Time-optimal Trajectory Generation Research Articles

Time and energy optimal trajectory generation for coverage motion in industrial machines

The increase in computer numerical control machine efficiency highly contributes to environmental emission reduction and energy-savings. Path and trajectory optimizations are used to improve machine efficiency in a coverage motion such as pocket milling, polishing, inspection, gluing, and additive manufacturing. Several studies have proposed coverage motion optimization in improving machine efficiency for time and energy consumption. Ensuring the smoothness and satisfaction of the machine constraints in coverage motion is necessary. This paper proposes a multi-objective path and trajectory optimization to obtain a trade-off between time and energy consumption for coverage motion. Jerk limited acceleration profiles describe the trajectory where velocity profiles generated for each linear segment attain desirable velocities. The energy model of an industrial two-axis feed drive system is used in finding solutions to the optimization problem. The non-dominated sorting genetic algorithm II generates a Pareto front for trade-off time and energy consumption solutions. Simulation results of the proposed method are validated through experiments using the industrial two-axis feed drive system. Experimental results show the effectiveness of the proposed approach where time reduction and energy savings are 10.05% and 2.10%, respectively. In addition, the optimized path has a lower maximum error of 76.6% compared to the constantly commanded velocity optimized path.

Time Optimal Trajectory Generation with Obstacle Avoidance by Using Optimal Control Theory for a Wheeled Mobile Robot

The design of the mobile robot path is important when obstacles are present in the environment. In the present study, the theory of optimal control for path design and obstacle avoidance via simultaneous minimization of the time and kinetic energy is proposed. Nonlinear equations of robot motion without simplification are considered in optimum control problems, and in order to prevent collisions, the potential functions are utilized. In the next phase, the cost function is proposed that includes velocity inputs, time, and the potential function for obstacle avoidance, in which the nonlinear equation of the motion of the mobile robot is deemed as a constraint. The final equations are numerically solved, and the capability and effectiveness of the presented method will be presented via different simulations on the mobile robot.

A Convex Programming Approach to Multipoint Optimal Motion Planning for Unicycle Robots

An important extension of point-to-point motion planning deals with navigating a robot optimally through a sequence of waypoints. The resulting multipoint problem is typically nonconvex due to the requirement to optimize the waypoint passage time, which has hindered the determination of globally optimal solutions. In this paper, a new motion planning technique is presented for multipoint problems involving unicycle robots. Our main finding is that, by adopting a cost function that weights a combination of path length and maneuver time, together with a suitable tightening of the control input constraints, such type of problems can be cast as a convex program. This can be solved in polynomial time to obtain a global optimum. The proposed motion planner is compared to time-optimal trajectory generation scheme based on nonlinear programming, and it can find better trajectories than this method while being computationally faster.

Kinematic Orienteering Problem With Time-Optimal Trajectories for Multirotor UAVs

In many unmanned aerial vehicle (UAV) applications for surveillance and data collection, it is not possible to reach all requested locations due to the given maximum flight time. Hence, the requested locations must be prioritized and the problem of selecting the most important locations is modeled as an Orienteering Problem (OP). To fully exploit the kinematic properties of the UAV in such scenarios, we combine the OP with the generation of time-optimal trajectories with bounds on velocity and acceleration. We define the resulting problem as the Kinematic Orienteering Problem (KOP) and propose an exact mixed-integer formulation together with a Large Neighborhood Search (LNS) as a heuristic solution method. We demonstrate the effectiveness of our approach based on Orienteering instances from the literature and benchmark against optimal solutions of the Dubins Orienteering Problem (DOP) as the state-of-the-art. Additionally, we show by simulation \color{black} that the resulting solutions can be tracked precisely by a modern MPC-based flight controller. Since we demonstrate that the state-of-the-art in generating time-optimal trajectories in multiple dimensions is not generally correct, we further present an improved analytical method for time-optimal trajectory generation.

A spline-based approach to smooth and time-optimal trajectory generation for CNC machines with guaranteed kinematic constraints

A spline-based approach to smooth and time-optimal trajectory generation for CNC machines with guaranteed kinematic constraints

Time-optimal trajectory generation in joint space for 6R industrial serial robots using Cuckoo search algorithm

The trajectory planning problem in industrial robotic applications has recently attracted the great attention of many researchers. In this paper, an optimal trajectory planning approach is proposed based on optimal time by utilizing the interpolation spline method. The method including a combination of cubic spline and 7th order polynomial is used for generating the trajectory in joint space for robot manipulators. Cuckoo Search (CS) optimization algorithm is chosen to optimize the joint trajectories based on objective, including minimizing total traveling time along the whole trajectory. The spline method has been applied to the PUMA robot for optimizing the joint trajectories with the CS algorithm based on the objective. With the trajectory planning method, the joint velocities, accelerations, and jerks along the whole trajectory optimized by CS meet the requirements of the kinematic constraints in the case of the objective. Simulation results validated that the used trajectory planning method based on the proposed algorithm is very effective in comparison with the same methods based on the algorithms proposed by earlier authors. Keywords: CS; industrial robots; interpolation; spline methods; trajectory planning.

Time-Optimal Trajectory Generation of Rotary Cranes with Collision Avoidance

This paper presents a new three-dimensional trajectory generation method for a rotary crane using a simple dynamics model. The proposed trajectory achieves fast motion and suppresses load-sway with obstacle avoidance, which is generated by a combination of the A* algorithm and a time-optimization approach. The former is used to generate a shortest-distance path for a transported load considering obstacle avoidance. The time-optimization scheme is applied to the path generated by the A* algorithm under crane dynamics and load-sway constraints. The proposed trajectory is represented by a polynomial function to provide smooth and practical motion. Simulation results demonstrate the effectiveness on load-sway suppression and obstacle avoidance.

A Time-optimal Trajectory Generation Approach with Non-uniform B-splines

A Time-optimal Trajectory Generation Approach with Non-uniform B-splines

Trajectory planning for unmanned aerial vehicles in complicated urban environments: A control network approach

Trajectory planning is crucial for Unmanned Aerial Vehicles (UAVs) applications. It is still a challenge to plan UAV trajectories in large-scale complicated three-dimensional urban environments, mainly due to the complexities associated with handling a tremendous number of obstacles. To relieve this difficulty, this study proposes a two-stage control network approach. The first stage is an offline planning stage, aiming at constructing a discrete control network in the working environment achieving collision avoidance and meanwhile considering UAV kinetic properties. The second stage is an online planning stage, where a feasible corridor is generated based on the shortest path in the control network, and the obtained route is smoothed by a three-dimensional Dubins curve algorithm; then, a time-optimal trajectory generation algorithm is applied to trace the designed spatial path. Numerical studies based on a virtual city as well as a large-scale real-world urban area are conducted. The results show that the proposed approach is able to identify reasonable UAV trajectories within negligible computational time.

Near Time Optimal Trajectory Generation for Over-Actuated Vehicles using Nonlinear Model Predictive Controller

Abstract The generation of time dependent paths is crucial for autonomous driving. While relatively simple models are sufficient for normal driving situations, more complex models are required the closer the trajectory is planned towards the handling limits. This paper considers a near time optimal trajectory generation for combined longitudinal and lateral dynamics for an over actuated vehicle. A nonlinear model predictive controller which accounts for actuator constraints is used to generate these trajectories. The predictive model is a reduced dynamic double track model with three degrees of freedom. The resulting trajectories show the ability of following a reference path with the use of all available actuators up to the handling limits.

Time-Optimal Trajectory Generation for Landing a Quadrotor Onto a Moving Platform

We propose a time-optimal trajectory generation algorithm for landing a quadrotor onto a translating (heaving) and tilting (pitching) platform. The proposed algorithm exploits the differential flatness of the system dynamics and optimizes the trajectory in the space of system flat outputs, i.e., system states and their derivatives. This reformulation of the problem improves computational efficiency and can incorporate input and state constraints during the landing maneuver, such as collision avoidance and time-varying final state constraints. In order to verify the optimality of the solution obtained from the proposed algorithm, a switching time search mechanism is also proposed for a subclass of time-optimal trajectory generation problems. Experimental results demonstrating the landing of a quadrotor onto a moving platform are presented to verify the effectiveness of the proposed trajectory generation algorithm.

Trajectory generation and optimization for five-axis on-the-fly laser drilling: a state-of-the-art review

The process of on-the-fly laser drilling is capable of achieving high throughputs and offers a highly productive approach for producing predefined groups of holes (clusters) to be laser drilled on freeform surfaced parts (e.g., gas turbine combustion chamber panels), current machine tool controllers are not equipped with appropriate trajectory functions that can take full advantage of the achievable laser drilling speeds. While the problem of contour following has received previous attention in time-optimal trajectory generation literature, on-the-fly laser drilling presents different technological requirements, needing a different kind of trajectory optimization solution. This paper presents industrial state of the art and a literature review in the area of trajectory generation/planning and optimization for robots and in particular, machine tools, and laser drilling technology.

Time-optimal trajectory generation for aerial coverage of urban building

This paper presents a hierarchical architecture for generating the cooperative trajectories of multiple unmanned aerial vehicles (UAVs) attached with camera sensors, which aim to cover buildings with optimal time in 3D urban environment. It incorporates the centralized high-level layer performing the mission analysis and task allocation functions yielding instructions that are transmitted to the UAVs, as well as the decentralized low-level fashion that the UAVs perform the trajectory generation function in turn. First, the mission features especially the theoretical coverage time of building envelope are extracted quantitatively, and the buildings are then allocated to the UAVs in order to convert the cooperative control problem into multiple single-vehicle control problems. Then, each UAV visits and scans its allocated buildings sequentially, and the corresponding coverage trajectories are obtained by the parallel circle strategy (PCS) and the time-optimal guidance vector field (TOGVF) transition method, as well as the interfered fluid dynamic system (IFDS) method for obstacle avoidance. Finally, our proposed method is verified in various scenarios, and the simulation results show its high efficiency with least time to solve the cooperative coverage problem.

An Efficient Approach of Time-Optimal Trajectory Generation for the Fully Autonomous Navigation of the Quadrotor

In this work, a time-optimal trajectory generation approach is developed for the multiple way-point navigation of the quadrotor based on the nonuniform rational B-spline (NURBS) curve and linear programming. To facilitate this development, the dynamic model of the quadrotor is formulated first. Then, the geometric trajectory regarding multiple way-point navigation is constructed based on the NURBS curve. With the constructed geometric trajectory, a time-optimal interpolation problem is imposed considering the velocity, acceleration, and jerk constraints. This optimization problem is solved in two steps. In the first step, a preliminary result is obtained by solving a linear programming problem without jerk constraints. Then by introducing properly relaxed jerk constraints, a second linear programming problem is formulated based on the preliminarily obtained result, and the time-optimal problem can be fully solved in this way. Subsequently, a nonlinear trajectory tracking controller is developed to track the generated trajectory. The feasibilities of the proposed trajectory generation approach as well as the tracking controller are verified through both simulations and real-time experiments. With enhanced computational efficiency, the proposed approach can generate trajectory for an indoor environment with the smooth acceleration profile and moderate velocity V≈1 m/s in real-time, while guaranteeing velocity, acceleration, and jerk constraints: Vmax=1 m/s, Amax=2 m/s2, and Jmax=5 m/s3. In such a case, the trajectory tracking controller can closely track the reference trajectory with cross-tracking error less than 0.05 m.

Rapid Generation of Time-Optimal Trajectories for Asteroid Landing via Convex Optimization

This paper presents a new method for rapid generation of time-optimal trajectories for asteroid landing via convex optimization. To overcome the nonconvex difficulty due to the free-flight time, a minimum-landing-error problem that can be convexified is proposed to serve as a gateway for solving the time-optimal control problem. The proposed method solves the reduced minimum-landing-error problem via convex optimization first and then searches for the minimum flight time through a combination of extrapolation and bisection methods. The effectiveness of the proposed methodology for rapidly generating time-optimal trajectories is validated through simulations of spacecraft landing on two asteroids with both finite thrust and low thrust.

Time optimal trajectory generation from polyline with velocity, acceleration and spatial deviation constraints

In this paper is presented a method for generating continuous and differentiable trajectory from an input path described by a polyline while maintaining accelerations and velocities constraints. The method in based on replacing the path corners with parabolic blends of constant acceleration. The complete spatial control of the resulted trajectory is obtained with a velocity reduction procedure which ensures that the trajectory doesn't deviate from the input path further than a settable value. The total time is minimized by replacing the non-maximized constant velocity sections with boost sequences containing maximized symmetrical accelerating and decelerating time frames while also keeping the velocity constraints. The method was successfully tested in practice and the results were very good even on complex input paths.

Laser manufacturing of microsieves for bioengineering applications

Laser drilling is a noncontact technology which allows high flexibility and full automation of the process. The research presented aimed at developing laser technology for manufacturing microsieves in thin Ni and Al foils. Involute and square distributions of holes were formed with an overall dimension of 3mm. Distance between adjacent holes was 25um to 100um, which meant fabrication of up to 10,000 openings per microsieve. Owing to optimisation of the optical system design and laser micromachining system parameters, holes with a desired diameter of around 12um were fabricated, limited only by diffraction divergence of laser beam. Full Text: PDF References M. Baumeister, T. Scholz, and K. Dickmann, Influence of Mie-scattering on high-speed micro-perforation considering brilliant laser radiation, J. Laser Appl. 22, 48 (2010). CrossRef K. Erkorkmaz et al. Time-optimal trajectory generation for 5-axis on-the-fly laser drilling, CIRP Ann.-Manuf. Techn. 60, 411 (2011). CrossRef M. Baumeister et al. Laser-Mikroperforation ?on-the-fly?: Faserlaser ermoglichen Porengrose CrossRef L. Li, D.K.Y. Low, M. Ghoreshi, J.R. Crookall, Hole Taper Characterisation and Control in Laser Percussion Drilling, CIRP Ann.-Manuf. Techn. 51, 153 (2002). CrossRef

Smooth time-optimal tool trajectory generation for CNC manufacturing systems

An optimization approach is proposed in this paper for generating smooth and time-optimal path constrained tool trajectory for Cartesian computer numerical control (CNC) manufacturing systems. The desired smooth time-optimal trajectory generation (STOTG) problem is formulated as a general optimal control problem. And axis jerk (derivative of acceleration with respect to time) constraints are introduced into this problem to remove discontinuities of the acceleration profiles. The desired smoothness of the trajectory can be accomplished by adjusting the values of jerk constraints. A control vector parameterization (CVP) method is applied to convert the optimal control problem into a nonlinear programming (NLP) problem which can be solved conveniently and effectively. The third derivative of the path parameter with respect to time (pseudo-jerk) and jerk act as optimization variables. The pseudo-jerk is approximated as piecewise constant, thus for at least second-order continuous parametric path, the resulted optimized trajectory with respect to time is also at least second-order continuous. Sequential quadratic programming (SQP) method is used to solve the NLP problem, through which numerical solution is obtained. Non-smooth (i.e. without considering jerk constraints) time-optimal trajectory generation (non-STOTG) problem is also considered in this paper for the purpose of comparison. Solutions of time-optimal trajectory generation (TOTG) problems for two test paths are performed to verify the effectiveness of the proposed approach.

Kinematics constrained five-axis tool path planning for high material removal rate

Traditional five-axis tool path planning methods mostly focus on differential geometric characteristics between the cutter and the workpiece surface to increase the material removal rate (i.e., by minimizing path length, improving curvature matching, maximizing local cutting width, etc.). However, material removal rate is not only related to geometric conditions such as the local cutting width, but also constrained by feeding speed as well as the motion capacity of the five-axis machine. This research integrates machine tool kinematics and cutter-workpiece contact kinematics to present a general kinematical model for five-axis machining process. Major steps of the proposed method include: (1) to establish the forward kinematical relationship between the motion of the machine tool axes and the cutter contact point; (2) to establish a tool path optimization model for high material removal rate based on both differential geometrical property and the contact kinematics between the cutter and workpiece; (3) to convert cutter orientation and cutting direction optimization problem into a concave quadratic planning (QP) model. Tool path will finally be generated from the underlying optimal cutting direction field. Through solving the time-optimal trajectory generation problem and machining experiment, we demonstrate the validity and effectiveness of the proposed method.

Time-optimal trajectory generation for 5-axis on-the-fly laser drilling

This paper presents a new and time-optimal trajectory generation technique for 5-axis on-the-fly laser drilling. Trajectories for individual hole clusters are optimized by minimizing the integral square of the 4th time derivative, and by adjusting the velocity and acceleration conditions at the hole locations to enable the maximum time compression (i.e., highest laser pulsing frequency). Axis velocity, acceleration, jerk, and hole elongation constraints are also considered. Individually optimized clusters are stitched together using time-optimal segments with nonzero velocity boundary conditions. The practicality and effectiveness of the algorithm is demonstrated in implementation results for producing a gas turbine combustion chamber component.