Application of transverse functions to control differentially driven wheeled robots using velocity fields

Abstract

Abstract. This paper deals with control of a nonholonomic unicycle-like robot in a cluttered environment with static obstacles. The proposed solution is based on a combination of a universal motion controller taking advantage of transverse functions with a navigation velocity field determining a path in a free task space. The motion controller is used to imitate an omnidirectional planar kinematics such that nonholonomic constraints become hidden for a navigation layer. Then it is possible to generate vector fields which govern motion of the omnidirectional frame. The controller using the transverse function is discussed in depth. In particular, a possible parametrization of this function is considered and analysis of an augmented dynamics is provided for different motion patterns. Next, construction of obstacles and potential design for star-like shapes are presented. The navigation algorithm is verified experimentally and the results are discussed.

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…With the development of artificial intelligence, intelligent circuits [ ] and robots have become a hot research topic in recent years [38][39][40][41][42][43]. In this section, the RZNN-2 model is applied to control the robotic manipulator to track a given trajectory under the attack of constant noise.…”

Archives of Control Sciences

“…where ε 3 = ∏ 3 i=1 ε i , with ε i being bounded positive coefficients. Assuming that ε 1 > 0, ε 2 ∈ (0, π) and ε 3 ∈ 0, 1 2 one can show that the full rank condition of matrix W (α) is satisfied (in [20] a more general case is discussed). To design the controller, derivative ∂ f T ∂ α is computed in basis X ( f T ) as follows, [15]:…”

“…From (87) follows that input η 3 is multiplied by term A T 1 A −1 T 2 , which can be adjusted by a proper selection of transverse function parameters. Referring to [20] one can prove that A T 1 A −1 T 2 is bounded as follows:…”