Abstract As explained in Chap. 6, any system with two inputs and up to four generalized coordinates can always be transformed into chained form. Then, since the -2UPS non-holonomic robot has two inputs (its leg lengths) and three generalized coordinates (its orientation parameters), its kinematics can be formulated in chained form. Given a system in chain form, its motion planning problem can be solved using well-established procedures (see [7] and the references therein) which means the motion planning problem for the analyzed spherical robot can be solved using one of these procedures, as Jakubiak did in [6] for a particular configuration of the system. In this case, Jakubiak used control functions given by truncated trigonometric series, as we already did in Chap. 5 for the 3 PU robot. Nevertheless, the use of these procedures requires a good understanding of sophisticated methods in non-linear control whose technicalities have proven a challenge to many practitioners who are not familiar with them. As an alternative, geometric motion planners have been proposed, for example, in [1]. The main advantage of this kind of motion planners is that they are based on elementary kinematics arguments. However, they generate stepped maneuvers, that is, maneuvers with intermediate instants with zero velocity that guide the moving platform to the desired orientation. This chapter presents a geometric motion planner able to steer the robot to the desired orientation through a differentiable path in the space of actuation variables. Part of the work presented in this chapter appeared in [5].
Motion Planning for the -2UPS Robot
2019-01-01
17 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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