Impulsive-actuation Part Positioning through Constrained Energy Balance Planning

Impulsive actuation has been researched in the past two decades as an inexpensive alternative to multi-degree-of-freedom precision positioning systems. The position of a sliding workpiece can be controlled by a 2-degree-offreedom actuation system through simple pushing path planning. However, the final part position as a result of the last touch of the actuator is subject to uncertainty in the friction model used for actuation planning, particularly the free-sliding distance undergone by the workpiece after losing contact with the actuator. This paper first reviews an impact planning method, then augments it using a restitutionbased model that results in an explicit actuator velocity function. Results are given for positioning of a continually rotating workpiece that show improvement over constant-velocity pushing actuation. Such a positioning system is applicable to dynamic positioning for precision metrology or positioning prior to manufacturing operations (e.g., magnetic chuck grinding with part being moved while the table is rotating). INTRODUCTION Precision positioning is a necessary practice in manufacturing, both from the standpoint of machine element actuation and workpiece positioning prior to processing. Particularly for workpiece actuation, research in precision positioning by pushing, sliding or tapping has been recently considered as an inexpensive alternative to more complex pick-and-place or vision / fiducial systems. Additionally in some applications, higher precision can be achieved by this method through avoidance of relative movement errors associated with gripper release. However, positioning by pushing is subject to the nonlinear and time-variant effects of friction at the sliding interface. This effect, particularly the stick-slip effect (stiction) must be accounted for in motion planning to ensure precision in sliding positioning. The case of pushing (i.e., constant contact) rather than impacting (i.e., brief energetic contact) is considered. This method would greatly simplify planning and mitigate the effects of uncertainty in the friction model, but is difficult to implement in a dynamic application where there is lateral motion between the pusher and part, such as actuating a part to center of rotation while the support surface (e.g., spindle base) is constantly rotating. However, pushing serves as a basis for the described method. ACTUATION BY PUSHING In the past 20 years, there have been numerous research efforts in the field of precision positioning by sliding the target object across a surface. Peshkin and Sanderson describe the motion of a sliding workpiece for all possible pressure distributions on the support surface [Peshkin & Sanderson]. Zesch and Fearing explore force-controlled pushing for microparts with positional results in the 1μm range [Zesch & Fearing]. Lynch and Mason have done extensive work on planning and control for stable pushing in the application of robotic manipulation as an alternative to pickand-place positioning, including feasibility studies through both kinematic and force analyses [Lynch & Mason 1995a; Lynch & Mason 1995b, 1996]. Lynch also explores friction estimation for pushed objects and openloop control for pushing the general polygonal shape, characterized by the “maneuverability” property [Lynch 1993, 1999]. IMPULSIVE ACTUATION Huang thoroughly examined manipulation by impulse for robotic applications, including path step planning, object translation and rotation modeling. Huang and Mason break the impulsive positioning problems into two subparts: the Inverse Sliding Problem and the Impact Problem [Huang & Mason]. The Inverse Sliding Problem Given an initial position and orientation and a desired final position and orientation for the target object, what initial translational and rotational velocities need to be imparted to the object? Given the strongly coupled generalized equations of motion in one dimension (ignoring the viscous frictional effect at low velocity),