To continuously generate trajectories for serial manipulators with high dimensional degrees of freedom (DOF) in the dynamic environment, a real-time optimal trajectory generation method based on machine learning aiming at high dimensional inputs is presented in this paper. First, a learning optimization (LO) framework is established, and implementations with different sub-methods are discussed. Additionally, multiple criteria are defined to evaluate the performance of LO models. Furthermore, aiming at high dimensional inputs, a database generation method based on input space dimension-reducing mapping is proposed. At last, this method is validated on motion planning for haptic feedback manipulators (HFM) in virtual reality systems. Results show that the input space dimension-reducing method can significantly elevate the efficiency and quality of database generation and consequently improve the performance of the LO. Moreover, using this LO method, real-time trajectory generation with high dimensional inputs can be achieved, which lays a foundation for continuous trajectory planning for high-DOF-robots in complex environments.
The traditional point-to-point trajectory planning is started from interpolation-based methods, such as polynomial interpolation @cite_9 @cite_3 and B-spline interpolation @cite_12 @cite_15 . In general, pure interpolation-based methods are able to accomplish required tasks, but difficult to achieve the optimal performance in specific aspects. To obtain optimal trajectories, non-linear optimization problems are constructed with optimal objectives based on time, energy and power consumption and constraints such as mechanical structure, time and obstacle avoidance @cite_7 . Von @cite_2 investigated the non-linear optimization with three separated criteria of minimum time, minimum energy and minimum power consumption and solved it by a numerical method of combining a direct collocation and an indirect multiple shooting method. @cite_13 presented the optimal planning problem tried to find the compromise between time, energy and power consumption and solved it by the Sequential Quadratic Programming (SQP) method. However, all aforementioned optimization-based methods are not real-time due to the complex computation of the non-linear optimization.
@cite_7 @cite_9 @cite_3 @cite_2 @cite_15 @cite_13 @cite_12
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We present a new optimization-based approach for robotic motion planning among obstacles. Like CHOMP (Covariant Hamiltonian Optimization for Motion Planning), our algorithm can be used to find collision-free trajectories from naA¯ve, straight-line initializations that might be in collision. At the core of our approach are (a) a sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary, and (b) an efficient formulation of the no-collisions constraint that directly considers continuous-time safety Our algorithm is implemented in a software package called TrajOpt. We report results from a series of experiments comparing TrajOpt with CHOMP and randomized planners from OMPL, with regard to planning time and path quality. We consider motion planning for 7 DOF robot arms, 18 DOF full-body robots, statically stable walking motion for the 34 DOF Atlas humanoid robot, and physical experiments with the 18 DOF PR2. We also apply TrajOpt to plan curvature-constrained steerable needle trajectories in the SE(3) configuration space and multiple non-intersecting curved channels within 3D-printed implants for intracavitary brachytherapy. Details, videos, and source code are freely available at: http: rll.berkeley.edu trajopt ijrr. This paper presents a minimum-time trajectory planning method and a tracking control scheme for robot manipulators. In the first step, we find the minimum-time trajectories by optimizing cubic polynomial joint trajectories using the evolution strategy. In the second step, by the use of the evolution strategy we tune the sliding mode controller parameters for the robot manipulator to track precisely the trajectories that were found in the previous step. Experimental results show that the proposed method is very useful. An online algorithm for computing a robot manipulator's trajectory in joint space with velocity and acceleration constraints is proposed. Our theoretical discussion is based on optimizing the minimum possible time for velocity and acceleration constraints while using cubic splines. A method for calculating the wandering time is also presented. This value of the time gives prehand knowledge to the user about the time after which the wandering phenomenon starts. Simulation results of the proposed algorithm are also presented to show its efficiency. Minimum time and minimum energy point-to-point trajectories for an industrial robot of the type Manutec r3 are computed subject to state constraints on the angular velocities. The numerical solutions of these optimal control problems are obtained in an efficient way by a combination of a direct collocation and an indirect multiple shooting method. This combination links the benefits of both approaches: A large domain of convergence and a highly accurate solution. The numerical results show that the constraints on the angular velocities become active during large parts of the time optimal motion. But the resulting stress on the links can be significantly reduced by a minimum energy trajectory that is only about ten percent slower than the minimum time trajectory. As a by-product, the reliability of the direct collocation method in estimating adjoint variables and the efficiency of the combination of direct collocation and multiple shooting is demonstrated. The highly accurate solutions reported in this paper may also serve as benchmark problems for other methods. We discuss the problem of minimum cost trajectory planning for robotic manipulators. It consists of linking two points in the operational space while minimizing a cost function, taking into account dynamic equations of motion as well as bounds on joint positions, velocities, jerks and torques. This generic optimal control problem is transformed, via a clamped cubic spline model of joint temporal evolutions, into a non-linear constrained optimization problem which is treated then by the Sequential Quadratic Programming (SQP) method. Applications involving grasping mobile object or obstacle avoidance are shown to illustrate the efficiency of the proposed planner. The grasping and stabilization of a spinning, noncooperative target satellite by means of a free-flying robot is addressed. A method for computing feasible robot trajectories for grasping a target with known geometry in a useful time is presented, based on nonlinear optimization and a look-up table. An off-line computation provides a data base for a mapping between a four-dimensional input space, to characterize the target motion, and an N-dimensional output space, representing the family of time-parameterized optimal robot trajectories. Simulation results show the effectiveness of the data base for computing grasping maneuvers in a useful time, for a sample range of spinning motions. The debris object consists of a satellite with solar appendages in Low Earth Orbit, which presents collision avoidance and timing challenges for executing the task.