Structure of the time-optimal control law for multiple arms handling a common object along specified paths

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space. >

ABSTRACTAn efficient trajectory optimisation approach combining the classical control variable parameterisation (CVP) with a novel smooth technology and two penalty strategies is developed to solve the trajectory optimal control problems. Since it is difficult to deal with path constraints in CVP method, the novel smooth technology is firstly employed to transform the complex constraints into one smooth constraint. Then, two penalty strategies are proposed to tackle the converted path and terminal constraints to decrease the computational complexity and improve the constraints satisfaction. Finally, a nonlinear programming problem, which approximates the original trajectory optimisation problem, is obtained. Error analysis shows that the proposed method has good convergence property. A general hypersonic cruise vehicle trajectory optimisation example is employed to test the performance of the proposed method. Numerical results show that the path and terminal conditions are well satisfied and better trajectory profiles are obtained, showing the effectiveness of the proposed method.

In this article, we focus on safe and effective completion of a rendezvous and docking task by looking at planning approaches and control with fuel-optimal rendezvous for a target spacecraft running on a near-circular reference orbit. A variety of existent practical path constraints are considered, including the constraints of field of view, impulses, and passive safety. A rendezvous approach is calculated by using a hybrid genetic algorithm with those constraints. Furthermore, a control method of trajectory tracking is adopted to overcome the external disturbances. Based on Clohessy–Wiltshire equations, we first construct the mathematical model of optimal planning approaches of multiple impulses with path constraints. Second, we introduce the principle of hybrid genetic algorithm with both stronger global searching ability and local searching ability. We additionally explain the application of this algorithm in the problem of trajectory planning. Then, we give three-impulse simulation examples to acquire an optimal rendezvous trajectory with the path constraints presented in this article. The effectiveness and applicability of the tracking control method are verified with the optimal trajectory above as control objective through the numerical simulation.

This paper addresses the trajectory optimization problem of quadrotor landing on a moving platform. Various state and control constraints are imposed, and a combined optimization objective of minimum-energy and minimum-time is considered. The contribution of the paper is to convert the original nonconvex optimal control problem into a second-order cone programming (SOCP) mainly utilizing the change of variables, equivalent transformation, and linearization. And the SOCP problem can be solved by the interior point method quickly. Then, a successive solution algorithm is proposed, which is found to be able to converge quickly. Especially, the algorithm is guaranteed to converge when the moving platform has a constant velocity vector. Numerical examples have been provided to show the efficiency and effectiveness of the proposed algorithm for quadrotor landing on moving platforms.

In this paper, we propose an approach for real-time collision-free trajectory planning of multiple robot manipulators in a common workspace. In recent years, robot arms are often introduced to factories in place of human beings, and it has become important how efficiently multiple robot arms can be operated in a small space. The problem of trajectory planning for multiple robot arms is often solved by graph search algorithms, however, it is difficult for the conventional approach to provide flexible trajectory planning to cope with unexpected situations such as robot arm failure. Therefore, we propose a combined method for Q-learning and RRT for the trajectory planning problem. The effectiveness of the proposed method is further verified using numerical experiments. The planned trajectories is able to guarantee a certain degree of optimality when the motion trajectory is generated by combining reinforcement learning than by using only the graph search algorithm. The results indicate that the time required to generate the motion trajectory is reduced by the proposed method.

Real-time trajectory optimization for collision-free asteroid landing based on deep neural networks

Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain

Trajectory Optimization for Planetary Multi-Point Powered Landing

Multimode electric propulsion system is widely used in deep space exploration. Its thrust is output in stages with the change of input power, which also means that continuous power changes lead to discontinuous thrust changes. In the design and optimization of low-thrust trajectory, the discontinuity of thrust is often neglected and regarded as a continuous parameter. The optimal design of low-thrust transfer trajectory constrained by multimode electric propulsion is studied, and the influence of thrust grading characteristics on the trajectory is analyzed in this paper. A specific optimization strategy is proposed, including three main steps: model discretization based on direct method, fast generation of initial value based on particle swarm optimization (PSO), and optimization based on sequential quadratic programming (SQP). The dynamic model and optimization model of low-thrust transfer trajectory is established. Then, the optimization model is discretized based on the direct method and the original optimal control problem is transformed into a parameter optimization problem in the form of nonlinear programming (NLP). A hybrid optimization algorithm based on PSO and SQP is proposed to solve the new NLP problem. PSO is used to search the initial value efficiently and guarantee the global performance of the initial value and SQP is used for local optimization based on initial value, which can give full play to the excellent global optimization performance of PSO and the outstanding local optimization performance of SQP. The effectiveness of the proposed optimization strategy is verified by a simulation example of the main belt asteroid Metis (1974 QU2) rendezvous mission with once Mars gravity assist. The results show that the optimal control curve obtained is in accordance with the optimal control form of bang-bang control derived from the theory, and the thruster has just two situations at any time: shutdown or startup with maximum thrust. In the working power range, increasing the number of thrust stages can improve the rate of energy utilization, thereby improving the efficiency of thruster, shortening the startup time and reducing fuel consumption. Meanwhile, ineffective grading should be avoided in the non-working power range.

The legged locomotion manipulation system (LMS) combines the powerful movement of the legged platform and the operation ability of the robotic manipulation arm, which can replace humans to perform dangerous tasks. This paper focuses on the legged locomotion manipulation system, composed of a quadruped locomotion platform with a six-degree-of-freedom (Dof) robotic arm. After the LMS completes movement tasks and reaches the designated position, the supporting foot point are not moved. The overall kinematics model is established with the parallel kinematics model of the legged LMS and the serial kinematics model of the robotic arm. In whole-body collaborative planning, the goal is to minimize the sum of the squares of all joint torques. With the constraints of whole-body kinematics and statics, dynamics, and stability, the trajectory optimization problem is converted into a nonlinear planning problem. By solving the nonlinear problem, we can get the optimal joint trajectory. Compared with independently planning trajectories of the quadruped locomotion platform and robotic arm, this algorithm can coordinate the motion of the whole joints, optimize the distribution, and reduce the system's power. Simulation experiments verify all algorithms.

In this paper, we introduce a new approach to control wheeled acrobots. The proposed method consist of two steps; stabilization and trajectory optimization. Fisrt, we apply hierarchical linearization and bakstepping method to stabilize systems in a neighborhood of an equilibrium point. Next, we solve a trajectory optimization problem of the closed-loop system using a direct collocation method. Using the trajectory optimization, we obtain a trajectory with which path constraints are satisfied. In a numerical simulation, the validity of the controller designed by the proposed method is verified.

Trajectory optimal control for a robotic arm with a high degree of freedom (DOF) is challenging. The design space for that problem is complex and the search for an optimal solution is demanding. The design of a robotic arm's trajectory is based on solving the inverse kinematics problem, considering additional refinements influenced by factors like total rotating angle, reachability time, minimum execution time, obstacle avoidance, and energy consumption minimization. Due to the complexity of the design space, in this paper, genetic algorithm (GA) optimization and whale optimization algorithm (WOA) have been used to achieve robotic arm trajectory control while maintaining a minimum reachability time. To validate the suggested techniques, a case study was conducted on a 6 DOF KUKA KR 4 R600 robot arm to control subject to its constraints. Sets of consecutive points forming four different paths were inputted to the algorithms. The goal was to reach all these points, in order, with a minimum total reachability time. As a result of this paper, we shown that the whale optimization algorithm provides better performance than the genetic algorithm with a factor of more than 2.5 while satisfying the reachability constraints.

Wepropose a variant of alternating direction method of multiplier (ADMM) to solve constrained trajectory optimization problems. Our ADMM framework breaks a joint optimization into small sub-problems, leading to a low iteration cost and decentralized parameter updates. Starting from a collision-free initial trajectory, our method inherits the theoretical properties of primal interior point method (P-IPM), i.e., guaranteed collision avoidance and homotopy preservation throughout optimization, while being orders of magnitude faster. We have analyzed the convergence and evaluated our method for time-optimal multi-UAV trajectory optimizations and simultaneous goal-reaching of multiple robot arms, where we take into consider kinematics-, dynamics-limits, and homotopy-preserving collision constraints. Our method highlights an order of magnitude’s speedup, while generating trajectories of comparable qualities as state-of-the-art P-IPM solver.

We investigate Holder regularity of adjoint states and optimal controls for a Bolza problem under state constraints. We start by considering any optimal solution satisfying the constrained maximum principle in its normal form and we show that whenever the associated Hamiltonian function is smooth enough and has some monotonicity properties in the directions normal to the constraints, then both the adjoint state and optimal trajectory enjoy Holder type regularity. More precisely, we prove that if the state constraints are smooth, then the adjoint state and the derivative of the optimal trajectory are Holder continuous, while they have the two sided lower Holder continuity property for less regular constraints. Finally, we provide sufficient conditions for Holder type regularity of optimal controls.

Numerical Solution of the Isaacs Equation for Differential Games with State Constraints