Dynamic manipulation enables efficient interaction tasks, such as throwing, which rely on finding one or more high-quality trajectories from the initial state to the goal state. While model-free learning methods have been used to acquire efficient robot manipulation configurations, traditional planning algorithms often struggle with multi-task specifications, high-dimensional, and multi-modal trajectory data. Prior generative model-based approaches, have made significant progress in the field of motion planning. Diffusion models, as an emerging generative model, have been widely applied to planning tasks in various environments and have gained attention for their ability in encoding multidimensional and multimodal trajectories. Here we propose our method that combines the diffusion model and model-free throwing methods. Specifically, we use a backward reachable tube to search for throwing configurations, and sample from posterior trajectory distribution conditioned on the throwing configurations. Several trajectory optimization methods are used to ensure the generation of effective throwing trajectories. Experimental results show that our method is effective in generating feasible, smooth, and collision-free throwing trajectories in both simulated and real-world tasks. Additionally, different trajectories are provided to enhance the multimodality of the throwing task.

Type-2 fuzzy controllers have been mostly viewed as black-box function generators. Revealing the analytical structure of any type-2 fuzzy controller is important as it will deepen our understanding of how and why a type-2 fuzzy controller functions and lay a foundation for more rigorous system analysis and design. In this study, we derive and analyze the analytical structure of an interval type-2 fuzzy controller that uses the following identical elements: two nonlinear interval type-2 input fuzzy sets for each variable, four interval type-2 singleton output fuzzy sets, a Zadeh AND operator, and the Karnik-Mendel type reducer. Through dividing the input space of the interval type-2 fuzzy controller into 15 partitions, the input-output relationship for each local region is derived. Our derivation shows explicitly that the controller is approximately equivalent to a nonlinear proportional integral or proportional differential controller with variable gains. Furthermore, by comparing with the analytical structure of its type-1 counterpart, potential advantages of the interval type-2 fuzzy controller are analyzed. Finally, the reliability of the analysis results and the effectiveness of the interval type-2 fuzzy controller are verified by a simulation and an experiment.

This paper presents workspace optimization of a MEMS flexure-based hexapod nanopositioner previously built by the National Institute of Standards and Technology (NIST). Workspace is one of the most important quality criteria for positioning devices. Given a lot of literature on workspace optimization of rigid body parallel robots, there is relatively less work done in their compliant counterparts due to the challenges in determining the workspace. In this paper, we present an analytical formulation and a search algorithm to determine the workspace of the flexure based parallel mechanisms. A novel adaptive genetic algorithm has been developed to conduct the single and bi-objective optimization for maximum translational and rotational workspace. These optimization results provide a guidance for the designer to improve the device for specific design requirements.

In order to achieve the high motion precision of the macro-micro parallel manipulator system for a large radio telescope, its real-time motion planning is dealt with in this paper. To uniquely determine the spatial position and orientation of the cable driven parallel manipulator, the real-time optimization is conducted according to the principle of uniform tension in the six driving cables. Synchronized points and the “judge and wait” mechanism ensure the continuity and synchrony of the trajectory tracking of the two parallel manipulators. The preadjustment of the micro parallel manipulator reduces the drastic dynamical coupling as a result of the fast movement of the micro manipulator. Besides, over-workspace avoidance procedure is introduced to restrict the micro parallel manipulator not to exceed it workspace. Experimental results validate the high precision of the macro-micro parallel manipulator system with supervisory controller and the motion prediction algorithm.