Marchello Roberto, Morandotti Marco, Shum Henry, Zoppello Marta
Dipartimento di Scienze Matematiche "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy.
Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, ON Canada N2L 3G1.
Acta Appl Math. 2022;178(1):6. doi: 10.1007/s10440-022-00480-3. Epub 2022 Mar 8.
The controllability of a fully three-dimensional -link swimmer is studied. After deriving the equations of motion in a low Reynolds number fluid by means of Resistive Force Theory, the controllability of the minimal 2-link swimmer is tackled using techniques from Geometric Control Theory. The shape of the 2-link swimmer is described by two angle parameters. It is shown that the associated vector fields that govern the dynamics generate, via taking their Lie brackets, all eight linearly independent directions in the combined configuration and shape space, leading to controllability; the swimmer can move from any starting configuration and shape to any target configuration and shape by operating on the two shape variables. The result is subsequently extended to the -link swimmer. Finally, the minimal time optimal control problem and the minimization of the power expended are addressed and a qualitative description of the optimal strategies is provided.
研究了一种完全三维的n连杆游泳机器人的可控性。通过阻力理论推导了低雷诺数流体中的运动方程后，利用几何控制理论的技术解决了最小二连杆游泳机器人的可控性问题。二连杆游泳机器人的形状由两个角度参数描述。结果表明，控制动力学的相关向量场通过取它们的李括号，在组合配置和形状空间中生成了所有八个线性独立方向，从而实现了可控性；通过对两个形状变量进行操作，游泳机器人可以从任何初始配置和形状移动到任何目标配置和形状。随后，该结果被扩展到n连杆游泳机器人。最后，解决了最短时间最优控制问题和功耗最小化问题，并对最优策略进行了定性描述。
