Abstract-This paper presents a throwing motion planner based on a goal manifold for two-point boundary value problem. The article outlines algorithmic and geometric issues for planar throwing of rigid objects with a nonprehensile end-effector. Special attention is paid to the challenge of controlling a desired 6-dimensional state of the object with a planar 3-DoF robot. Modeling of the contacts is discussed using a state vector of the coupled robot and object dynamics. Robustness against uncertainty due to varying model parameters such as object inertia and friction between the end-effector and the object is investigated. An approach for obtaining manifolds of terminal constraints from the goal configuration is described. Classification of these constraints is given. Finally, feasible trajectory generation conditions for successful execution of the generated optimal controls are discussed.

Abstract-This paper discusses an online dynamic motion generation scheme for nonprehensile object manipulation by using a set of predefined motions and a trajectory deformation algorithm capable of incorporating positional and velocity boundary constraints. By creating optimal trajectories offline and deforming them online, computational complexity during execution is reduced considerably. As tight convex hulls of the deformed trajectories can be found, possible obstacles or workspace boundaries can be circumnavigated precisely without collision. The approach is verified through experiments on an inclined planar air-table for volleyball scenario using two 3-DoF robots.

Abstract-The planning and execution of real-world robotic tasks largely depend on the ability to generate feasible motions online in response to changing environment conditions or goals. A spline deformation method is able to modify a given trajectory so that it matches the new boundary conditions, e.g. on positions, velocities, accelerations, etc. At the same time, the deformed motion preserves velocity, acceleration, jerk or higher derivatives of motion profile of precalculated trajectory. The deformed motion possessing such properties can be expressed by translation of original trajectory and spline interpolation. This spline decomposition considerably reduces the computational complexity and allows the real-time execution. Formal feasibility guarantees are provided for the deformed trajectory and for the resulting torques. These guarantees are based on the special properties of Bernstein polynomials used for the deformation and on the structure of the chosen computed torque control scheme. The approach is experimentally evaluated in a number of planar volleyball experiments using 3-DoF robots and human participants.

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Throwing an object by a powered robot system is of great importance in unmanned environments. In this paper, we consider the problem of throwing a point-mass object to minimize uncertainty in the object's landing position, given uncertainty in (1) the robot's initial configuration and (2) friction at the joints. Our analysis assumes that the robot's throw is executed using open-loop torque commands, and it relies on the linearized sensitivities of (a) landing location with respect to release state, (b) release state with respect to initial robot configuration and (c) joint friction. Moreover, the effectiveness of the proposed method is evaluated by MonteCarlo simulations.

Abstract-Deformation of optimal trajectories has a great potential in various applications due to the ability of realtime recomputation of the overall trajectory when applying new boundary conditions. This paper presents a novel approach where optimal trajectories are created offline through numerical direct optimal control methods. Afterwards the trajectories are deformed online with a spline deformation approach, providing minimum acceleration deviation between optimal and deformed trajectories and considerably reducing the computational complexity of the algorithm during run time. A feasibility check based on upper bounds for the deformed trajectory, the controller tracking error and the resulting torque is provided. This guarantees correct task execution in the presence of bounded disturbances and unmodeled dynamics.

This paper presents a new device and a method for dynamic manipulation. The device consists of a planar robotic arm and an elastic beam as an end-effector. Using it the elastic end-effector will tend to increase performance and energy efficiency while executing dynamic and repetitive tasks. Through the control of the beam vibration and resonant modes, we modify the state of manipulated objects. For lightweight objects the control is provided through the intermittent contacts without changing dynamics of the beam. However, we show that by using proper synchronization technique continuous-phase contacts are also possible. Juggling and dribbling of a ball are considered to be an alternating non-prehensile catching and throwing task. Such alternating decelerating and accelerating impacts on the ball and the curvature of the beam at the time of impact will stabilize the cyclic orbit of the ball. By proper analysis of continuous-time contact and dynamics of the beam we establish a rhythmic movement of the system. With the variation of frequency and amplitude of the beam it is possible to switch between different dynamic actions such as juggling, dribbling, throwing, catching and balancing.