TRAJECTORY GENERATION AND CONTROL FOR NON-CIRCULAR CNC TURNING

A trajectory generation method which is based on NURBS interpolation is studied to improve the fitting accuracy and smoothness of non-circular cross section and obtain higher accuracy of the final non-circular profile control. After using the NURBS, the most optimized and smooth trajectory for the linear actuator can be obtained. For the purpose of machining the non-circular cross section by CNC turning, the fast response linear actuator has been used. The control algorithm which is compound control of proportional-integral-differential （PID） and iterative learning control has been developed for non-circular profile generation. By using the NURBS interpolation and the compound control of PID and iterative learning control, the final motion accuracy of linear actuator has been improved, therefore, the machining accuracy of the non-circular turning can be improved.

On-line trajectory generation of midcourse cooperative guidance for multiple interceptors

The cooperative interception trajectories generation of multiple interceptors to hypersonic targets is studied.First,to solve the problem of on-line trajectory generation of the single interceptor,a generation method based on neighborhood optimal control is adopted.Then,when intercepting the strong maneuvering targets,the single interceptor is insufficient in maneuverability,therefore,an on-line multiple trajectories generation algorithm is proposed,which uses the multiple interceptors intercept area(IIA)to cover the target's predicted intercept area(PIA)cooperatively.Through optimizing the interceptors'zero control terminal location,the trajectories are generated on-line by using the neighborhood optimal control method,these trajectories could make the IIA maximally cover the PIA.The simulation results show that the proposed method can greatly improve the interception probability,which provides a reference for the collaborative interception of multiple interceptors.

Bio-inspired Collision-free 4D Trajectory Generation for UAVs Using Tau Strategy

Inspired by the general tau theory in animal motion planning, a collision-free four-dimensional （4D） trajectory generation method is presented for multiple Unmanned Aerial Vehicles （UAVs）. This method can generate a group of optimal or near-optimal collision-free 4D trajectories, the position and velocity of which are synchronously planned in accordance with the arrival time. To enlarge the shape adjustment capability of trajectories with zero initial acceleration, a new strategy named intrinsic tau harmonic guidance strategy is proposed on the basis of general tau theory and harmonic motion. In the case of multiple UAVs, the 4D trajectories generated by the new strategy are optimized by the bionic Particle Swarm Optimization （PSO） algorithm. In order to ensure flight safety, the protected airspace zone is used for collision detection, and two collision resolution approaches are applied to resolve the remaining conflicts after global trajectory optimization. Numerous simulation results of the simultaneous arrival missions demonstrate that the proposed method can effectively provide more flyable and safer 4D trajectories than that of the existing methods.

Bioinspired 4D Trajectory Generation for a UAS Rapid Point-to-Point Movement

A bioinspired trajectory generation approach for Unmanned Aerial System （UAS） rapid Point-to-Point （PTP） movement was presented. The approach was based on general tau theory developed by biologists from observing and studying the behavior of birds and some other animals. We applied the bioinspired approach to the rapid PTP movement problem of a rotary UAS and derived two different trajectory planning strategies, namely, the tau coupling strategy and the intrinsic tau gravity guidance strategy. Based on general tau theory, according to the dynamic model of UAS, we presented a new strategy named intrinsic tau jerk guidance which can fit the movement that the initial acceleration of the UAS is zero. With new strategies, flight trajectory generation examples with a UAS were presented. The kinematics and dynamics analyses of the UAS for rapid PTP movement were presented with simulation results which show that the generated trajectories were feasible.

Reference Trajectory Generation for 3-Dimensional Walking of a Humanoid Robot

Humanoid walking planning is a complicated task because of the high number of degrees of freedom （DOFs） and the variable mechanical structure during walking. In this paper, a planning method for 3- dimensional （3-D） walking movements was developed based on a model of a typical humanoid robot with 12 DOFs on the lower body. The planning process includes trajectory generation for the hip, ankle, and knee joints in the Cartesian space. The balance of the robot was ensured by adjusting the hip motion. The angles for each DOF were obtained from 3-D kinematics calculation. The calculation gave reference trajectories of all the DOFs on the humanoid robot which were used to control the real robot. The simulation results show that the method is effective.

Optimal midcourse trajectory cluster generation and trajectory modification for hypersonic interceptions

The hypersonic interception in near space is a great challenge because of the target’s unpredictable trajectory, which demands the interceptors of trajectory cluster coverage of the predicted area and optimal trajectory modification capability aiming at the consistently updating predicted impact point(PIP) in the midcourse phase. A novel midcourse optimal trajectory cluster generation and trajectory modification algorithm is proposed based on the neighboring optimal control theory. Firstly, the midcourse trajectory optimization problem is introduced; the necessary conditions for the optimal control and the transversality constraints are given.Secondly, with the description of the neighboring optimal trajectory existence theory(NOTET), the neighboring optimal control(NOC)algorithm is derived by taking the second order partial derivations with the necessary conditions and transversality conditions. The revised terminal constraints are reversely integrated to the initial time and the perturbations of the co-states are further expressed with the states deviations and terminal constraints modifications.Thirdly, the simulations of two different scenarios are carried out and the results prove the effectiveness and optimality of the proposed method.

Integrated Entry Guidance for Reusable Launch Vehicle

A method for the implementation of integrated three-degree-of-freedom constrained entry guidance for reusable launch vehicle is presented. Given any feasible entry conditions, terminal area energy management interface conditions, and the reference trajectory generated onboard then, the method can generate a longitudinal guidance profile rapidly, featuring linear quadratic regular method and a proportional-integral-derivative tracking law with time-varying gains, which satisfies all the entry corridor constraints and meets the requirements with high precision. Afterwards, by utilizing special features of crossrange parameter, establishing bank-reversal corridor, and determining bank-reversals according to dynamically adjusted method, the algorithm enables the lateral entry guidance system to fly a wide range of missions and provides reliable and good performance in the presence of significant aerodynamic modeling uncertainty. Fast trajectory guidance profiles and simulations with a reusable launch vehicle model for various missions and aerodynamic uncertainties are presented to demonstrate the capacity and reliability of this method.

Adaptive Walking Control of Biped Robots Using Online Trajectory Genera- tion Method Based on Neural Oscillators

This work concerns biped adaptive walking control on irregular terrains with online trajectory generation. A new trajectory generation method is proposed based on two neural networks. One oscillatory network is designed to generate foot trajectory, and another set of neural oscillators can generate the trajectory of Center of Mass （CoM） online. Using a motion engine, the characteristics of the workspace are mapped to the joint space. The entraining property of the neural oscillators is exploited for adaptive walking in the absence of a priori knowledge of walking conditions. Sensory feedback is applied to modify the gen- erated trajectories online to improve the walking quality. Furthermore, a staged evolutionary algorithm is developed to tune system parameters to improve walking performance. The developed control strategy is tested using a humanoid robot on ir- regular terrains. The experiments verify the success of the presented strategy. The biped robot can walk on irregular terrains with varying slopes, unknown bumps and stairs through autonomous adjustment of its walking patterns.

Energy-optimal trajectory planning for solar-powered aircraft using soft actor-critic

High-Altitude Long-Endurance(HALE)solar-powered Unmanned Aircraft Vehicles(UAVs)can utilize solar energy as power source and maintain extremely long cruise endurance,which has attracted extensive attentions from researchers.Trajectory optimization is a promising way to achieve superior flight time because of the finite solar energy absorbed in a day.In this work,a method of trajectory optimization and guidance for HALE solar-powered aircraft based on a Reinforcement Learning(RL)framework is introduced.According to flight and environment information,a neural network controller outputs commands of thrust,attack angle,and bank angle to realize an autonomous flight based on energy maximization.The validity of the proposed method was evaluated in a 5-km radius area in simulation,and results have shown that after one day-night cycle,the battery energy of the RL-controller was improved by 31%and 17%compared with those of a Steady-State(SS)strategy with a constant speed and a constant altitude and a kind of statemachine strategy,respectively.In addition,results of an uninterrupted flight test have shown that the endurance of the RL controller was longer than those of the control cases.

Trajectory optimisation in electrical discharge machining of three-dimensional curved and twisted channels

Numerical control electrical discharge machining(NC EDM) is one of the most widely used machining technologies for manufacturing a closed blisk flow path, particularly for three-dimensional(3D) curved and twisted flow channels. In this process, tool electrode design and machining trajectory planning are the key factors affecting machining accessibility and efficiency. Herein, to reduce the difficulty in designing the electrode and its motion path in the closed curved and twisted channels, a heuristic search hybrid optimisation strategy based on channel grids is adopted to realise the initial electrode trajectory design search and optimised size reduction. By transferring the trajectory optimisation constraints from the complex free-form surface to numbered grids, the search is found to be more orderly and accurate. The two trajectory indicators, namely argument angle and minimum distance, are analysed separately for the optimised results of the adaptive learning particle swarm optimisation algorithm, demonstrating that they can meet the actual processing requirements.Experimental results of NC EDM indicate that the motion path generated by this design method can meet the machining requirements of 3D curved and twisted flow channels.

Optimal trajectory design accounting for the stabilization of linear time-varying error dynamics

This study is dedicated to the development of a direct optimal control-based algorithm for trajectory optimization problems that accounts for the closed-loop stability of the trajectory tracking error dynamics already during the optimization.Consequently,the trajectory is designed such that the Linear Time-Varying(LTV)dynamic system,describing the controller’s error dynamics,is stable,while additionally the desired optimality criterion is optimized and all enforced constraints on the trajectory are fulfilled.This is achieved by means of a Lyapunov stability analysis of the LTV dynamics within the optimization problem using a time-dependent,quadratic Lyapunov function candidate.Special care is taken with regard to ensuring the correct definiteness of the ensuing matrices within the Lyapunov stability analysis,specifically considering a numerically stable formulation of these in the numerical optimization.The developed algorithm is applied to a trajectory design problem for which the LTV system is part of the path-following error dynamics,which is required to be stable.The main benefit of the proposed scheme in this context is that the designed trajectory trades-off the required stability and robustness properties of the LTV dynamics with the optimality of the trajectory already at the design phase and thus,does not produce unstable optimal trajectories the system must follow in the real application.

A local toolpath smoothing method for a five-axis hybrid machining robot

Smooth transitions between two adjacent five-axis toolpaths can reduce feedrate fluctuation,improving machining quality and efficiency.Hybrid robots’flexibility to adjust the orientation is advantageous in five-axis machining,but their kinematic issues raise challenges for toolpath smoothing.This paper proposes a G3continuous toolpath smoothing method for a hybrid robot.B-splines in the machine coordinate system(MCS)are inserted at corners to synchronize five-axis transitions.The transition errors of the tool position and orientation paths are estimated with the golden section method.These approximation errors are constrained by adaptively modifying the B-splines,i.e.,adding anchor points and optimizing the control points.A bisection search method is proposed for these geometric modifications,guaranteeing the user-defined error tolerance limit.Compared to the method based on the workpiece coordinate system(WCS),the proposed framework generates a smoother trajectory under the same error tolerance limit.Simulations and experiments are provided to validate the effectiveness.

Probabilistic movement primitive based motion learning for a lower limb exoskeleton with black-box optimization

As a wearable robot,an exoskeleton provides a direct transfer of mechanical power to assist or augment the wearer’s movement with an anthropomorphic configuration.When an exoskeleton is used to facilitate the wearer’s movement,a motion generation process often plays an important role in high-level control.One of the main challenges in this area is to generate in real time a reference trajectory that is parallel with human intention and can adapt to different situations.In this paper,we first describe a novel motion modeling method based on probabilistic movement primitive(ProMP)for a lower limb exoskeleton,which is a new and powerful representative tool for generating motion trajectories.To adapt the trajectory to different situations when the exoskeleton is used by different wearers,we propose a novel motion learning scheme based on black-box optimization(BBO)PIBB combined with ProMP.The motion model is first learned by ProMP offline,which can generate reference trajectories for use by exoskeleton controllers online.PIBB is adopted to learn and update the model for online trajectory generation,which provides the capability of adaptation of the system and eliminates the effects of uncertainties.Simulations and experiments involving six subjects using the lower limb exoskeleton HEXO demonstrate the effectiveness of the proposed methods.

Autonomous gliding entry guidance with geographic constraints

This paper presents a novel three-dimensional autonomous entry guidance for relatively high lift-to-drag ratio vehicles satisfying geographic constraints and other path constraints. The guidance is composed of onboard trajectory planning and robust trajectory tracking. For trajectory planning, a longitudinal sub-planner is introduced to generate a feasible drag-versus-energy profile by using the interpolation between upper boundary and lower boundary of entry corridor to get the desired trajectory length. The associated magnitude of the bank angle can be specified by drag profile, while the sign of bank angle is determined by lateral sub-planner. Two-reverse mode is utilized to satisfy waypoint constraints and dynamic heading error corridor is utilized to satisfy no-fly zone constraints. The longitudinal and lateral sub-planners are iteratively employed until all of the path constraints are satisfied. For trajectory tracking, a novel tracking law based on the active disturbance rejection control is introduced. Finally, adaptability tests and Monte Carlo simulations of the entry guidance approach are performed. Results show that the proposed entry guidance approach can adapt to different entry missions and is able to make the vehicle reach the prescribed target point precisely in spite of geographic constraints.

A robust online path planning approach in cluttered environments for micro rotorcraft drones

We present in this paper a robust online path planning method, which allows a micro rotorcraff drone to fly safely in GPS-denied and obstacle-strewn environments with limited onboard computational power. The approach is based on an effi- ciently managed grid map and a closed-form solution to the two point boundary value problem （TPBVP）. The grid map assists trajectory evaluation whereas the solution to the TPBVP generates smooth trajectories. Finally, a top-level trajectory switching algorithm is utilized to minimize the computational cost. Advantages of the proposed approach include its conservation of com- putational resource, robustness of trajectory generation and agility of reaction to unknown environment. The result has been realized on actual drones platforms and successfully demonstrated in real flight tests. The video of flight tests can be found at： http：//uav.ece.nus.edu.sg/robust-online-path-planning-Lai2015.html.

Smooth free-cycle dynamic soaring in unspecified shear wind via quadratic programming

Harvesting wind energy is promising for extending long-endurance flights,which can be greatly facilitated by a flight technique called dynamic soaring.The presented study is concerned with generating model-based trajectories with smooth control histories for dynamic soaring maneuvers exploiting wind gradients.The desired smoothness is achieved by introducing a trigonometric series parameterization for the controls,which are formulated with respect to the normalized time.Specifically,the periodicity of the trigonometric functions is leveraged to facilitate the connection of cycles and streamline the problem formulation.Without relying on a specified wind profile,a freefinal-time quadratic programming-based control strategy is developed for the online correction of the flight trajectory,which requires only the instant wind information.Offline and online numerical studies show the trade-off to achieve the smoothness and demonstrate the effectiveness of the proposed method in a varying wind field.