Trajectory Planning Strategy Research Articles

Improving fuel efficiency of connected and automated transit buses on signallised corridors

This study proposes a trajectory planning strategy for connected and automated transit buses travelling on signallised corridors. The goal is to improve the fuel efficiency of transit buses by taking into consideration of traffic signal timings and bus schedules. The strategy takes advantage of the emerging connected vehicle technologies, allowing for utilising real-time information, including traffic signal timings, bus schedules and dynamic speed limits for trajectory optimisation. The authors construct the proposed strategy as a Min-Sum-Min Model and solve it by integrating Simultaneous Perturbation Stochastic Approximation and Pontryagin's Maximum Principle. The effectiveness of the proposed strategy is demonstrated in a real-world case study. It is discovered that the reduction in bus energy consumption by the proposed strategy is up to 27.8 and 16.4%, respectively, when compared with an aggressive strategy and an alternative strategy.

Time-optimal fold out of large-scale manipulators with obstacle avoidance

The autonomous operation of large-scale construction machines is of growing interest in the recent years. In this work, the optimal fold out and fold in maneuvers of the boom of a mobile concrete pump are considered. The five degrees of freedom large-scale manipulator (boom) of the mobile concrete pump is operated in an environment with several obstacles and its motion is restricted to meet a number of system and safety constraints. A trajectory planning strategy is presented in this work, which allows to obtain nearly time-optimal trajectories. The presented approach features a rather low computational complexity, which, in contrast to the state of the art, exhibits very fast calculation times. The feasibility of the proposed trajectory planning strategy is analyzed by simulation results for a realistic scenario of a real-world mobile concrete pump.

Q-learning trajectory planning based on Takagi–Sugeno fuzzy parallel distributed compensation structure of humanoid manipulator

NAO is the first robot created by SoftBank Robotics. Famous around the world, NAO is a tremendous programming tool and he has especially become a standard in education and research. Aiming at the large error and poor stability of the humanoid robot NAO manipulator during trajectory tracking, a novel framework based on fuzzy controller reinforcement learning trajectory planning strategy is proposed. Firstly, the Takagi–Sugeno fuzzy model based on the dynamic equation of the NAO right arm is established. Secondly, the design and the gain solution of the state feedback controller based on the parallel feedback compensation strategy are studied. Finally, the ideal trajectory of the motion is planned by reinforcement learning algorithm so that the end of the manipulator can track the desired trajectory and realize the valid obstacle avoidance. Simulation and experiment shows that the end of the manipulator based on this scheme has good controllability and stability and can meet the accuracy requirements of trajectory tracking accuracy, which verifies the effectiveness of the proposed framework.

Novel method for six-legged robots turning valves based on force sensing

According to previous studies, usually multi-degree-of-freedom (DOF) manipulators are installed on robots to perform the valve turning task, and vision systems are used to detect the valve data. However, vision systems are limited in the environment with less visibility and the internal force always occurs as the multi-DOF manipulator is compelled to follow the valve exactly by a firm grasp. In this paper, a novel valve turning method based on force sensing is proposed and implemented to the six-legged robot. Firstly, the method can enable the robot to judge the valve position through force sensing in the case of poor vision situation. Moreover, a 0-DOF tool is installed on the body of the robot. By integrating with the body, the tool has enough workspace to perform the operation task. Compared with the multi-DOF manipulator, loose grasp achieved by the 0-DOF tool helps to reduce the internal force during the valve turning process. In addition, the real-time trajectory planning strategy is designed for the robot. Based on the above initiatives, experiments are carried out to demonstrate effectiveness of the method.

Research on Cooperative Planning Technique of Gliding Trajectory for Multi-aircraft

In order to make multi-aircraft cooperating with each other and reaching the specified target area at the same time, the gliding trajectory cooperating planning is studied. The trajectory planning model is established. For a single aircraft, online trajectory generation based on the height vs velocity (H-V) profile is achieved, and a feedback linearization tracking guidance law is designed. For multi-aircraft, a multi-aircraft trajectory planning strategy based on time coordination is designed. Multi-aircraft trajectory cooperating planning under two different operational backgrounds is simulated. Simulation results show that the algorithm can achieve multi-aircraft trajectory cooperating planning, and multi-aircraft can reach the target area at the same time.

A new path-constrained trajectory planning strategy for spray painting robots - rev.1

In this paper, a novel method for planning spray painting trajectories for industrial robots is presented. The proposed method takes as input an arbitrary parametric description of the end-effector path in the operative space. The method is aimed at providing feasible motion profiles without resorting to optimization routines and without the need for a dynamic description of the painting robot. The motion law is then defined by the algorithm to achieve end-effector speed limitation, in order to comply with the constraints imposed by the spray painting process and by the manipulator specifications. Subsequently, a sequence of look-ahead filtering operations on the speed profiles ensures joint acceleration limitation. The proposed method has been tested on an industrial painting robot, showing its effectiveness, which is experimentally evaluated against the results obtained with the original manufacturer’s proprietary planning method. The improvements include, other then the required end-effector speed and joint acceleration limitation, a sensible reduction of the cycle time, and of the torque effort requirement. The method is of simple implementation and can be useful for other robot-oriented industrial tasks.

The man-machine motion planning of rigid-flexible hybrid lower limb rehabilitation robot

At present, in view of the question that the general lower limb rehabilitation training robot is only achieving motion training of lower limb’s flexion and extension. A kind of the lower limb rehabilitation robot is conceived which can achieve lower limb adduction or abduction and internal or external rotation in sports training, and it is aimed to research the robot’s structure and motion planning. When analyzing the typical movement forms of the lower limb, the relation of man–machine coordinated movement is also considered. A kind of lower limb rehabilitation training robot is conceived, which consists of the rigid mobile device and the flexible drive system. The influence coefficient method is used to analyze the kinematics of the robot. According to the rehabilitation training of man–machine cooperation relations, the trajectory planning strategy is studied. A robot configuration that meets the needs of rehabilitation motion trajectory planning is drawn by setting the parameters of the robot mechanism and simulation. According to the trajectory of the training program, the simulation analysis of the state of wire movement is carried out. The experimental study of adduction and abduction of the lower extremities was carried out, proving the effectiveness of robot mechanism.

Adaptive non‐linear trajectory tracking control for lane change of autonomous four‐wheel independently drive electric vehicles

Since autonomous four-wheel independently drive electric vehicles have the characteristics of parameter uncertainties, non-linearities and redundant actuators, trajectory tracking control for lane change of autonomous electric vehicles is regarded as a challenging task. A novel non-linear trajectory tracking control strategy is designed for lane changing manoeuvre. First, a dynamic trajectory planning strategy is proposed to update the desired trajectory according to the real-time information acquired through vehicle-to-vehicle communications. Second, a robust adaptive non-linear fuzzy backstepping controller is presented to produce the generalised forces/moment of autonomous electric vehicles, and the stability of this proposed adaptive controller is proven by the Lyapunov theory. Then, the quadratic optimisation goal function of tire energy dissipated power is constructed, and the optimal control allocation method is proposed to produce the desired longitudinal and lateral tire forces of autonomous electric vehicles. Finally, simulation results manifest that the proposed adaptive control strategy has the distinguished tracking performance.

C2 continuous time-dependent feedrate scheduling with configurable kinematic constraints

We present a configurable trajectory planning strategy on planar paths for offline definition of time-dependent C2 piecewise quintic feedrates. The scheduler can be applied to any path with a sufficiently smooth piecewise parametric representation and it can be used in different formulations subdivided in strict and relaxed. In the first case, control on chord tolerance, as well as on the Cartesian components of velocity, acceleration and jerk is ensured. Since the relaxed formulations can usually still ensure the desired bounds while simultaneously producing faster motions, the configurability feature is useful not only when reduced motion control is required but also when full kinematic control has to be guaranteed. When Pythagorean-hodograph spline curves are considered, the corresponding accurate and efficient CNC interpolator algorithms can be exploited, as shown in the numerical experiments.

Quadrotor Thrust Vectoring Control with Time and Jerk Optimal Trajectory Planning in Constant Wind Fields

This paper proposes a trajectory planning and control strategy to optimally visit a given set of waypoints in the presence of wind. First, aerodynamic properties of quadrotors which affect trajectory planning and tracking performance are investigated. Blade flapping, induced and parasitic drag are derived and an extended method to identify all coefficients from flight test data is developed. Then, a three-step approach is suggested to optimize the trajectory. These steps reduce the size of the optimization problem and thereby increase computational efficiency while still guaranteeing near optimal results. The trajectories are optimized for minimal aerodynamic drag and minimal jerk. The derived smooth trajectory generation is compared with traditional trajectory planning consisting of discrete point to point tracking followed by low-pass filtering. The new trajectories yield a clear reduction in maximal needed thrust and in Euler angle aggressiveness. A thrust vectoring controller is designed, which exploits the a priori trajectory information and identified aerodynamic properties. Its performance is compared to a standard PID controller and results show a reduction in tracking delay and an increase in thrust and attitude angle margins, which overall enable faster flight.

Trajectory Optimization of Electrostatic Spray Painting Robots on Curved Surface

In this paper, a new practical electrostatic rotating bell (ESRB) cumulative rate model of painting is derived, and an experimental study on painting is carried out. First, the experimental method is used to obtain the radial thickness profile function of the spatial paint distribution of static spray. Then, a spatial trajectory-planning scheme for a spray-painting robot based on a rectangular model is presented. This method designs the spatial path of the spray-painting robot by using the cuboid model method after the optimal value is taken as the width d of the overlapping area of the two spray-painting strokes in the plane. The experimental results illustrate that the paint thickness basically meets the requirements, and the experimental results verify the effectiveness of the trajectory optimization method.

Spiral trajectory planning approach for underground cavity measurements based on laser scanning

Underground cavity three-dimensional measurements constitute an important and challenging task in underground mining. The laser scanning method is a relatively precise and efficient way to address this problem, but it is limited by the unevenness of the point cloud that reduces the scanning efficiency. In this paper, an approach that can increase the evenness of the point cloud in underground laser scanning is proposed. The approach is based on a spiral trajectory planning strategy. The scanning trajectory is generated from previous scan by solid geometry. Exceptions are discussed and solutions are proposed. The approach was used in an actual laser scanning system and experiments were carried out in a gold mine in Hebei Province, North China. To assess the results, 3D Delaunay triangulation network of laser points was built in accordance to a semispherical-planer projection rule, and the area of each triangle in the network was calculated. The coefficient of variance of the triangular area indicated that the new approach can increase the evenness of the laser points efficiently.

Human-robot collaboration while sharing production activities in dynamic environment: SPADER system

Interactive robot doing collaborative work in hybrid work cell need adaptive trajectory planning strategy. Indeed, systems must be able to generate their own trajectories without colliding with dynamic obstacles like humans and assembly components moving inside the robot workspace. The aim of this paper is to improve collision-free motion planning in dynamic environment in order to insure human safety during collaborative tasks such as sharing production activities between human and robot. Our system proposes a trajectory generating method for an industrial manipulator in a shared workspace. A neural network using a supervised learning is applied to create the waypoints required for dynamic obstacles avoidance. These points are linked with a quintic polynomial function for smooth motion which is optimized using least-square to compute an optimal trajectory. Moreover, the evaluation of human motion forms has been taken into consideration in the proposed strategy. According to the results, the proposed approach is an effective solution for trajectories generation in a dynamic environment like a hybrid workspace.

A swing constrained time-optimal trajectory planning strategy for double pendulum crane systems

In practice, overhead crane systems are widely used and the traditional control methods for a crane system usually treat it as a single pendulum system. However, when the hook mass cannot be ignored or the payload is too large, the crane system may behave more like a double pendulum system, which leads to the fact that traditional control methods are not suitable in this situation. In this paper, we focus on the control problem of a double pendulum crane system and propose a time-optimal trajectory planning method with the consideration of various constraints which can achieve the objectives of both accurate trolley positioning and double pendulum swing suppression. Specifically, the discrete system model is obtained using the discretization technique firstly. Then by deeply analyzing and considering a series of constraints, we formulate a quasiconvex optimization problem. After that, the bisection method is chosen to solve the obtained optimization problem with the corresponding time-optimal trajectory constructed conveniently. A tracking controller is also designed for the double pendulum crane system, which achieves proper trolley tracking performance. At last, both simulation and experimental results are included to illustrate the superior performance of the proposed trajectory planning method.

Jerk Trajectory Planning for Assistive and Rehabilitative Mechatronic Devices

This paper presents an effective application of Jerk to plan trajectory and control undesirable effects (e.g. patient’s hesitations and tremors) in active rehabilitation training using some mechatronic devices. Jerk is the time derivative of acceleration, and it is associated to the rapidly changing of forces. It is more sensible than other parameters (e.g. speed or acceleration) to intercept undesirable conditions as the patient’s tremors or sub-movements. This study proposes an innovative regulator system based on Minimum Jerk trajectory planning and formulation. The trajectory planning strategy of limb rehabilitation is described considering the clinical therapy requirements and patients’ needs. A case study based on a path shape that simulates a point-to-point motion is illustrated to demonstrate the effectiveness of the proposed solution. The study presents the kinematic analysis of the mechatronic device and the formulation of the objective function to minimize Jerk along the trajectory. A controller was developed to attenuate the micro sub-movements that recreated the patient hesitations. A set of simulations of the mechatronic model was performed highlighting the reduction of the jerk peak magnitude and the deviation from pre-determined trajectory when the controller was activated, improving the rehabilitation training.

Conceptual Design and Trajectory Planning of a Precision Repetitive-Scanning Stage With Separated Drive Unit for Energy Saving

Precision repetitive-scanning stages, which exist in lithographic reticle systems, scanning probe microscopes, and scanning electrodischarge machines, have been widely used in modern precision industry. To design such stages, energy consumption has become one of the most important criteria due to energy crisis and practical heat-reduction request. Considering the motion characteristics of such stages, it would lead to an energy-saving nature if the accelerated and constant-speed motions are driven by two separated drive units (SDUs). Inspired by this thought, we propose a novel concept of precision repetitive-scanning stage especially equipped with a separate permanent-magnet drive unit for accelerated motion. In order to exploit the function of SDUs for achieving high energy-saving performance, a modified repetitive-scanning trajectory is proposed. For this trajectory, complete analytic formulas allowing real-time planning are provided to match the permanent-magnet drive force, which results in a sufficient utilization of the SDUs’ drive ability. Finally, a precision repetitive-scanning stage prototype is set up. Comparative experimental results demonstrate that the proposed structural concept and its matched trajectory can significantly save energy without any motion accuracy deterioration. Essentially speaking, the proposed conceptual design and trajectory planning strategy provide a good guidance for precision repetitive-scanning system on energy saving, which could be applied to industry of semiconductor manufacturing, precision detection, microfabrication, and so on.

The Study of S-Shaped Acceleration and Deceleration Curve and the Trajectory Planning Strategy Analysis

The invention of the Numerical Control (NC) technology have brought the new revolution of manufacturing since 20th century intermediate stage. Computer Numerical Control (CNC ) technology is the foundation of the modern manufacturing technology, integrating the traditional manufacturing technology, modern control technology and modern optical-electromechanical technology.[1,2]As the core of CNC technology, CNC system is requesting higher precision and higher speed as it develops. So it is necessary to meet the requirements of the machining surface quality and avoid the occurrences of the processing speed decline or even stall, which depends on the good controls of the acceleration and deceleration of the feed shaft [3].This article briefly analyzes some existing strategies of the acceleration and deceleration, then mainly introduces the s-shaped acceleration and deceleration curve method and the trajectory planning strategy of it.

Inter-Vehicle Communication Aided Trajectory Planning for Automated Vehicles

Trajectory planning is a key to achieve safe and efficient driving of automated vehicles. We propose a trajectory-planning suite that enables the generation of a safe and comfortable trajectory through receiving cooperative messages (e.g. CAM and DENM) to detect the obstacle vehicles. We also present a collision probability model to improve the accuracy of vehicles' decision-making. Our approach mainly experiences three steps. The trajectory generation module first generates a candidate set of eligible trajectories by synthetically considering the current yaw angle, velocity, and physical characteristics of the vehicle. Then the state prediction module predicts the position and velocity of the potential obstacle vehicle with respect to the transmission delay. The trajectory selection module finally chooses a best suitable trajectory to follow in terms of the current context. Moreover, we also investigate the effects of the communication performance on the trajectory planning. The extensive simulations show that the proposed trajectory-planning scheme is capable of guiding vehicles smoothly and safely across a common traffic situation against other obstacle vehicles.

Avoiding the singularities of 3-RPR parallel mechanisms via dimensional synthesis and self-reconfigurability

This paper deals with the avoidance of singularities of 3-RPR parallel mechanisms, for a given workspace. Two approaches are proposed: (1) the dimensional synthesis of such robots for a prescribed singularity-free workspace, and (2) their reconfiguration via actuation redundancy. The proposed approach for the dimensional synthesis of 3-RPR parallel mechanisms considers the constraints required for obtaining the optimal mechanism geometry in order to contain a desired workspace while avoiding singularities. A relaxation method based on the McCormick relaxation is presented to convexify the associated optimization problem. To prevent the relaxation from becoming too loose, a branch-and-prune algorithm is proposed, which converges to the globally optimal solution. Upon a different approach, a 3-RPR PM with self-reconfiguration capability is introduced. This redundant manipulator can change its geometry to obtain singularity-free paths between prescribed points inside its workspace. The proposed trajectory planning strategy works in 2 phases: the first where the mechanism acts as a 2-PRPR PM, and the second where it behaves as a 3-RPR PM. Finally, several case studies are presented to demonstrate the performance of the proposed algorithms. The running times of the proposed algorithms are remarkably low compared to those of other methods proposed in the literature.

Dynamics and Trajectory Planning for Reconfigurable Space Multibody Robots

A free-floating space robot equipped with multiple reconfigurable manipulators is designed and investigated in this paper. Lockable passive cylindrical joints (PCJs) are utilized to make the manipulator have the ability of changing its length and twisted angle. Each cylindrical joint, connecting two adjacent rigid links, has no embedded actuators but a brake mechanism. Normally, the mechanism is locked during the operation. When in the reconfiguration stage, two manipulators grasp each other to form a closed loop. Then one PCJ is unlocked, whose relative rotation and translation can be changed by the active torques at other joints. This system is a typical space multibody system. The dynamics of the space robot with unlocked cylindrical joints and a closed structural loop is investigated. The equations of motion are derived through Maggi–Kane's method. The obtained mathematical model is free of multipliers, which makes it suitable for controller design. A trajectory planning algorithm capable of avoiding the configuration singularity of the manipulators is proposed. A slide mode controller embedded with an extended state observer (ESO) is designed for the trajectory tracking control. Numerical simulations demonstrate the effectiveness of the trajectory planning and control strategy for the reconfiguration process.