Implementation of weave patterns by path parameterization in the simulation of welding processes by the finite element method

Skill-based Shared Control

“…Let the skill model S i (s; ρ i ) describe some motion pattern -that is specific to a given application domain, e.g. [7] exemplifies various weave patterns in welding. Here, we state a particular form used to represent wave and cycloid skills.…”

“…III-A our skill set S is sub-divided by a number of skill models S i . We identify the model S i and corresponding values for θ i by solving (7) for each model and chose the skill that results in the smallest error ε i .…”

“…Note that we make a differentiation between Θ SE i and Θ T O i . Depending on the application goals you can restrict the range of possible values that θ i can take in both ( 7) and ( 9): for example, we may wish to set the underlying trajectory initial orientation α c to the value estimated in (7) -this is enforced in (9) by setting the constraint α c = α c where α c is the value found by solving (7). Notice also that since we have derived explicit equations for x, u in terms of parameters θ i , we are able to remove the equations of motion 1 as an equality constraint.…”

“…We implemented our method within the CasADi framework [2], and leverage the plugin for SNOPT [12] to solve (7) and (9). Our method runs in an MPC loop: given a window of previous operator inputs, we estimate θ i for all skills i in separate processing threads, identify the intended skill by comparing the cost of fittings (8), compute an optimal θ * i by solving (9) -resulting in a trajectory of states x(θ * i ) and controls u(θ * i ), from which we execute the first step.…”

“…(1a) and (1b)). During task execution, the operator will often employ various motion patterns to achieve different goals: in concrete spraying, an operator will switch between circular and sweeping motions to regulate the rate of concrete deposition and create a smooth lining [3]; in robot assisted welding, the operator's expertise on the desired weld determine the choice among different weave patterns [7]; in plastering, different patterns yield different moulds [4]; and in the cleaning process of the train's front panels, expert cleaners repeatedly employ spiral brushing motion patterns [21]. These motion patterns, which we will call skills, are crucial to the success of the tasks.…”