Impulsive Motion Planning for Positioning and Orienting a Polygonal Part

Abstract

In this paper, the authors analyze the dynamic behavior of a rigid polygonal part struck on a horizontal surface under the action of friction and present how to propel the part to a desired configuration through the impulsive operation. In the dynamic analysis of the impulsive operation, the part motion is typically analyzed in two phases, impact motion and sliding motion. These are usually analyzed in reverse order of occurrence. The authors characterize the impact and sliding dynamics with friction for polygonal parts and develop an approach to compute the inverse dynamic solution for motion planning of the impulsive operation. Finally, the authors verify the effectiveness of the simulation results and the developed motion plans through comparison with experimental results using a high-speed video camera.

Ball Positioning in Robotic Billiards: A Nonprehensile Manipulation-Based Solution

“…For positioning flat objects (axi-symmetric and polygonal ones) on a plane with the action of sliding friction, Huang et al [25] and Han and Park [26] use inverse numerical algorithms. The flowchart representing the forward dynamics of the ball, given in Figure 11, shows that some of the dynamics are not explicitly expressed by equations, but by numerical procedures.…”

Planning Velocities of Free Sliding Objects as a Free Boundary Value Problem

“…The resulting forces and torque have the same form as in Han and Park (2001), in which these equations were derived by using the principle of virtual work. In general, there is no closed-form solution for the integrals (15), (16), and (17); numerical computation procedures for friction forces F X , F Y and torque T for general objects are presented in Appendix B.…”

“…Partridge and Spong (2000) applied this model to predict the trajectory of the air hockey puck after impacting with the table wall, and also presented a planner to strike the puck and follow a desired trajectory. Han and Gilmore (1993) studied multi-body impact with friction, and the results have been used in Han and Park (2001) for calculating the striking velocity. Recently, Spong (2001) investigated the controllability of an air hockey puck subject to impact from a mallet, and characterized the reachable subset of velocities achievable with a single impact between the puck and mallet.…”

“…The planning method proposed here is different from the previous methods (Huang 1997;Han and Park 2001). In previous methods, qualitative relationships between the initial velocities and displacements were first derived based on the equations of free sliding objects.…”

Unconstrained dynamic planar manipulation with one joint manipulator

“…Another approach to move the object is by using nonprehensile techniques [14]. In this approach, instead of using grasping, the manipulation tasks are performed by using pushing [17] [2], throwing [13], bating [3], toppling [18] [11], juggling [12], part dropping [8] [16] [4], impact [6] [7]. Nonprehensile manipulation methods can be further divided into two categories, namely, quasi-static and dynamic nonprehensile manipulation.…”