energy saving, safety, traffic efficiency and computational efficiency, a multi-objective hierarchical EMS with less computational burden is proposed by incorporating resistance network (RN) triggered motion planning and alternating direction method of multipliers (ADMM) based convex torque optimization. Specifically, the RN method is employed to characterize and decouple the complex interaction relationship within connected scenario from internal mechanism perspective, enabling the velocity profile optimization issue that with fixed end time constraint and online correction mechanism for traffic flow uncertainty. According to the velocity profile optimized in cloud level, the convex formulation of model predictive control (MPC) based torque distribution problem is formulated in vehicle level, and an efficient ADMM algorithm is used for its solution, with the aim of satisfying energy saving and practical application requirements simultaneously. Based on real connected information, the superiorities of proposed EMS are verified by both simulation and hardware-in-loop (HIL) experiment.

Optimal Control of Pitch and Rotational Velocity for a Cyclorotor Wave Energy Device

The development of optimal control strategies for cyclorotor wave energy converters (WECs) is at an early stage. In this paper, we present new methods and solutions for optimal pitch and/or rotational velocity control strategies for different configurations of cyclorotor-based WECs, in both monochromatic and panchromatic waves. The cyclorotor is modelled with the use of an approximate two-dimensional mathematical model, where hydrofoils are approximated as point source vortices in potential waves. The goal of the developed control strategy is to determine the optimal velocity profile, and/or pitch angle variations, for maximum energy conversion, in terms of generated mechanical shaft power. The solutions, obtained with the use of spectral methods, show a clear benefit in using a variable velocity for cyclorotors with either one or two hydrofoils, in monochromatic waves, with a typical increase in energy capture of 30-40%, while the optimal pitching did not significantly increase the value of the absorbed wave energy. We also present control results for panchromatic waves, assuming all the properties of incoming wave packages, within a 10 s time interval, are known. The obtained solutions have shown significant benefit in joint optimal pitch and velocity control, especially in the case of panchromatic waves. It has been also shown that successful implementation of cyclorotor control strategies requires optimal configuration of the static characteristics of the cyclorotor. In conclusion, we discuss the optimal control benefits and highlight problems which must be solved for further successful development of these control strategies.

Supporting the Transition Towards Electromobility in the Construction and Mining Sector: Optimization Framework and Demonstration on an Electrical Hauler

AbstractThe paper presents a framework for the integration of the system's design variables, state variables, control strategies, and contextual variables into a design optimization problem to assist early-stage design decisions. The framework is based on a global optimizer incorporating Dynamic Programming, and its applicability is demonstrated by the conceptual design of an electrical hauler. Pareto front of optimal design solutions, in terms of time and cost, together with optimal velocity profiles and battery state-of-charge is visualized for the given mining scenario.

Co-optimization strategy of unmanned hybrid electric tracked vehicle combining eco-driving and simultaneous energy management

Combining eco-driving optimization and simultaneous proper energy management, this paper proposes an efficient co-optimization strategy of unmanned hybrid electric tracked vehicles (HETVs) based on a hierarchical control framework to achieve accurate path tracking and optimal energy management simultaneously. Constrained by a pre-known reference path, a deep Q-learning (DQL) algorithm with the AMSGrad optimizer is designed in the upper layer to optimize the velocity of both side tracks to find the best trade-off between energy economy and accurate path tracking. Based on the optimal velocity profile obtained from the upper layer, an explicit model predictive control method is designed in the lower layer to distribute the power between the engine generator and battery in real time to achieve approximate optimal fuel economy. Simulation results verify that the designed DQL method only requires 0.67 s on average for real-time velocity planning, which is markedly lower than the dynamic programming algorithm. In addition, the proposed method also exhibits higher rapidity and optimality for velocity planning than the traditional DQL algorithm. Compared with the model predictive control, dynamic programming and a process without velocity planning, the proposed co-optimization strategy achieves good fuel economy, accurate path tracking and high computational efficiency.

Limiting reactive power flow peaks in wave energy systems

Optimal control of wave energy converters has been shown to require an injection of power into the WEC system to maintain an optimal velocity profile. While this consumption of power results in an overall increase in energy capture, it also brings more stringent requirements on the power take-off (PTO) system. Specifically, the PTO must cater for bi-directional power flow and a source available for the provision of this reactive power, either via a storage device, or the electrical grid itself. However, one aspect which has received relatively little attention is the magnitude of the reactive power peaks, which may have implications for the required overall power rating of the system. In particular, though reactive power flow may only be required for a small fraction of the wave period, reactive power peaks well in excess of active power levels bring a potentially significant capital cost in terms of system power rating, along with a unfavourable capacity factor rating. This paper examines the circumstances under which reactive power flow peaks exceed active power levels and proposes a solution which puts a finite (nonzero) limit on reactive power flow, consistent with active power levels. The problem is solved as a nonlinear constrained optimisation problem, while the consequences of imposing such a limit on energy capture are also examined.

Attitude stabilization of Marine Satellite Tracking Antenna using Model Predictive Control

Attitude stabilization is a necessary function for a shipboard Marine Satellite Tracking Antenna (MSTA), which is responsible for making the antenna dish track the geostationary satellite in the presence of severe environment. A control scheme based on Model Predictive Control (MPC) is proposed to stabilize the antenna dish of an MSTA, and the detailed design process from algorithm design to Hardware-in-the-loop (HIL) simulation is explained. Due to the use of stepper motor as the actuator, the MPC is proposed to deal with the speed acceleration and deceleration problems of stepper motors, which can result in the optimal velocity profile. The MPC algorithm is implemented in Field Programmable Gate Array (FPGA) with three different data types. In addition to using traditional floating-point and fixed-point data types to represent values in MPC, a special data type, half-precision floating-point, is also explored for the first time. The comparison results are presented and analyzed in terms of FPGA resource usage and algorithm execution time. The performance of the proposed control scheme is validated in HIL simulation, which is creatively implemented in a low-cost System On Chip (SOC) FPGA. The HIL simulation results demonstrate that the proposed control scheme in fixed-point MPC can satisfy the requirements of the MSTA.

Velocity Optimization of Pure Electric Vehicles with Traffic Dynamics and Driving Safety Considerations

As Electric Vehicles (EVs) become increasingly popular, their battery-related problems (e.g., short driving range and heavy battery weight) must be resolved as soon as possible. Velocity optimization of EVs to minimize energy consumption in driving is an effective alternative to handle these problems. However, previous velocity optimization methods assume that vehicles will pass through traffic lights immediately at green traffic signals. Actually, a vehicle may still experience a delay to pass a green traffic light due to a vehicle waiting queue in front of the traffic light. Also, as velocity optimization is for individual vehicles, previous methods cannot avoid rear-end collisions. That is, a vehicle following its optimal velocity profile may experience rear-end collisions with its frontal vehicle on the road. In this article, for the first time, we propose a velocity optimization system that enables EVs to immediately pass green traffic lights without delay and to avoid rear-end collisions to ensure driving safety when EVs follow optimal velocity profiles on the road. We collected real driving data on road sections of US-25 highway (with two driving lanes in each direction and relatively low traffic volume) to conduct extensive trace-driven simulation studies. Results show that our velocity optimization system reduces energy consumption by up to 17.5% compared with real driving patterns without increasing trip time. Also, it helps EVs to avoid possible collisions compared with existing collision avoidance methods.