The planning and execution of real-world robotic tasks largely depends 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 the 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 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 degree-of-freedom robots and human participants.

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 Monte-Carlo simulations.

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.

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.

Catching is one of the most complex tasks in the area of dynamic manipulation. Exact information on the position and orientation of a rigid object is crucial in order to accomplish manipulation tasks. Both motion planner and control strategy use these data to achieve the desired contact of a predefined surface with a nonprehensile end-effector, e.g. flat plate. This paper presents a multi-level approach for robust task planning and execution for planar catching of rigid bodies. On the top level the choice of the best catching strategy is made. Different catching actions are introduced and classified based on relative translational and rotational velocities between the end-effector and the object. A motion planner is implemented on the middle level that produces smooth motion trajectories depending on the chosen strategy. Yet, some uncertainties occur during task execution due to sensory data, trajectory tracking and unmodeled dynamics. Therefore, a robust tracking control is implemented on the bottom level to guarantee task execution in presence of uncertainty in robot parameters. A sustainable framework is being used taking the dynamics of the robot, the object and the environment into account to create a consistent and versatile catching system.

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.