Time-optimal Trajectory Planning Research Articles

Time-Optimal Trajectory Planning and Tracking for Autonomous Vehicles

Time-Optimal Trajectory Planning and Tracking for Autonomous Vehicles

Online and Scalable Motion Coordination for Multiple Robot Manipulators in Shared Workspaces

Multi-robot motion coordination is essential to make robots work safely and efficiently in a shared workspace, ensuring task completion while avoiding interference between each other’s motions. Achieving online replanning and scaling to large numbers of robots are particularly challenging. In this paper, we present a motion coordination method for multiple robot manipulators with given targets. The approach separates the problem into a global coordination stage and a local trajectory replanning stage. Online reactivity and scalability are achieved by means of coordination in a reduced space and efficient trajectory replanning. We first introduce the method for systems with two robots, then extend it to systems with an arbitrary number of robots. The method determines whether kinematically-feasible and non-interfering trajectories leading all the robots to their targets exist. The approach generates time-efficient trajectories if solutions exist, or provides information for switching targets if solutions cannot be found. We show formally and empirically that the method has low computational overhead and scales quadratically with the number of robots. Experiments are conducted with up to three real 7-DOF robots and up to ten simulated robots. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In underground mining, a key process is that of tunneling, i.e., drilling and blasting rock to excavate tunnels that lead to sources of ore. Drilling is carried out by rigs equipped with multiple robotic arms. A key factor affecting the efficiency of tunneling is the time to completion of drilling operations. In current industrial practice, these operations are carried out manually by an operator steering the arms on the drill rig. Time to completion can be drastically reduced if the arms could operate concurrently, intelligently optimizing and coordinating their motions. However, existing methods for multi-arm motion coordination are inadequate, as they fail to cater to one or more of the following real-world constraints: several robot arms work in close proximity and their workspaces are overlapping; task completion times are uncertain due to rock density and drill bit breakage; and contingencies such as unexpected delays in motion or stops sometimes happen. These constraints exist also in other industrial applications, like manufacturing and assembly. This paper proposes a framework which enables multiple high-DOF robot manipulators to safely and efficiently work in a shared workspace. The method allows to adjust robot trajectories while robots move, and is shown to scale well with the number of robots. Motions are generated and adjusted by time-optimal trajectory planning, whose computational overhead is small enough for online operation and benefits task completion efficiency, safety, and productivity. Experiments using three 7-DOF robots suggest that this approach is practically feasible, and simulations with up to 10 robots attest to its scalability.

Safety Compliant, Ergonomic and Time-Optimal Trajectory Planning for Collaborative Robotics

Safety Compliant, Ergonomic and Time-Optimal Trajectory Planning for Collaborative Robotics

Efficient and Robust Time-Optimal Trajectory Planning and Control for Agile Quadrotor Flight

Efficient and Robust Time-Optimal Trajectory Planning and Control for Agile Quadrotor Flight

Sampling-based time-optimal path parameterization with jerk constraints for robotic manipulation

In this paper, a sampling-based time-optimal path parameterization (S-TOPP) method is proposed to address time-optimal trajectory planning problems with bounded jerks. The key insight of S-TOPP is that a tree of feasible nodes connected by edges is established to find a time-optimal trajectory on the temporal dimension. The tree establishment process includes two major phases at each stage, namely sampling and one-step backtracking. In the sampling phase, a new sampling strategy integrating historical information is proposed to obtain superior samples whereby fewer samples can be controlled automatically, reducing the calculation loss. In one-step backtracking phase, a “lazy” strategy is used to lazily skip constraint-checking when evaluating local connections, enabling S-TOPP to avoid checking the vast majority of nodes that have no chance of being in an optimal trajectory. Simulations and real-world experiments validate the feasibility and practicability of S-TOPP. Results show that S-TOPP is an effective solution to jerk-bounded time-optimal trajectory planning, with features that are more in line with the needs of the practical tasks compared with other methods.

Research on Mechanism Design and Kinematic Characteristics of Self-Propelled Photovoltaic Cleaning Robot

A hydraulic drive-based self-propelled photovoltaic panel cleaning robot was developed to tackle the challenges of harsh environmental conditions, difficult roads, and incomplete cleaning of dust particles on the photovoltaic panel surface in photovoltaic power plants. The robot has the characteristics of the crawler wheel drive, rear-wheel-independent turning and three-point-independent suspension design, which makes it adhere to the walking requirements of complex environmental terrains, more flexible in turning and automatically levelling so that the stability of the boom mechanism during walking can be ensured. The kinematics model of the upper arm structure equipped with the end cleaning device was built, and the optimized Circle chaotic map and nonlinear weight factor were introduced to enhance the search ability and convergence speed of the sparrow algorithm. Furthermore, the boom running track was optimized in combination with the seven-order non-uniform B-spline curve. Through optimization, the running time of the boom was reduced by 18.7%, and the cleaning efficiency of photovoltaic panel surface was increased. The effectiveness of self-propelled photovoltaic panel cleaning robot cleaning and the reliability of time-optimal trajectory planning were confirmed through simulation and experiment.

On the use of adjoint gradients for time-optimal control problems regarding a discrete control parameterization

AbstractIn this paper, we discuss time-optimal control problems for dynamic systems. Such problems usually arise in robotics when a manipulation should be carried out in minimal operation time. In particular, for time-optimal control problems with a high number of control parameters, the adjoint method is probably the most efficient way to calculate the gradients of an optimization problem concerning computational efficiency. In this paper, we present an adjoint gradient approach for solving time-optimal control problems with a special focus on a discrete control parameterization. On the one hand, we provide an efficient approach for computing the direction of the steepest descent of a cost functional in which the costs and the error in the final constraints reduce within one combined iteration. On the other hand, we investigate this approach to provide an exact gradient for other optimization strategies and to evaluate necessary optimality conditions regarding the Hamiltonian function. Two examples of the time-optimal trajectory planning of a robot demonstrate an easy access to the adjoint gradients and their interpretation in the context of the optimality conditions of optimal control solutions, e.g., as computed by a direct optimization method.

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.

Time and Energy Optimal Trajectory Planning of Wheeled Mobile Dual-Arm Robot Based on Tip-Over Stability Constraint

Trajectory planning and avoidance of tipping are the main keys to success in the mobile dual-arm manipulation, especially when the dual-arm or moving platform is running fast. The forces and moments between wheel-terrain and body-arm have been analyzed by kinematics and force analysis of a robot to define tip-over stability constraint. Then, an improved tip-over moment stability criterion for a wheeled mobile dual-arm robot is presented and defines tip-over stability constraint based on it. To improve the motion stability of the robot, this paper presents an optimal joint trajectory planning model based on time and energy. The quintic B-spline curve and an improved NSGA-II algorithm, which are time and energy, are applied to multi-objective optimization. The simulation results show that the motion stability of a robot is improved based on the tip-over stability constraint. This trajectory planning method based on the stability constraint can be applied to other mobile robots as well.

Robot Time-Optimal Trajectory Planning Based on Quintic Polynomial Interpolation and Improved Harris Hawks Algorithm

Time-optimal trajectory planning is one of the most important ways to improve work efficiency and reduce cost and plays an important role in practical application scenarios of robots. Therefore, it is necessary to optimize the running time of the trajectory. In this paper, a robot time-optimal trajectory planning method based on quintic polynomial interpolation and an improved Harris hawks algorithm is proposed. Interpolation with a quintic polynomial has a smooth angular velocity and no acceleration jumps. It has widespread application in the realm of robot trajectory planning. However, the interpolation time is usually obtained by testing experience, and there is no unified criterion to determine it, so it is difficult to obtain the optimal trajectory running time. Because the Harris hawks algorithm adopts a multi-population search strategy, compared with other swarm intelligent optimization algorithms such as the particle swarm optimization algorithm and the fruit fly optimization algorithm, it can avoid problems such as single population diversity, low mutation probability, and easily falling into the local optimum. Therefore, the Harris hawks algorithm is introduced to overcome this problem. However, because some key parameters in HHO are simply set to constant or linear attenuation, efficient optimization cannot be achieved. Therefore, the nonlinear energy decrement strategy is introduced in the basic Harris hawks algorithm to improve the convergence speed and accuracy. The results show that the optimal time of the proposed algorithm is reduced by 1.1062 s, 0.5705 s, and 0.3133 s, respectively, and improved by 33.39%, 19.66%, and 12.24% compared with those based on particle swarm optimization, fruit fly algorithm, and Harris hawks algorithms, respectively. In multiple groups of repeated experiments, compared with particle swarm optimization, the fruit fly algorithm, and the Harris hawks algorithm, the computational efficiency was reduced by 4.7019 s, 1.2016 s, and 0.2875 s, respectively, and increased by 52.40%, 21.96%, and 6.30%. Under the optimal time, the maximum angular displacement, angular velocity, and angular acceleration of each joint trajectory meet the constraint conditions, and their average values are only 75.51%, 38.41%, and 28.73% of the maximum constraint. Finally, the robot end-effector trajectory passes through the pose points steadily and continuously under the cartesian space optimal time.

Time-Optimal Trajectory Planning of Flexible Manipulator Moving along Multi-Constraint Continuous Path and Avoiding Obstacles

To solve the trajectory planning problem of the flexible manipulator under various constraints such as end-camera attitude, drive space, and obstacles during video inspection along a continuous path in narrow three-dimensional space, this paper proposes a time-optimal trajectory planning method from the initial configuration to the final configuration. The trajectory planning problem is transformed into a multi-constraint optimization problem. First, to realize continuous video inspection in an unstructured complex environment, by analyzing the geometric model of the two-segment flexible manipulator with a camera at the end, the pose constraints between the camera and the shooting surface are formulated by the space vector method, the driving constraints are formulated based on kinematics, and the obstacle constraints are formulated by space mapping. Then, a multi-constraint optimization model is constructed to generate the smooth trajectory of the drive cable of the flexible manipulator by minimizing the total time of continuous path motion. Compared with the conventional point-to-point collision avoidance planning solution method, this paper starts from the global perspective and investigates the less considered continuous path trajectory planning problem; also, the swarm intelligence algorithm artificial jellyfish search algorithm (JS) is employed to optimize the solution and find the minimum time trajectory conforming to a variety of complex constraints. Finally, a simulation is conducted with CoppeliaSim, and the continuous path video inspection experiment is carried out in the 500KV GIS (Gas Insulated Switchgear) equipment, the simulation and experimental results indicate that the planned drive cable trajectory is smooth and effective. In addition, each path point is tracked and obstacles are avoided safely. When the flexible manipulator moves along the whole path, the pose of the camera satisfies the relaxed attitude constrain The proposed method can guide the two-segment flexible manipulator to complete the continuous video inspection task of the GIS cavity wall and conductive column surface.

Application of an improved whale optimization algorithm in time-optimal trajectory planning for manipulators.

To address the issues of unstable, non-uniform and inefficient motion trajectories in traditional manipulator systems, this paper proposes an improved whale optimization algorithm for time-optimal trajectory planning. First, an inertia weight factor is introduced into the surrounding prey and bubble-net attack formulas of the whale optimization algorithm. The value is controlled using reinforcement learning techniques to enhance the global search capability of the algorithm. Additionally, the variable neighborhood search algorithm is incorporated to improve the local optimization capability. The proposed whale optimization algorithm is compared with several commonly used optimization algorithms, demonstrating its superior performance. Finally, the proposed whale optimization algorithm is employed for trajectory planning and is shown to be able to produce smooth and continuous manipulation trajectories and achieve higher work efficiency.

A Time Optimal Trajectory Planning of the Metamorphic Industrial Robot

A Time Optimal Trajectory Planning of the Metamorphic Industrial Robot

General Extremal Field Method for Time-Optimal Trajectory Planning in Flow Fields

We present an algorithm to compute time-optimal trajectories for light vehicles in unsteady flow fields, with applications to long-range, low-power aircraft as well as underwater vehicles in ocean currents. The proposed approach aims at unifying various works from the literature on extremal fields and extends it by several features. First, we propose an exact scheme to deal with still obstacles. While being directly useful for pure obstacles, it is also of particular interest to ensure the validity of computation at the borders of the problem domain. Second, we demonstrate the method ability to deal with trajectory planning for long-range airborne missions with real weather data. Lastly, the source code, written in Python, is made open to the community to accelerate research in the domain.

A finite and fast time-optimal trajectory planning based on velocity sinking method for robots along specified path

Time-optimal trajectory planning is used in many areas of industrial robots and has a wide range of applications. This paper presents a finite and fast computation method for calculating time-optimal robot trajectories along specified geometric paths, namely the velocity sinking method. The velocity sinking method differs from those proposed in the existing literature which solve uncertain optimization problem. Firstly, the maximum velocity in multiple state constraints is calculated using a path parameterization method. Then, the pseudo maximum velocity trajectory is calculated using a numerical integration method. Finally, the time-optimal trajectory planning under path constraints is determined using an iterative velocity sinking algorithm. The experiment demonstrates the effectiveness and efficiency of this method in industrial robotic settings.

Time-Optimal Trajectory Planning of 6-DOF Manipulator Based on Fuzzy Control

Currently, the teaching programming or offline programming used by an industrial manipulator can manually set the running speed of the manipulator. In this paper, to consider the running speed and stability of the manipulator, the time-optimal trajectory planning (TOTP) of the manipulator is transformed into a nonlinear optimal value search problem under multiple constraints, and a time-search algorithm based on fuzzy control is proposed, so that the end of the manipulator can run along the given path in Cartesian space for the shortest time, and the angular velocity and angular acceleration of each joint is within a limited range. In addition, a simulation model of a 6-DOF manipulator is established in MATLAB, taking a straight-line trajectory of the end of the manipulator in Cartesian space as an example, and the effectiveness and efficiency of the algorithm proposed in this paper are proved by comparing the execution time with the bisection algorithm and the traditional gradient descent method.

Hybrid deterministic non-deterministic data-parallel algorithm for real-time unmanned aerial vehicle trajectory planning in CUDA

The development of autonomous Unmanned Aerial Vehicles (UAVs) is a priority to many civilian and military organizations. Real time optimal trajectory planning is an essential element for the autonomy of UAVs. The use of metaheuristic algorithms for solving such complex optimization problems with non-linearity and multimodality has gained popularity recently. In this paper, we use a non-deterministic Flower Pollination Algorithm (FPA) to deal with the problem's complexity and compute feasible and quasi-optimal trajectories for fixed-wing UAVs in complex 3D environments, taking into account the vehicle's flight properties. The global optimization algorithm is improved with the addition of a deterministic 2-opt local search providing a significant improvement. To achieve real-time performance, the proposed trajectory planner in implemented and parallelized following the data-parallel paradigm on a Graphics Processing Unit (GPU) using the Compute Unified Device Architecture (CUDA) resulting in a 253.4x speedup compared to the sequential implementation on CPU. The parallel implementation is able to compute quasi-optimal trajectories in just 0.369 s.

A Time-Optimal Trajectory Planning Strategy for an Aircraft With a Suspended Payload via Optimization and Learning Approaches

In this article, a real-time interactive time-optimal trajectory planning (TOTP) strategy is proposed for aircraft slung-load systems, in which the practical performance is guaranteed by taking advantage of convex optimization and reinforcement learning (RL) techniques. To the best of our knowledge, it is the first TOTP solution for an aircraft suspension system subject to path, velocity, acceleration, and cable tension constraints, where a practice-oriented RL policy is designed to interact with the system online. Specifically, by exploring the differential flatness property of the system, the states are projected into path coordinate space, where all the physical constraints are formulated in the TOTP with convex forms. Then, the TOTP is transformed into a large sparse optimization problem after discretization, which can be efficiently solved using convex solvers. Subsequently, a deep RL network is designed to optimize the TOTP results, where efficient learning is achieved in the solution space, thereby guaranteeing practical reliability and strong robustness via online interaction in applications. In addition, by incorporating convex optimization and learning techniques, the gap between simulation and experiment is successfully bridged, where the physical feasibility and efficient learning are ensured in the framework. Finally, comparative simulations and experimental results are included to show the effectiveness of the proposed strategy.

Time-Optimal Trajectory Planning of Six-Axis Manipulators Based on the Improved Direct Collocation Method with FMU

The trajectory planning method with dynamics is the key to improving the motion performance of manipulators. The optimal control method (OCM) is a key technology to solve optimal problems with dynamics. There are direct and indirect methods in OCM; indirect methods are difficult to apply to engineering applications, and so direct methods are widely applied instead. The direct collocation method (DCM) is a technology in OCM to transform an optimal control problem (OCP) to a nonlinear problem (NLP), so that plenty of solvers can be used directly. However, the general DCM, for which it has been found that the explicit form of the right-hand-side (RHS) functions of state equations of the complex system in the OCP is hard to derive, is limited to solving the OCP of three-axis manipulators. This paper proposes an improved DCM to solve the OCP of six-axis manipulators, which can find the solution of the time-optimal trajectory for the motion of six-axis manipulators based on the improved DCM. The proposed method derives the RHS equations implicitly by introducing a Functional Mock-up Unit (FMU), which simplifies the representation of the RHS equations as a black-box model, so that the DCM can be applied to the OCP of six-axis manipulators. A simulation case of a three-axis manipulator accomplished in a related study works as a reference compared with our improved method to verify the solution consistence between the DCM using the explicit RHS equations or using the implicit RHS equations, and the loss of computational efficiency is acceptable. In the meantime, a simulation solution and an experiment of six-axis manipulators, which is a novel advancement, are presented to validate the proposed method.

An Online Time-Optimal Trajectory Planning Method for Constrained Multi-Axis Trajectory With Guaranteed Feasibility

Online time-optimal trajectory planning exists in a wide range of applications such as computer numerical control (CNC) manufacturing, robotics and autonomous vehicles. Generally, the methods to generate such time-parameterized trajectory can be categorized as offline methods and online methods. Offline methods tend to generate time-optimal trajectory while it is computationally prohibitive for high frequency real-time applications. Current online methods are computationally efficient but either deal with the sparse waypoint trajectories or sacrifice the time optimality a lot. This letter innovatively proposed a time-optimal switching trajectory index coordination (TOS-TIC) strategy to solve the online time-optimal planning problem for continuous multi-axis trajectories. The proposed method is able to generate time-optimal trajectory for continuous geometric paths while considering high order kinematic constraints. The time-optimality of the trajectory planned by TOS-TIC is nearly the same as the offline planned optimal results. Meanwhile, the proposed method is computationally efficient for online applications. The proposed TOS-TIC planning strategy is an universal approach and firstly able to solve the online time-optimal trajectory planning problem for constrained continuous multi-axis trajectories, which has excellent application prospect in modern automatic industry and intelligent robots/vehicles.