Abstract
This paper proposes a motion planning algorithm for dynamic nonholonomic systems represented in a second-order chained form. The proposed approach focuses on the so-called holonomy resulting from a kind of motion that traverses a closed path in a reduced configuration space of the system. According to the author’s literature survey, control approaches that make explicit use of holonomy exist for kinematic nonholonomic systems but does not exist for dynamic nonholonomic systems. However, the second-order chained form system is controllable. Also, the structure of the second-order chained form system analogizes with the one of the first-order chained form for kinematic nonholonomic systems. These survey and perspectives brought a hypothesis that there exists a specific control strategy for extracting holonomy of the second-order chained form system to the author. To verify this hypothesis, this paper shows that the holonomy of the second-order chained form system can be extracted by combining two appropriate pairs of sinusoidal inputs. Then, based on such holonomy extraction, a motion planning algorithm is constructed. Furthermore, the effectiveness is demonstrated through some simulations including an application to an underactuated manipulator.
Highlights
Nonholonomic systems—dynamical systems with non-integrable differential constraints—have attracted attention as challenging robotic systems in the fields of motion planning and control [1,2,3,4].The most symbolical control problem is characterized by Brockett’s theorem [5]
For a class of kinematic nonholonomic systems, holonomy is defined as “the extent to which a closed path in the base space fails to be closed in the configuration space” [14], where the base space is a reduced configuration space
This paper addresses a motion planning problem for the second-order chained form system
Summary
Nonholonomic systems—dynamical systems with non-integrable differential constraints—have attracted attention as challenging robotic systems in the fields of motion planning and control [1,2,3,4]. Inspired by the structural difference and analogy between the first- and second-order chained form systems, it is found that a combination of two appropriate pairs of sinusoidal inputs can be used to extract the holonomy. In Reference [34], the author has applied the holonomy-based motion planning algorithm into an underactuated manipulator and discussed singularities of the system transformation therein Instead of such discussion, this paper examine an effect from the parameters of control inputs (see the second last paragraph, that is, the paragraph before Remark 5). The paper is concluded with directions for future work
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