Control Lyapunov Functions for Underactuated Soft Robots

Researchers Huy Pham and Zach J. Patterson have introduced a new control framework designed to solve a fundamental challenge in soft robotics: achieving stable, precise control of inherently underactuated systems operating under tight physical limits. Their paper, "Control Lyapunov Functions for Underactuated Soft Robots," presents a method that formulates control as an optimization problem. It enforces a rapidly exponentially stabilizing control Lyapunov function (CLF) as a convex inequality constraint, simultaneously satisfying the complex, underactuated full-body dynamics and strict actuator bounds. This approach directly addresses the shortcomings of common nonlinear strategies, like PD control, which often assume full actuation and ignore practical input limits.

The team validated their framework in simulation across three robotic platforms of increasing underactuation: a simple two-link tendon-driven "finger," a trimmed helicoid manipulator, and a highly underactuated spiral robot. When compared against several established baseline methods from the literature, their controller demonstrated superior performance. Results showed significant improvements in task-space accuracy for both set-point regulation and trajectory tracking, all while maintaining guaranteed Lyapunov convergence—a formal proof of stability—under the enforced input constraints. This represents a critical step toward deploying reliable, dynamically complex soft robots in real-world applications where safety and predictability are paramount.