Step Climbing Control of Snake Robot with Prismatic Joints.

The ultimate goal of this research study is to perform continuous rather than sequential movements of prismatic joints for effective motion of a snake robot with prismatic joints in a complex terrain. We present herein a control method for robotic step climbing. This method is composed of two parts: the first involves the shift reference generator that generates the joint motion for climbing a step, and the other is use of the trajectory tracking controller, which generates the joint motion for the head to track the target trajectory. In this method, prismatic joints are divided into those that are directly controlled for climbing a step and those that are represented as redundancies. By directly controlling the link length, it is possible to prevent the trailing part from back motion when climbing a step, and to avoid a singular configuration in the parts represented as redundancies. A snake robot that has rotational and prismatic joints and can move in three-dimensions was developed, and the effectiveness of the proposed method was demonstrated by experiments using this robot. In the experiment, it was confirmed that the proposed method realizes the step climbing, and the link length limitation using the sigmoid function works effectively.

Unified Approach to the Motion Design for a Snake Robot Negotiating Complicated Pipe Structures.

A unified method for designing the motion of a snake robot negotiating complicated pipe structures is presented. Such robots moving inside pipes must deal with various "obstacles," such as junctions, bends, diameter changes, shears, and blockages. To surmount these obstacles, we propose a method that enables the robot to adapt to multiple pipe structures in a unified way. This method also applies to motion that is necessary to pass between the inside and the outside of a pipe. We designed the target form of the snake robot using two helices connected by an arbitrary shape. This method can be applied to various obstacles by designing a part of the target form specifically for given obstacles. The robot negotiates obstacles under shift control by employing a rolling motion. Considering the slip between the robot and the pipe, the model expands the method to cover cases where two helices have different properties. We demonstrated the effectiveness of the proposed method in various experiments.

A Novel Path-Following-Method-Based Polynomial Fuzzy Control Design.

This article presents a novel path-following-method-based polynomial fuzzy control design. By examining the stabilization problem, the nonconvex stabilization criterion represented in terms of bilinear sum-of-squares (SOS) constraints is proposed to complement the existing convex stabilization criteria. Based on the polynomial Lyapunov function and considering the operation domain, the stabilization control is designed with a systematic region of attraction (ROA) analysis method. Since the proposed stabilization criterion remains in nonconvex form, the conservativeness caused by the transformation from nonconvex (bilinear SOS) constraints into convex (SOS) constraints can be avoided. Moreover, the restriction on the Lyapunov function candidates for the convex transformation in the literature does not exist in the proposed nonconvex stabilization criterion. The stabilization analysis for polynomial fuzzy control systems is concerned with the double fuzzy summation problem that can be treated as the copositivity problem. Therefore, the SOS-based copositive relaxation technique is applied for the proposed stabilization criterion. Since the proposed nonconvex stabilization criterion is represented in terms of bilinear SOS constraints, the path-following method is employed for solving the bilinear SOS problem. Finally, design examples are provided to demonstrate that the proposed nonconvex stabilization criterion complements the existing convex stabilization criteria.

Relaxed Stabilization and Disturbance Attenuation Control Synthesis Conditions for Polynomial Fuzzy Systems.

This article presents both stabilization and disturbance attenuation control synthesis conditions for a class of polynomial fuzzy systems. The sum of squares conditions is relaxed by restricting the domain of the polynomial variables that represent the membership functions as well as by using the line integral polynomial fuzzy Lyapunov function. For the disturbance attenuation problem, we consider the transformation of the Hamilton-Jacobi-Isaacs equation into a set of inequalities and a policy iteration algorithm to approximate its value function. Furthermore, we propose an alternative path following to find the initial L2 gain stabilizing control policy. Five examples are provided to demonstrate the effectiveness of the proposed conditions.

Polynomial fuzzy observer designs: a sum-of-squares approach.

This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.