This paper presents a method for designing the gait of a snake robot that moves in a complicated environment. We propose a method for expressing the target form of a snake robot by connecting curve segments whose curvature and torsion are already known. Because the characteristics of each combined shape are clear, we can design the target form intuitively and approximate a snake robot configuration to this form with low computational cost. In addition, we propose two novel gaits for the snake robot as a design example of the proposed method. The first gait is aimed at moving over a flange on a pipe, while the other is the crawler gait aimed at moving over rough terrain. We demonstrated the effectiveness of the two gaits on a pipe and rough terrain in experiments.

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.

In this paper, we develop an articulated mobile robot that can climb stairs, and also move in narrow spaces and on 3-D terrain. This paper presents two control methods for this robot. The first is a 3-D steering method that is used to adapt the robot to the surrounding terrain. In this method, the robot relaxes its joints, allowing it to adapt to the terrain using its own weight, and then, resumes its motion employing the follow-the-leader method. The second control method is the semi-autonomous stair climbing method. In this method, the robot connects with the treads of the stairs using a body called a connecting part, and then shifts the connecting part from its head to its tail. The robot then uses the sensor information to shift the connecting part with appropriate timing. The robot can climb stairs using this method even if the stairs are steep, and the sizes of the riser and the tread of the stairs are unknown. Experiments are performed to demonstrate the effectiveness of the proposed methods and the developed robot.

This paper presents a new sum-of-squares (SOS, for brevity) design framework for robust control of polynomial fuzzy systems with uncertainties. Two kinds of robust stabilization conditions are derived in terms of SOS. One is global SOS robust stabilization conditions that guarantee the global and asymptotical stability of polynomial fuzzy control systems. The other is semiglobal SOS robust stabilization conditions. The latter is available for very complicated systems that are difficult to guarantee the global and asymptotical stability of polynomial fuzzy control systems. The main feature of all the SOS robust stabilization conditions derived in this paper are to be expressed as nonconvex formulations with respect to polynomial Lyapunov function parameters and polynomial feedback gains. Since a typical transformation from nonconvex SOS design conditions to convex SOS design conditions often results in some conservative issues, the new design framework presented in this paper gives key ideas to avoid the conservative issues. The first key idea is that we directly solve nonconvex SOS design conditions without applying the typical transformation. The second key idea is that we bring a so-called copositivity concept. These ideas provide some advantages in addition to relaxations. To solve our SOS robust stabilization conditions efficiently, we introduce a gradient algorithm formulated as a minimizing optimization problem of the upper bound of the time derivative of an SOS polynomial that can be regarded as a candidate of polynomial Lyapunov functions. Three design examples are provided to illustrate the validity and applicability of the proposed design framework. The examples demonstrate advantages of our new SOS design framework for the existing linear matrix inequality approaches and the existing convex SOS approach.

This paper proposes control method for a snake robot to ascend and descend steps. In a multiplane step environment, it is necessary for locomotion to transfer from one plane to another. When a snake robot moves, it touches several planes as its body is long and thin. In this paper, we propose a control method to track the trajectory of a snake robot in a step environment. We decomposed the 3-D motion of the robot into two simple models by introducing an assumption that simplifies the model and controller, and derive a model of the robot as a hybrid system with switching. The control method consists of a tracking controller, a method for shifting the robot's part connecting the planes, and active lifting to control the shape of the robot. Ascent and descent experiments confirm the effectiveness of the proposed controller and the method for shifting the connecting part of the robot's body.

The snake robot, which mimics the mechanism of real snakes, is expected to be used in various environments. This article addresses the challenge of snake robots autonomously adapting to and moving inside and outside pipes having complex shapes using a helical rolling motion. We consider that an irregular helical form can be defined as a combination of three components, namely the axis, cross-sectional shape, and pitch angle, and that it is easier to consider deformations that have compliance only in a specific direction. Our proposed method deforms the cross-sectional shape of the snake robot locally so that it adopts the shape of the pipe accurately. Experiments were conducted using our developed snake robot to verify the effectiveness of the proposed method, and it was demonstrated that the proposed method can be used for a snake robot moving inside and outside of straight pipes and outdoor tree, including those having noncircular and varying cross sections.