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 database for learning can be obtained by either recording the former data, or artificially generating. @cite_17 evenly chose variables in motion range to generate samples and drew a comparison of databases with different sizes. Hauser @cite_11 uniformly sampled an axis-aligned range of variables to generate a database. Besides, a lifelong learning mode was presented to continuously generate examples with a separate background thread. In addition, the sensitivity of the required database size to the input dimension and the requirement for the database to guarantee the quality of solutions were discussed. However, for the cases with high dimensional inputs, the above database generation methods of randomly or evenly choosing sample variables in the motion range are time-consuming. Thus, finding a way to elevate the efficiency of database generation is a key issue to be solved.
@cite_11 @cite_17
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This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for real-time applications in robotics, since it can produce near globally optimal solutions orders of magnitude faster than standard methods. This paper establishes theoretical conditions on how many and where samples are needed over the space of problems to achieve a given approximation quality. The framework is applied to solve globally optimal collision-free inverse kinematics problems, wherein large solution databases are used to produce near-optimal solutions in a submillisecond time on a standard PC. Many real-world tasks require fast planning of highly dynamic movements for their execution in real-time. The success often hinges on quickly finding one of the few plans that can achieve the task at all. A further challenge is to quickly find a plan which optimizes a desired cost. In this paper, we will discuss this problem in the context of catching small flying targets efficiently. This can be formulated as a non-linear optimization problem where the desired trajectory is encoded by an adequate parametric representation. The optimizer generates an energy-optimal trajectory by efficiently using the robot kinematic redundancy while taking into account maximal joint motion, collision avoidance and local minima. To enable the resulting method to work in real-time, examples of the global planner are generalized using nearest neighbour approaches, Support Vector Machines and Gaussian process regression, which are compared in this context. Evaluations indicate that the presented method is highly efficient in complex tasks such as ball-catching.