Jerk Limits Research Articles

Determination and description of a vehicle's maximum jerk capacity

Both Transient Optimal and Quasi-Steady-State vehicle modelling are frequently used for minimum time manoeuvre and minimum lap-time simulations for motorsport/vehicle development purposes. Quasi-Steady-State methods have been shown to perform such tasks with low computational cost but produce results with measurable deviation from equivalent Transient Optimal studies. It is hypothesised that bounding point-mass models with jerk limits will improve alignment with Transient Optimal simulations through the consideration of transient behaviours such as control application rates and inertia. This work presents a new method for the determination of a vehicle's maximum jerk capacity from a seven degree-of-freedom vehicle model. A range of results from this proposed technique are presented and show the sensitivity of jerk capacity to changes in control application rate limits and yaw inertia, as well as current vehicle velocity, acceleration, and jerk. It is proposed that further exploration of the validity of the jerk limit calculation method take place through characterisation of said limits and application to a point-mass model, after which comparison to Transient Optimal and Quasi-Steady-State equivalents can occur.

Optimal Path Planning Algorithm with Built-In Velocity Profiling for Collaborative Robot.

This paper proposes a method for solving the path planning problem for a collaborative robot. The time-optimal, smooth, collision-free B-spline path is obtained by the application of a nature-inspired optimization algorithm. The proposed approach can be especially useful when moving items that are delicate or contain a liquid in an open container using a robotic arm. The goal of the optimization is to obtain the shortest execution time of the production cycle, taking into account the velocity, velocity and jerk limits, and the derivative continuity of the final trajectory. For this purpose, the velocity profiling algorithm for B-spline paths is proposed. The methodology has been applied to the production cycle optimization of the pick-and-place process using a collaborative robot. In comparison with point-to-point movement and the solution provided by the RRT* algorithm with the same velocity profiling to ensure the same motion limitations, the proposed path planning algorithm decreased the entire production cycle time by 11.28% and 57.5%, respectively. The obtained results have been examined in a simulation with the entire production cycle visualization. Moreover, the smoothness of the movement of the robotic arm has been validated experimentally using a robotic arm.

A safety-guaranteed game-theoretical velocity planning for autonomous vehicles on sharp curve roads

In this paper, a safety-guaranteed game-theoretical velocity planning framework in a hierarchical manner is proposed to generate safe, ride comfort, and travel efficiency-balanced velocity for autonomous vehicles (AVs). In the upper layer, a bang-bang decision-making method is utilized to determine which planning mode to be implemented based on acceleration and jerk constraints, including a comfort mode, an efficiency mode, and a game mode. In the lower layer, asymmetric jerk limits based on comfort characteristics sensibility analysis and safe velocity simultaneously considering longitudinal and lateral stability are firstly developed to maintain ride comfort and driving safety, respectively on curve roads, especially sharp curves where vehicle stability may be not fully considered in most researches. Based on these, a non-cooperative game-theoretical velocity planning method is presented to solve the conflict between comfort mode and efficiency mode by optimizing his own objective based on the other’s action. Finally, for the sake of solving efficiency and accuracy, a chaos optimization-based algorithm (COA) is designed to solve for the Stackelberg equilibrium solution of the bilevel game optimization problem. Three experimental tests are carried out to comprehensively demonstrate the effectiveness, robustness, and real time of the proposed framework. The results show that the proposed method can provide the great performance of ride comfort, travel efficiency, and longitudinal-lateral stability in real time in the velocity planning process.

Modified tool radius compensation in the Archimedes' spiral tool path for high speed machining of circular geometry

A key role in HSM (High Speed Machining) is played by the NC program code, which guides the tool along a programmed path without jumps in velocity and acceleration. The commonly used CAM (Computer Aided Manufacturing) software offers many operations for dynamic machining, but the generated code is difficult to edit. An alternative is to use parameterized technology cycles. Unfortunately, the circular pocket cycle available on the Siemens Sinumerik 840D controller was not designed for HSM machining. The purpose of the article is to program an Archimedes' spiral using modified tool radius compensation. The parametric NC code was implemented on the Siemens Sinumerik 840D controller as a technology cycle. The obtained trajectory of the tool meets the curvature continuity condition (C2 continuity). The algorithm uses 3 NC program blocks to define the spiral, regardless of its length. Tool positions are calculated directly by the interpolator during the tool's circular motion (G2/G3). Spiral step is achieved by an additional contour offset (OFFN function), and also by multiple repetitions of circles (TURN function). The change in the effective tool radius value during active tool radius compensation (G41/G42) moves the tool away from the contour along the length of the entire NC block. Several spiral programming variants that are used in cycles were analyzed to identify the feed rate drops at joining points between program blocks. During the process, the trajectory and feed rate were recorded using the Sinumerik Trace function. A problem with the Siemens Sinumerik controller was identified when machine axes exceed the acceleration limit. Synchronized actions were implemented to reduce the feed rate, with the acceleration and jerk limit that are specified in the part program being taken into account. The presented cycle, with the graphical user interface, highlights the potential for HSM milling. The conducted experiment shows the need to supplement the Siemens Sinumerik controller with Archimedes' spiral interpolation. New technology cycles will increase productivity and open up new possibilities, such as tapered threads milling.

A Cartesian-Based Trajectory Optimization with Jerk Constraints for a Robot

To address the time-optimal trajectory planning (TOTP) problem with joint jerk constraints in a Cartesian coordinate system, we propose a time-optimal path-parameterization (TOPP) algorithm based on nonlinear optimization. The key insight of our approach is the presentation of a comprehensive and effective iterative optimization framework for solving the optimal control problem (OCP) formulation of the TOTP problem in the (s,s˙)-phase plane. In particular, we identify two major difficulties: establishing TOPP in Cartesian space satisfying third-order constraints in joint space, and finding an efficient computational solution to TOPP, which includes nonlinear constraints. Experimental results demonstrate that the proposed method is an effective solution for time-optimal trajectory planning with joint jerk limits, and can be applied to a wide range of robotic systems.

A novel feed rate scheduling method with acc-jerk-continuity and round-off error elimination for non-uniform rational B-spline interpolation

Abstract Feed rate scheduling is a critical step in computer numerical control machining, as it has a close relationship with machining time and surface quality. It has now become a hot issue in both industry and academia. In this article, we present a novel and complete S-shape-based feed rate scheduling method for three-axis non-uniform rational B-spline (NURBS) tool paths, which can reduce high chord errors and round-off errors, and generate continuous velocity, acceleration, and jerk profile. The proposed feed rate scheduling method consists of three modules: a bidirectional scanning module, a velocity scheduling module, and a round-off error elimination module. The bidirectional scanning module aims to guarantee the continuity of the feed rate at the junctions between successive NURBS blocks, where the chord error, tangential acceleration, and tangential jerk limitations are considered. After the NURBS blocks have been classified into two cases by the previous module, the velocity scheduling module first calculates the actual maximum feed rate. It then generates the feed rate profiles of all NURBS blocks according to the proposed velocity profile. Later, the round-off error elimination module is applied to adjust the actual maximum feed rate so that the total interpolation time becomes an integer multiple of the interpolation period, which leads to the elimination of round-off errors. Finally, benchmarks are conducted to verify the applicability of the proposed method. Compared with the traditional method, the proposed method can save the interpolation time by $4.67$ to $14.26\% $.

Effect of CNC Interpolator Parameter Settings on Toolpath Precision and Quality in Corner Neighborhoods

Surface quality, machining time, and precision of the final workpiece are key criteria of optimization in CNC machining. These criteria are influenced by multiple factors, such as path interpolation, feed drive system settings, machine dynamics, and the manufacturing process. The properties of the output of the interpolator indirectly influence all subsequent phases of the machining process, thus influencing the quality of the end product. This paper focuses on the effects of interpolator settings on toolpath quality and precision in corner neighborhoods for the commercial Heidenhain iTNC interpolator. A novel method of toolpath quality evaluation suitable for interpolator output toolpaths is proposed, and the effect of multiple CNC parameters on toolpath quality and precision in corner neighborhoods is quantified based on results obtained on a testing toolpath and verified on a toolpath composed of linear segments only. Both toolpath quality and precision were found to depend primarily on the parameters of limit frequency, contour tolerance, and corner jerk settings with precision additionally depending on angle size. The results show that both toolpath quality and precision in corner neighborhoods can be successfully controlled by the corner jerk limit parameter settings. The presented methodology provides a practical guide for CNC parameter settings in Heidenhain interpolators aimed at predicting toolpath quality and precision in corner neighborhoods.

Orientation smoothing in multi-axis additive manufacturing

In multi-axis processes, such as material extrusion like Fused Filament Fabrication (FFF), the orientation of the tool relatively to the workspace is usually set by the CAM software to an angle that is locally constant relative to the manufacturing surface. However, in the case of large curvature gradients or small curvature radius of the surface or the path, this method leads to significant variations of the tool orientation. These variation require large compensating movements of the axes to maintain the desired deposition tool orientation along the path. Kinematic constraints such as acceleration or jerk limits can lead to a reduction of the path velocity or noticeable positioning errors along the movement, as well as unwante vibrations, which means poor process conditions and defects in the parts. The paper presents a post path planning algorithm that allows smooth in of the tool orientation to avoid jerky compensation motion of the CNC system by varying the orientation within a defined tolerance. This tolerance depends on the deposition process, and is determined experimentally for a FFF process. The proposed methodology was successfully validated b the manufacturing of two sample parts using a robotic additive manufacturing cell.

A comparison of free trajectory quasi-steady-state and transient vehicle models in minimum time manoeuvres

Lap-time optimisation programs utilising Quasi-Steady-State (QSS) vehicle models are computationally efficient, though inherent simplifications produce inaccuracies. An analysis of the prediction capabilities of a new QSS lap-time optimisation method is presented. A transient vehicle model is formulated with seven degrees-of-freedom (DOF) dynamics. The QSS vehicle model utilises point-mass dynamics, where accelerations are constrained by a bi-quintic piecewise spline surface produced with an identical transient vehicle model. Notable changes to the development of the new QSS model include, evaluation of the acceleration envelope in natural coordinate frame, and the implementation of a normal jerk limit which acts to artificially mimic the yaw inertia resistance during change of direction manoeuvres. Results of the minimum time solution are shown for left-hand turn, double lane change and full circuit analysis based on Adria International Raceway. An accuracy improvement against previous QSS models is presented. Minimum time results for the new QSS model are within for left turn, for Adria full circuit, and for double lane change. Optimal accelerations, track centreline offset and velocities are presented and compared.

End control damping algorithm for a stabilized gun turret system for the satisfaction of the collision avoidance requirement

This paper presents a collision avoidance algorithm for stabilized gun turrets and its real-time implementation. With the help of new collision avoidance algorithm, all types of turrets can be driven more efficiently and safely according to the specified speed, acceleration and jerk limits. Even in situations such as avoiding obstacles, deceleration/acceleration, if the user issues new commands which does not cause a collision, the algorithm starts to apply the new commands providing flexibility to the user. Since all possible worst scenarios are examined one by one, it is guaranteed that the algorithm provides collision free motion in both simulations and real-time tests. A configuration space where worst scenarios can occur is created for the performance measurement of the algorithm, and the same space is used in all tests. By giving different speed commands in the specified configuration space, the performance of the algorithm at different speeds is observed on the stabilized gun turret. For the measurement of the performance under the noisy speed commands, a custom noisy speed command of about 1000 s is created and both simulation and real-time tests are performed. As a result of these tests, it is shown that there is no collision. Finally, by adding cascade position control loop, the departure from the starting point to the desired target point is achieved without any collision. The most important feature that distinguishes this algorithm from others is both speed and position can be controlled and during transition phase, the target point can be changed instantly. In addition, no target position is required for the system to move collision-free, only axis speed commands are sufficient. Since the algorithm does not intervene in the speed and torque loops in contrast to potential field-based methods, it can be added to ready-to-use systems by manipulating only the speed references.

A new approach to time-optimal trajectory planning with torque and jerk limits for robot

In this study, a new convex optimization (CO) approach to time-optimal trajectory planning (TOTP) is described, which considers both torque and jerk limits. The key insight of the approach is that the non-convex jerk limits are transformed to linear acceleration constraints and indirectly introduced into CO as the linear acceleration constraints. In this way, the convexity of CO will not be destroyed and the number of optimization variables will not increase, which give the approach a fast computation speed. The proposed approach is implemented on random geometric path of a 6-DOF manipulator. Compared with a similar method, the results show that the torque and jerk limits are addressed by a reasonable increase in the computation time. In addition, the maximum value of joint jerk reduces by over 80% and the joint torque curves are smoother in the comparison, which demonstrates that this approach has the ability to effectively restrain acceleration mutation.

Nonlinear output path following control using a two-loop robust model predictive control approach

In this paper, output tracking of a geometric path for a nonlinear uncertain system with input and state constraints is considered. We propose an enhanced two-loop model predictive control approach for output tracking of a nonlinear uncertain system. Additionally, we propose an optimal version of output path following control problem to improve the controller synthesis. Satisfaction of the dynamical constraints of a system such as velocity, acceleration and jerk limitations is added to the problem introducing a new augmented system. The recursive feasibility of the proposed method is demonstrated, and its robust stability is guaranteed such that relaxation on the terminal constraint and penalty are achieved. To validate the theoretical benefits of the proposed controller, it is simulated on a SCARA robot manipulator and the results are compared with a two-loop model predictive controller successfully.

Real-Time Local Optimal Bézier Corner Smoothing for CNC Machine Tools

A straight line or G01 is the most common path in computer numerical control (CNC) contour machining. However, non-smooth corners introduce discontinuous movement along each axis during machining. The commonly used strategy is to redesign a corner into a smooth corner path. Therefore, optimal corner smoothing should simultaneously find an optimal corner path and a corner speed that satisfied the axis motion limits. To achieve this goal, we use particle swarm optimization (PSO) to find the optimal Bezier curve and the optimal corner speed, then convert the axis constraints into polynomial inequalities and use fitness selection to deal with axis acceleration and jerk limits. For real-time operation, we establish a look-up table with the optimal corner speed and corner path models for use by a CNC controller. In the experiment, the YCM NXV560A vertical machining center was used to conduct a real machining test on a Taiwan contour, and the feasibility of the controller to generate the optimal corner strategy for various linear paths was verified.

Development of an Adaptive-Feedrate Planning and Iterative Interpolator for Parametric Toolpath with Normal Jerk Constraint

Compared to conventional linear and circular segments, the parametric curve has advantages in approximating and machining, guaranteeing higher machining precision and better machining quality. Therefore, in Computer Numerical Control (CNC) systems, parametric toolpath has become more and more popular for its high-performance in practical machining and the performance of the parametric interpolator has become a standard to illustrate the advanced CNC systems. In this paper, adaptive-feedrate planning and the iterative interpolator have been developed to generate sampling points with respect to error and higher order kinematic constraints. Firstly, a jerk-limited feedrate profile and look-ahead algorithm are utilized to provide reachable feedrate at critical points. Afterwards, normal jerk (i.e. the jerk in a normal direction) are limited to improve machining precision and quality. In theory, it is proved that the normal jerk limitations have relationship with curvature derivative and a novel iterative interpolator is proposed to ensure the normal jerk limitation by considering the corresponding constraints at curvature derivative extreme points. Finally, simulation and experiments are conducted to demonstrate the efficiency and contour performance of the proposed method compared to conventional method and time-optimal method.

Waiter Robots Conveying Drinks

Robots have been reportedly seen serving food in several restaurants in many parts of the world. New ventures have been deploying mechanical partners which promote the growth in service robotics. However, robots are considerably incompetent when it comes to beverage and soup delivery. The physical challenge behind the clumsy motion of these machines is found to be its jerky motion control. Jerk control solutions are widely studied in a constrained environment but not well introduced in dynamic environments. In this paper, we will begin by examining developed kinematics solutions, open-source packages from Robot Operating System and the constraints of motion planning. The proposed solution in this paper provides a quick system response with jerk limits using spline velocity profiles. The solution will introduce the concepts of a state machine design that enables the robot to behave and move reactively; effectively balancing its desired velocity and position without spilling a drop of customer satisfaction. Experiments have proven that robots can move at higher velocity without any crashing, spilling, or docking issues. The smooth velocity control proposed will improve the capabilities of waiter robot and service operations in restaurants.

Crossing principle-based feedrate planning method for 5-axis CNC milling with drive constraints

ABSTRACT The careful selection of the feedrate is necessary during the numerical control (NC) machining process, to prevent drive characteristics such as velocity, acceleration, and jerk of each axis from exceeding their physical limits, as this can damage the structure of the machine tool. In this study, a new off-line feedrate interpolation method based on the constraint intersection principle is proposed that can satisfy the chord error, velocity, acceleration, and jerk limits of the drive axes. The relationship between the feedrate of the cutter tip and the driving characteristics of each axis is established by changing the kinematics formula. Based on the principle of cross-constraints, the constraint overshoot of the driving axis in a sensitive area on the feed path can be prevented effectively, thereby ensuring the geometric accuracy and machine drive characteristics. Furthermore, illustrated examples are provided to validate the feasibility and applicability of the proposed feedrate interpolation method.

Data Based Parameter Setting Method for Adaptive Cruise Control

Recent years, advanced driver assistance system (ADAS) has been highly developed and widely used. Among various ADAS techniques adaptive cruise control (ACC) is the fundamental of longitudinal control. The tradeoffs among safety, comfort and traffic efficiency are the main issue in ACC design process. In this study, large amount of road tests was carried out to explore the circumstance characteristics in ACC usages scenarios. Based on statistical analysis of road test data, a method for ACC safety performance evaluation is proposed. Furthermore, the effects of parameters such as following distance, jerk limit and time delay to ACC safety performance are discussed. Finally, a way of ACC parameter designing is developed, this method can obtain best comfort and traffic efficiency after safety request is guaranteed. In this study, regulations and realistic constrains of production vehicles are considered. Different from theoretical simulation, production-oriented ACC system is restricted in maximum deceleration, maximum braking jerk, detection latency, actuation latency, calculation capacity etc. For this reason, all the analysis is based on statistical results and requests from actual products, no computationally expensive optimal method is implemented. The proposed method may not get optimal results in theoretical simulation but is very instructive in production-oriented ACC system design.

Spline-Based Trajectory Generation for CNC Machines

Manufacturing of workpieces with computerized numerical control machines requires computing machine tool trajectories that fast and accurately track the desired workpiece contour. This paper presents a novel B-spline trajectory generation method for machine tools. The method solves an optimal control problem to minimize the motion time of the tool, while taking into account the velocity, acceleration, and jerk limits of the tool axes. Furthermore, it directly includes the allowed workpiece tolerance, by constraining the trajectory to lie inside a tube around the nominal geometry contour. This allows exploring the tradeoff between accuracy and productivity, while computing near-optimal trajectories. The presented method creates fluent connections between segments that build up the contour by simultaneously optimizing trajectories for multiple segments. On the other hand, limiting the amount of simultaneously optimized segments and using an efficient problem formulation keeps the computation time acceptable. The trajectory generation method is validated in simulation by comparison with industrial benchmarks, showing a reduction in machining time of more than ${\text{10}}\%$ . The comparison to a state-of-the-art corner smoothing approach shows that the presented method obtains similar or slightly faster trajectories, at a computation time that is up to 45 times lower. In addition, the method is validated experimentally on a three-axis micromilling machine. To easily generate trajectories for different workpieces and machines, the method is included in a user-friendly open-source software toolbox.

Distributed-mass payload dynamics and control of dual cranes undergoing planar motions

Abstract Unwanted oscillations caused by the operator-commanded motions lower the capable operating speeds and degrade the safety of dual cranes moving distributed-mass payloads. Mounting numbers of works have been devoted to the dynamics and control of dual cranes. However, few studies have been dedicated to the accurate estimation of natural frequency, which is a critical factor for controlling the dual cranes. This paper develops a new method to predict the natural frequency of dual planar cranes with different cable lengths. Furthermore, a modified extra-insensitive (MEI) input shaper is proposed to suppress the oscillations of the payload swing and pitch in the dual cranes. The MEI shaper has good robustness to large changes in the frequency, and has good performance in the jerk limitation. Simulated and experimental investigations are performed on small-scale dual cranes transporting a slender beam to validate the system dynamic behavior and the effectiveness of the MEI shaper.

Receding Horizon LQT Control for Vehicle Driveability under Tip-in Condition

Abstract When the vehicle is under the Tip-in condition, the low-frequency longitudinal vibration occurs which generates a large jerk and makes a bad impact on the riding comfort. Under the Tip-in condition, the vehicle dynamic performance requires quick engine torque rise process, while quick torque rise process will lead to bad riding comfort. Therefore, in this paper an engine torque compensation controller is designed taking vehicle driveability as the optimization goals, and using the vehicle jerk limit as the boundary condition. First, according to the vehicle dynamic analysis, the control-oriented model of the vehicle driveline is established and verified by the real vehicle experimental data. Second, the Receding Horizon Linear Quadratic Tracking (RHLQT) algorithm taking vehicle acceleration as the tracking target is designed. Finally, by simulating on the hardware-in-the-loop (HIL) platform, the vehicle driveability under the control of the RHLQT, PID and the torque rising slope limit method are compared and analyzed. The result shows that the proposed control algorithm can achieve both good dynamic performance and acceptable riding comfort of the vehicle.