Speed Trajectory Research Articles

Thermal management optimization strategy of electric vehicle based on dynamic programming

In order to further tap the energy saving potential of the thermal management system of pure electric vehicles and to improve the driving range under low temperature environment, a vehicle thermal management control strategy based on dynamic programming was designed. Firstly, based on the AmeSim and Simulink co-simulation platform, a refined simulation model of the vehicle thermal management system was built, including the battery system, drive system and heat pump system models. Then, a vehicle thermal management control strategy based on forward dynamic programming algorithm was proposed. By optimizing the control trajectory of compressor speed, PTC ( Positive Temperature Coefficient) power and waste heat mode, both economy and cabin comfort were improved. Finally, the simulation based on CLTC (China Light Vehicle Test Cycle) working condition verifies the effectiveness of the control strategy.

Analysis of Model Predictive Intersection Control for Autonomous Vehicles

Autonomous vehicles are in the main focus for automotive companies and urban traffic engineers as well. As their penetration rate in traffic becomes more and more pronounced due to improvement in sensor technologies and the corresponding infrastructure, new methods for autonomous vehicle controls become a necessity. For instance, autonomous vehicles can improve the performance of urban traffic and prevent the formation of congestions with the usage of Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) communication based control methods. One of the key area for improvement is centralized intersection control for autonomous vehicles, by which traveling times can be reduced and efficiency of traffic flow can be improved, while safety of passengers can be guaranteed through constraints built in the centralized design. The paper presents the analysis of a Model Predictive Control (MPC) method for the coordination of autonomous vehicles at intersections by comparing it with an offline constraint optimization considering time and energy optimal intervention of vehicles. The analysis has been evaluated in high-fidelity simulation environment CarSim, where the speed trajectories, traveling times and energy consumptions have been compared for the different methods. The simulations show that the proposed time-optimal MPC intersection control method results in similar traveling times of that given by the time-optimal offline constraint optimization, while the energy optimal optimization re-quires significantly more time for the autonomous vehicle to achieve. Due to the possibility of a congestion forming in the latter case, the proposed centralized MPC method is more applicable in real traffic scenarios.

Eco-Driving Optimization Based on Variable Grid Dynamic Programming and Vehicle Connectivity in a Real-World Scenario

In a context in which the connectivity level of last-generation vehicles is constantly on the rise, the combined use of Vehicle-To-Everything (V2X) connectivity and autonomous driving can provide remarkable benefits through the synergistic optimization of the route and the speed trajectory. In this framework, this paper focuses on vehicle ecodriving optimization in a connected environment: the virtual test rig of a premium segment passenger car was used for generating the simulation scenarios and to assess the benefits, in terms of energy and time savings, that the introduction of V2X communication, integrated with cloud computing, can have in a real-world scenario. The Reference Scenario is a predefined Real Driving Emissions (RDE) compliant route, while the simulation scenarios were generated by assuming two different penetration levels of V2X technologies. The associated energy minimization problem was formulated and solved by means of a Variable Grid Dynamic Programming (VGDP), that modifying the variable state search grid on the basis of the V2X information allows to drastically reduce the DP computation burden by more than 95%. The simulations show that introducing a smart infrastructure along with optimizing the vehicle speed in a real-world urban route can potentially reduce the required energy by 54% while shortening the travel time by 38%. Finally, a sensitivity analysis was performed on the biobjective optimization cost function to find a set of Pareto optimal solutions, between energy and travel time minimization.

An ECMS Based on Model Prediction Control for Series Hybrid Electric Mine Trucks

This paper presents an equivalent consumption minimization strategy (ECMS) based on model predictive control for series hybrid electric mine trucks (SHE-MTs), the objective of which is to minimize fuel consumption. Two critical works are presented to achieve the goal. Firstly, to gain the real-time speed trajectory on-line, a speed prediction model is established by utilizing a recurrent neural network (RNN). Specifically, a hybrid optimization algorithm based on the genetic algorithm (GA) and the particle swarm optimization algorithm (PSOA) is used to enhance the prediction precision of the speed prediction model. Then, on this basis, an ECMS based on MPC (ECMS-MPC) is proposed. In this process, to improve the real-time and working condition adaptability of the ECMS-MPC, the power-optimal fuel consumption mapping model of the range extender is established, and the equivalent factor (EF) is real-time adjusted by means of the PSOA. Finally, taking a cement mining road as the research object, the proposed strategy is simulated with the collected actual vehicle data. The experimental results indicate that the prediction precision of the proposed speed prediction model is over 98%, realizing on-line speed prediction effectively. Furthermore, compared to the existing real-time EMSs, its fuel-saving rate had an increase of more than 13%. This indicates that the designed ECMS-MPC is able to offer a novel and effective method for the on-line energy management of the SHE-MTs.

Longitudinal joint modeling for assessing parallel interactive development of latent ability and processing speed using responses and response times.

To measure the parallel interactive development of latent ability and processing speed using longitudinal item response accuracy (RA) and longitudinal response time (RT) data, we proposed three longitudinal joint modeling approaches from the structural equation modeling perspective, namely unstructured-covariance-matrix-based longitudinal joint modeling, latent growth curve-based longitudinal joint modeling, and autoregressive cross-lagged longitudinal joint modeling. The proposed modeling approaches can not only provide the developmental trajectories of latent ability and processing speed individually, but also exploit the relationship between the change in latent ability and processing speed through the across-time relationships of these two constructs. The results of two empirical studies indicate that (1) all three models are practically applicable and have highly consistent conclusions in terms of the changes in ability and speed in the analysis of the same data set, and (2) additional analysis of the RT data and acquisition of individual processing speed measurements can reveal the parallel interactive development phenomena that are difficult to detect using RA data alone. Furthermore, the results of our simulation study demonstrate that the proposed Bayesian Markov chain Monte Carlo estimation algorithm can ensure accurate model parameter recovery for all three proposed longitudinal joint models. Finally, the implications of our findings are discussed from the research and practice perspectives.

A Link Real-time Travel Time Estimation on Speed-time Field Traversing Incorporating LSTM Neural Network

A travel time estimation method based on Speed-time field traversal including LSTM neural network was proposed to increase the real-time and accuracy of travel time estimation. The node departure speed of the traditional piecewise truncated quadratic speed trajectory model was optimized by the road node arrival speed, considering the impact of road conditions on travel time. The node arrival speed was modeled as time series and predicted in the short-term future by combining the LSTM neural network model to construct a spatiotemporally continuous speed trajectory, to estimate the link’s travel time. The method was tested on an actual road and gave considerably improved estimates and results compared to the original method, using LSTM neural network to predict node departure speed and the technique using node arrival speed. According to experimental results, the proposed method performs well in both smooth and crowded traffic circumstances, serving as a benchmark for precise real-time travel time estimation on urban roads.

Predictive Cruise Control Under Cloud Control System for Urban Bus Considering Queue Dissipation Time

The driving conditions of urban consecutive signalized intersections are one of the main research scenarios for vehicle speed trajectory optimization, and typical for bus driving, where frequent acceleration and deceleration before and after the intersection can intensify the energy consumption of the bus. Prior research has predictive cruise controlled under Intelligent Transportation System, which is not feasible to directly communicate with controllers' units of Intelligent Connected Vehicles. Besides, the effect of queue dissipation is a topic that has received less attention in recent related work. Therefore, this paper proposes a vehicle-cloud hierarchical architecture based on Cloud Control System at first, under which a predictive cruise control for urban buses is deployed. Given the impact of intersection queue length and dissipation time on vehicle driving, a queue dissipation time estimation model based on shockwave theory is proposed to predict changes in intersection traffic state. The queue dissipation time equivalent to the extension of the red-light window is reflected in the constraints of the Receding Distance Horizon Dynamic Programming (RDHDP) algorithm for solving the optimal control problem. Eventually, comparison simulations, a segment of realistic trip between adjacent stops, are presented. The results show that the proposed method saves 44.94%-56.74% of energy consumption and at least 26.8s of waiting time compared to human drivers, and 22.72%-41.27% of energy consumption compared to vehicle with the Intelligent Vehicle Infrastructure Cooperative Systems.

The Bidirectional Association Between Cognitive Function and Gait Speed in Chinese Older Adults: Longitudinal Observational Study.

Cognitive and gait speed decline are common conditions in older adults and are often associated with future adverse consequences. Although an association between cognitive function and gait speed has been demonstrated, its temporal sequence remains unclear, especially in older Chinese adults. Clarifying this could help identify interventions to improve public health in older adults. This study aims to examine the longitudinal reciprocal association between gait speed and cognitive function and the possible temporal sequence of changes in both factors in a national longitudinal cohort. Data were derived from 2 waves (2011 baseline and 2015 follow-up) of the China Health and Retirement Longitudinal Study (CHARLS). Participants 60 years or older, without dementia or Parkinson disease at baseline, and with completed data on gait speed and cognition at both baseline and follow-up were included. Usual gait speed was measured over two 2.5-m walks. Mental intactness and episodic memory were used to assess global cognitive function. Cross-lagged panel models and linear mixed-effects models were used to examine the association between cognition and gait speed over time. Standardized coefficients were reported. A total of 3009 participants (mean age 66.4 years, SD 5.4 years; 1422/3009, 47.26%, female participants) were eligible for inclusion in our analyses. Cross-lagged panel analyses revealed that after accounting for baseline gait speed, cognition, and potential confounders, baseline global cognition (β=.117, 95% CI 0.082-0.152; P<.001), mental intactness (β=.082, 95% CI 0.047-0.118; P<.001), and episodic memory (β=.102, 95% CI 0.067-0.137; P<.001) were associated with subsequent gait speed. Simultaneously, baseline gait speed was also associated with subsequent global cognition (β=.056, 95% CI 0.024-0.087; P=.001), mental intactness (β=.039, 95% CI 0.008-0.069; P=.01), and episodic memory (β=.057, 95% CI 0.023-0.092; P=.001). The comparison of standardized cross-lagged coefficients suggested that the effect size of baseline global cognition on subsequent gait speed was significantly larger than the reverse effect (χ12=6.50, P for difference=.01). However, the effects of both mental intactness and episodic memory on subsequent gait speed were not significantly stronger than those of the reverse pathway (χ12=3.33, P for difference=.07 and χ12=3.21, P for difference=.07). Linear mixed-effects analyses further supported these bidirectional relationships, revealing that lower baseline cognitive scores predicted steeper declines in gait speed trajectory, and slower baseline gait speed predicted more declines in cognitive trajectory over time. There is a longitudinal bidirectional association between usual gait speed and both global cognitive function and specific domains of mental intactness and episodic memory among Chinese older adults. Baseline global cognition is likely to have a stronger association with subsequent gait speed than the reverse pathway. This interlinkage is noteworthy and may have implications for public health. Maintaining normal cognitive function may be an important interventional strategy for mitigating age-related gait speed reduction.

Developmental trajectory of transmission speed in the human brain

The structure of the human connectome develops from childhood throughout adolescence to middle age, but how these structural changes affect the speed of neuronal signaling is not well described. In 74 subjects, we measured the latency of cortico-cortical evoked responses across association and U-fibers and calculated their corresponding transmission speeds. Decreases in conduction delays until at least 30 years show that the speed of neuronal communication develops well into adulthood.

Hierarchical cooperative eco‐driving control for connected autonomous vehicle platoon at signalized intersections

AbstractVehicles in the platoon can sufficiently incorporate the information via V2X communication to plan ecological speed trajectories and pass the intersection smoothly. Most existing eco‐driving studies mainly focus on the optimal control of a single vehicle at an individual signalized intersection, while rarely involving the cooperative optimization of a group of vehicles at successive signalized intersections. In this study, a hierarchical cooperative eco‐driving control for a connected autonomous vehicle (CAV) platoon is proposed to enhance traffic mobility and energy efficiency, wherein the velocity trajectory of the leading vehicle at each isolated signalized intersection is planned using the pseudo‐spectral method, and then the cooperative optimization of following vehicles in the platoon is conducted via rolling optimization, with the aim of improving driving comfort, safety and energy economy for the platoon. The simulation results highlight that the proposed hierarchical cooperative eco‐driving strategy can lead to preferable vehicle‐following behaviours and platoon driving performance, and the overall energy consumption and trip time of vehicle platoon are respectively reduced by 26.10% and 2.83%, compared with that under manual driving. Furthermore, the overall energy economy is promoted by 4.95% and 4.60%, compared with cooperative adaptive cruise control and intelligent driver model‐based platoon control strategies.

Evaluating the Effectiveness of Speed Humps Related to Speed Profile and Noise Profile

Speed humps are an effective traffic calming measure to improve the safety of road users. On the other hand, speed humps have certain drawbacks, such as increasing emergency response time, causing damage to cars, and high noise levels due to excessive traffic. These impacts further vary with different hump profiles. Thus, the primary objective of this research is to investigate how the geometric profile of speed humps affects vehicle speed and noise level. The secondary objective is to find the Level of Service in the presence and absence of a speed hump by using VISSIM microsimulation. In this study, Lake Drive Road, Nawala, was selected with four different speed hump profiles. The Sound Meter smartphone application was used for noise monitoring. A drone camera footage was utilized to capture vehicle flows while speed trajectories of each vehicle were developed using tracking software. The developed speed profiles were used for the simulation purpose. Then, a Multiple Linear Regression (MLR) model was developed and validated to predict the hump height for the desired speed reduction and desired noise level for each selected four-vehicle category. Further, the average noise levels were found to be higher than the Central Environmental Authority's permissible noise level, and it increases with the height of the hump. It was also observed that as the height of the hump increases, vehicle speed decreases. The largest speed reduction, 42.13 %, was observed in passenger cars, while the lowest speed reduction, 23.5 %, was observed in motorcycles. Therefore, speed analysis findings reveal that passenger cars have a significant speed reduction when compared to other categories. However, the average speed reduction for all vehicles was identified as 33.85 %, and VISSIM simulations revealed that the average Level of Service (LOS) drops to LOS C from LOS A due to the presence of the speed hump. KEYWORDS: Level of Service, Speed hump profile, Speed hump, VISSIM

Speed Trajectory Optimization Method for Electric Vehicles Based on Driving Style

In real driving conditions, speed trajectory optimization is an important part of the energy-saving driving assistance system of smart cars, and it can contribute to increase the cruising range. However, the existing speed trajectory optimization research for vehicles mainly focuses on energy consumption and does not consider whether the optimized trajectory can meet the driver’s driving style requirements. In response to this problem, this article establishes an electric vehicle energy consumption model and discusses the difference between the trajectory reflecting driving style (TRDS) and the optimal trajectory of energy consumption (OTOEC). Based on the driving speed trajectory and acceleration trajectory of the driver, this article obtains trajectory clusters reflecting the driving style of the driver by trajectory data mining and establishes the driving style characteristic space (DSCS) based on these clusters and proposes a speed trajectory optimization method based on driving style finally. Compared with the TRDS, the energy consumption of the trajectory obtained by this method can reduce significantly. The trajectory obtained by the method can reflect the driving style of the driver to a large extent compared with the OTOEC. The simulation results verify the effectiveness of the method.

Event-Driven Energy-Efficient Driving Control in Urban Traffic for Connected Electric Vehicles

The traffic light in urban areas dominates the traffic flow, resulting in variation of energy consumption of the vehicles involved. To mitigate the impact of traffic bias on the energy efficiency of electric vehicles (EVs), this article proposes an event-driven energy-efficient driving control (EEDC) strategy based on a receding horizon two-stage control framework, which harnesses the Internet of Vehicles to incorporate the traffic light and preceding vehicle for adaption of different driving scenarios. At the core of the first stage are the vehicle driving event classification rules, which classified the urban traffic scenarios into four events. This article contributes to empirical solutions on the design of the traffic scenario classifier considering conflict goals, including driving efficiency and safety. In the second stage, the speed trajectory in each driving event is optimized using Pontryagin’s minimum principle to reduce vehicle energy consumption. A real-time solution for the energy-efficient driving problem is derived with the consideration of vehicle dynamics, control input, and speed limit constraints. Finally, extensive simulations and road tests are conducted to evaluate the effectiveness of the EEDC. The results show that the EEDC is excellent in energy efficiency improvement over two benchmark strategies in different traffic scenarios while satisfying the constraints in inter-vehicle driving safety and travel time. Moreover, the road tests demonstrate that the EEDC is capable of energy saving in real-world driving.

Robust Optimization of Energy-Saving Train Trajectories Under Passenger Load Uncertainty Based on p-NSGA-II

Railway electrification has attracted substantial interest in recent years as a key part of the global effort to achieve transport decarbonization. To improve the energy efficiency of train operations, of particular interest is the optimization of train speed trajectories. However, most studies formulate the problem as a single-objective optimization model and do not take into account train mass uncertainty associated with the passenger load variations. This article formulates a biobjective robust optimization model to minimize both the energy consumption and journey time, in which the robustness against the uncertain train mass is considered and viewed as a decision-maker preference. A novel multiobjective optimization algorithm, namely, p-nondominated sorting genetic algorithm-II (NSGA-II), is proposed, incorporating the original NSGA-II and a proposed preference dominance criterion to handle the DM preference. With the proposed p-NSGA-II, not only all solutions will converge to the optimal Pareto front but also solutions with better robustness in the Pareto front will be automatically selected and retained; meanwhile, the spread of the selected solutions is maintained. The effectiveness of the p-NSGA-II to generate a set of performance-robust driving schemes is verified by numerical case studies. The results show that the p-NSGA-II can achieve up to 40.59% robustness improvement compared to the original NSGA-II.

Integrated Convex Speed Planning and Energy Management for Autonomous Fuel Cell Hybrid Electric Vehicles

Fuel cell hybrid electric vehicles (FCHEVs) have zero harmful emissions, fast refueling times, and long driving ranges. Autonomous FCHEVs add benefits such as collision avoidance and driver convenience yet increase vehicle energy usage due to sensors and computation. Thus, it is important to optimize vehicle speed trajectories and the energy management strategy (EMS) of autonomous FCHEVs to minimize energy use. This article uniquely proposes to achieve this goal using convex optimization, with detailed vehicle loss calculations that can be run in real time. The two novel approaches proposed are: 1) the successive method, which solves the speed problem then the EMS problem, and 2) the integrated method, which uniquely feeds back the fuel cell efficiency to the speed algorithm to solve the problem in an iterative integrated manner. The simulation results show that the integrated method uses 0.19% to 2.37% less hydrogen than the successive method on short drive cycles with varying accessory loads, and 10.12%–21.62% less hydrogen than an arbitrary constant speed profile. On longer real-world drive cycles, the integrated method reduces hydrogen use by 1.43% to 2.82% just through speed optimization. Compared to a dynamic programming benchmark, which is not implementable in real time, the integrated method uses less than 1% more hydrogen.

A Parallel Supervision System for Vehicle CO2 Emissions Based on OBD-Independent Information

A parallel supervision system is built in this paper in order to realize accurate vehicle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rm CO_{2}$</tex-math></inline-formula> emission estimation and prediction. On-board diagnostics (OBD)-independent information is used as the model input to avoid costly specialized equipment. More importantly, the OBD-independent model does not rely on an excessive number of internal variables and is capable of predicting carbon emissions from vehicle-level predictive information (future road conditions and planned speed trajectories). Based on the parallel theory, the actual traffic environment is considered the physical world, while the combined <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rm CO_{2}$</tex-math></inline-formula> model (which consists of physical and data-driven models) is the core part of the artificial world. The physical model uses a cascaded structure with engine speeds and torques as intermediate variables, and the data-driven model relies on a modified long short-term memory (LSTM) neural network. When the historical data are sufficient in size and diversity, the data-driven model is appropriate and achieves more accurate estimations; otherwise, the physical model is preferable because of its greater robustness. In real applications, the supervision system selects the suitable model for adapting to different vehicles; this approach can leverage both the learning ability and physics-based knowledge of the system. A validation is conducted using real-world experimental results to demonstrate the effectiveness of the proposed supervision system. According to comprehensive comparisons between the obtained measurements and estimations, both the physical and data-driven models achieve sufficient accuracy. When the historical data are insufficient, the data-driven model exhibits some deficiencies, while the physical model indicates more robustness even when some primary parameters (gear ratios) are unknown. Moreover, the deterioration factor (DF) of vehicle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rm CO_{2}$</tex-math></inline-formula> emissions is modelled to represent the performance of aged vehicles. This parallel supervision system can monitor real-time carbon emissions from actual traffic scenarios, providing a new method for reaching the target of carbon neutrality.

Hierarchical optimal control framework to automatic train regulation combined with energy-efficient speed trajectory calculation in metro lines

In high-density metro lines, frequent disturbances could lead to a domino effect of train delays if no adjustment strategy is imposed timely. In this paper, to enhance train timetable adherence and reduce energy consumption, we provide a hierarchical optimal control framework for the automatic train regulation problem with energy-efficient speed trajectory based on the model predictive control method. Specifically, by considering the dynamic passenger flows, the non-linear train regulation model is proposed at the higher level to enhance timetable adherence, while at the lower level the energy-efficient speed trajectories of the trains are generated on-line in a distributed manner. The interaction of real-time information exists between the higher level and the lower level, i.e., the upper model provides the train running time and the numbers of onboard passengers to the lower model, while the lower model feedbacks the updated train information (e.g., the actual arrival time) to the upper model, which provides the potential for the proposed framework to respond to disturbances at the operational stage. Moreover, a customized model predictive control method combined with Radau pseudospectral method (RPM) is designed to generate the energy-efficient train speed trajectory at the lower level in response to uncertain operational conditions. Numerical cases based on the Beijing Metro Yizhuang line demonstrate the effectiveness and robustness of our proposed hierarchical optimal control framework to deal with uncertain disturbances.

Optimization of energy and time predicts dynamic speeds for human walking.

Humans make a number of choices when they walk, such as how fast and for how long. The preferred steady walking speed seems chosen to minimize energy expenditure per distance traveled. But the speed of actual walking bouts is not only steady, but rather a time-varying trajectory, which can also be modulated by task urgency or an individual's movement vigor. Here we show that speed trajectories and durations of human walking bouts are explained better by an objective to minimize Energy and Time, meaning the total work or energy to reach destination, plus a cost proportional to bout duration. Applied to a computational model of walking dynamics, this objective predicts dynamic speed vs. time trajectories with inverted U shapes. Model and human experiment (N=10) show that shorter bouts are unsteady and dominated by the time and effort of accelerating, and longer ones are steadier and faster and dominated by steady-state time and effort. Individual-dependent vigor may be characterized by the energy one is willing to spend to save a unit of time, which explains why some may walk faster than others, but everyone may have similar-shaped trajectories due to similar walking dynamics. Tradeoffs between energy and time costs can predict transient, steady, and vigor-related aspects of walking.

Effect of Chamfer Form and Parameters on the Characteristics of Finite Length Journal Bearing under Impact Load

Journal bearings in typical applications are subjected to misalignment due to several causes, such as shaft deformation under load and errors related to the installation and manufacturing processes. Misalignment has well-known severe negative consequences on the performance of the bearings. This paper deals with the bearing chamfer to reduce these consequences of misalignment, and two forms of bearing edge modification are considered in the analysis. These forms are linear and curved chamfering of the bearing edges, where the height of the chamfer in the circumferential direction and the length of the modification in the longitudinal direction are considered as geometrical design parameters. The investigation includes a numerical solution of the hydrodynamic lubrication problem of finite length journal bearing, considering 3D misalignment cases using the finite difference method. This includes the assessment of the chamfer forms and their effects on the bearing performance in terms of the main bearing design parameters. Furthermore, the stability of the chamfered bearings is also investigated under impact load. Results showed that both chamfer forms are beneficial for a certain limit of the design parameters in reducing the maximum pressure and coefficient of friction and in elevating the film thickness levels, extending the range of misalignment in which the journal bearing can operate safely. In addition, the chamfered bearings in both forms showed more stability range in terms of the critical speed and shaft center trajectories under impact load. The bearings with the curved chamfer, where the slope is continuous at the start of modification, showed more uniform film thickness levels, and their shaft center trajectories were closer to the perfectly aligned bearing in the stable operating range of the system.

Robotic-Arm-Based Force Control in Neurosurgical Practice

This research proposes an optimal robotic arm speed shape in neurological surgery to minimise a cost functional that uses an adaptive scheme to determine the brain tissue force. Until now, there have been no studies or theories on the shape of the robotic arm speed in such a context. The authors have applied a robotic arm with optimal speed control in neurological surgery. The results of this research are as follows: In this article, the authors propose a control scheme that minimises a cost functional which depends on the position error, trajectory speed and brain tissue force. This work allowed us to achieve an optimal speed shape or trajectory to reduce brain retraction damage during surgery. The authors have reached two main conclusions. The first is that optimal control techniques are very well suited for robotic control of neurological surgery. The second conclusion is that several studies on functional cost parameters are needed to achieve the best trajectory speed of the robotic arm. These studies could attempt to optimise the functional cost parameters and provide a mechanical characterisation of brain tissue based on real data.