Informed Sampling-Based Motion Planning for Manipulating Multiple Micro Agents Using Global External Electric Fields

Online manipulation of multiple micro- and nanoscale agents is of major interest for various research applications. Among the biggest limitations of wireless external actuation are its global and coupled influences in the workspace, which limit the robust manipulation of multiple agents independently and simultaneously. In this paper, we propose novel motion planning algorithms, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tt Bi$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tt iSST$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tt Ref$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tt iSST$ </tex-math></inline-formula> , to quickly generate time-optimal trajectories for multiple agents sharing global external fields. Both algorithms are extended by the stable sparse rapidly-exploring random tree kinodynamic motion planning algorithm. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tt Bi$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tt iSST$ </tex-math></inline-formula> uses a bidirectional approach to speed up the searching process. A novel connection process is proposed to connect the two trees efficiently by applying an optimization procedure. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tt Ref$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tt iSST$ </tex-math></inline-formula> uses the workspace information to quickly generate global-routing trajectories as references, then guides the search process more effectively by getting more accurate heuristics according to the reference global-routing trajectories. A transition matrix similar to that in Markov Decision Processes is used to form the reference trajectory. Compared with the state-of-the-art <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tt iSST$ </tex-math></inline-formula> algorithm, the proposed algorithms quickly update feasible solutions and converge to a near-optimal, minimum-time solution to increase the efficiency of the simultaneous manipulation of multiple micro agents using global external fields. Extensive analysis and physical experiments are presented to confirm the effectiveness and the performance of the motion planning algorithms. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Autonomous manipulation of multiple micro- and nanoscale agents is of major interest for various research applications. Wireless actuation is a promising way to position those objects. The commonly used non-contact actuation techniques include magnetic actuation, electrical field actuation, optical tweezers, and actuated flows, etc. Among the biggest limitations of wireless external actuation are its global and coupled influences in the workspace, which limit the capability to robustly manipulate multiple agents independently and simultaneously. In this paper, we propose novel bidirectional informed sampling-based motion planning algorithms to quickly generate time-optimal trajectories for multiple agents sharing global external fields. Novel heuristics and informed reference trajectory are used to guide the search for manipulating multiple agents under global fields. Numerical simulations and physical experiments are presented to demonstrate the performance of the motion planning design. The proposed algorithm guarantees anytime performance and quickly converges to a near-optimal minimum time solution for multiple agents. Although we focus on the electric-field actuated multiple-micro-agent system, the proposed motion planning strategies are not limited to the actuation and can be generalized to other field-based applications, in which the actuation among a group of multiple agents are coupled or intertwined.