Motion Planning of a Second-Order Nonholonomic Chained Form System Based on Holonomy Extraction

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.