Nonlinear Least-Squares Method Considering Input Constraints for Lizard-Inspired Single-Actuated Robot

The purpose of this paper is to design a path-following control system of a Lizard-Inspired Single-Actuated robot (LISA) based on the nonlinear least-squares method, considering input constraints. LISA is an entirely new robot capable of driving with one degree of freedom, enabling both propulsion and rotation using a single actuator. Previously proposed robots drivable with one degree of freedom often suffer from theoretical leg slippage issues. By adopting a four-bar linkage mechanism morphology, LISA resolves this inherent leg slippage problem in single-degree-of-freedom robots. This paper focuses on LISA’s motion control system, designing a path-following control system using the nonlinear least-squares method. The objective function for the nonlinear least-squares problem is designed using LISA’s motion characteristics. To achieve this, the motion characteristics are formulated, including the turning angle, stride length, posture, LISA’s propulsion direction, and LISA’s position coordinates in the absolute coordinate system. Subsequently, a path-following control system based on the nonlinear least-squares method is designed. The key point in the control system design is to combine the Levenberg–Marquardt method with a step-size adjustment algorithm to account for LISA’s geometric constraints. This enables the design of a control system that satisfies LISA’s input angle constraints. The effectiveness of the designed control system is verified through numerical simulations using reference paths with three distinct properties: straight lines, circles, and quadratic equations. The results confirm that the designed control system is effective in tracking the reference paths while accounting for the input constraints.