Actuation-constrained control framework for optimal microswarm navigation with swarm stability guarantee

Swarm navigation of micro-/nanorobots has been attracting extensive attention, as it is a vital technique for microrobotic applications, for example, targeted drug delivery/therapy and micromanipulation. Researchers have shown that, controlled by a global magnetic field, millions of micro-/nanorobots can assemble and then efficiently navigate to targeted locations. However, current navigation control schemes for microswarms do not consider constraints on swarm actuation, for example, motion direction and rotating angular velocity, which would result in non-optimal navigation performance and even failure. In this work, we propose an actuation-constrained control framework for microswarms that explicitly treats important swarm motion properties as hard constraints in both trajectory planning and motion control. In our framework, we derive a constrained coarse-to-fine differential dynamic programming (DDP)-based trajectory planner that can generate the optimal trajectory in obstacle environments under the constraint of microswarm rotational angular velocity to maintain stable swarm assembly. Regarding trajectory tracking, we formulate a nonholonomic model predictive control (MPC) scheme, which makes the swarm optimally track the planned trajectory while complying with constraints on motion direction and rotational angular velocity. By our framework, microswarms can navigate with stable swarm assembly and the fastest motion speed, realizing optimal navigation performances. A series of comparative simulations and experiments validate the advantages of our framework in terms of swarm stability and navigation speed. Experimental results also show that our framework can work with different environmental morphologies, for example, discrete obstacles and channels, showing high adaptability to working scenarios. Navigation with moving obstacles and fluid flow further proves the capability of our framework for dynamic environments.