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 non-linear optimization is likely to get stuck into local minimum and generally solved with multiple initial guesses to obtain the global minimum, which is significant costly and hard to operate in real-time. Therefore, quickly seeking for the global minimum is still challenging. A promising idea is learning from former data to reduce the on-line calculation time @cite_20 @cite_21 @cite_14 . Lampariello et at. @cite_17 and @cite_19 solved the non-linear optimization by optimal database generation off-line and regression prediction on-line and applied it in catching flying objects and bipedal walking. However, the methods are limited in specific applications and cases with low dimensional inputs. @cite_10 proposed a trajectory prediction method, employing the previous data to speed up generating new trajectories. In addition, high dimensional inputs are considered and a high dimensional situation descriptor is defined. Hauser @cite_11 extended this method by considering more general context of nonlinear optimization problems and presented a general learning global optima (LGO) framework.
@cite_14 @cite_11 @cite_21 @cite_19 @cite_10 @cite_20 @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. In this paper we introduce the LeGO (Learning for Global Optimization) approach for global optimization in which machine learning is used to predict the outcome of a computationally expensive global optimization run, based upon a suitable training performed by standard runs of the same global optimization method. We propose to use a Support Vector Machine (although different machine learning tools might be employed) to learn the relationship between the starting point of an algorithm and the final outcome (which is usually related to the function value at the point returned by the procedure). Numerical experiments performed both on classical test functions and on difficult space trajectory planning problems show that the proposed approach can be very effective in identifying good starting points for global optimization. Control of robot locomotion profits from the use of pre-planned trajectories. This paper presents a way to generalize globally optimal and dynamically consistent trajectories for cyclic bipedal walking. A small task-space consisting of stride-length and step time is mapped to spline parameters which fully define the optimal joint space motion. The paper presents the impact of different machine learning algorithms for velocity and torque optimal trajectories with respect to optimality and feasibility. To demonstrate the usefulness of the trajectories, a control approach is presented that allows general walking including transitions between points in the task-space. Trajectory planning and optimization is a fundamental problem in articulated robotics. Algorithms used typically for this problem compute optimal trajectories from scratch in a new situation. In effect, extensive data is accumulated containing situations together with the respective optimized trajectories--but this data is in practice hardly exploited. This article describes a novel method to learn from such data and speed up motion generation, a method we denote tajectory pediction. The main idea is to use demonstrated optimal motions to quickly predict appropriate trajectories for novel situations. These can be used to initialize and thereby drastically speed-up subsequent optimization of robotic movements. Our approach has two essential ingredients. First, to generalize from previous situations to new ones we need a situation descriptor--we construct features for such descriptors and use a sparse regularized feature selection approach to improve generalization. Second, the transfer of previously optimized trajectories to a new situation should not be made in joint angle space--we propose a more efficient task space transfer. We present extensive results in simulation to illustrate the benefits of the new method, and demonstrate it also with real robot hardware. Our experiments in diverse tasks show that we can predict good motion trajectories in new situations for which the refinement is much faster than an optimization from scratch. 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.