Matthew J. Travers

Modulation of orthogonal body waves enables high maneuverability in sidewinding locomotion

Significance We examined the turning behavior of snakes performing sidewinding locomotion using a hypothesized two-wave control template. Sidewinders achieved exceptional maneuverability using two types of turns, shallow differential turns and sharp reversal turns, which we hypothesized are controlled by modulating horizontal wave amplitude and vertical wave phase offset, respectively. We tested these hypothesized control schemes using a modular snake robot capable of sidewinding, resulting in similar behaviors, and explored two-wave parameter space, resulting in discovery of a third turning mechanism that is not seen in snakes. Thus, we show that complex behaviors such as turning while sidewinding can emerge from independent modulations of each of the two waves comprising this control template, underscoring the utility of robots to test biological hypotheses. Many organisms move using traveling waves of body undulation, and most work has focused on single-plane undulations in fluids. Less attention has been paid to multiplane undulations, which are particularly important in terrestrial environments where vertical undulations can regulate substrate contact. A seemingly complex mode of snake locomotion, sidewinding, can be described by the superposition of two waves: horizontal and vertical body waves with a phase difference of ±90°. We demonstrate that the high maneuverability displayed by sidewinder rattlesnakes (Crotalus cerastes) emerges from the animal’s ability to independently modulate these waves. Sidewinder rattlesnakes used two distinct turning methods, which we term differential turning (26° change in orientation per wave cycle) and reversal turning (89°). Observations of the snakes suggested that during differential turning the animals imposed an amplitude modulation in the horizontal wave whereas in reversal turning they shifted the phase of the vertical wave by 180°. We tested these mechanisms using a multimodule snake robot as a physical model, successfully generating differential and reversal turning with performance comparable to that of the organisms. Further manipulations of the two-wave system revealed a third turning mode, frequency turning, not observed in biological snakes, which produced large (127°) in-place turns. The two-wave system thus functions as a template (a targeted motor pattern) that enables complex behaviors in a high-degree-of-freedom system to emerge from relatively simple modulations to a basic pattern. Our study reveals the utility of templates in understanding the control of biological movement as well as in developing control schemes for limbless robots.

Kinematic gait synthesis for snake robots

Snake robots are highly articulated mechanisms that can perform a variety of motions that conventional robots cannot. Despite many demonstrated successes of snake robots, these mechanisms have not been able to achieve the agility displayed by their biological counterparts. We suggest that studying how biological snakes coordinate whole-body motion to achieve agile behaviors can help improve the performance of snake robots. The foundation of this work is based on the hypothesis that, for snake locomotion that is approximately kinematic, replaying parameterized shape trajectory data collected from biological snakes can generate equivalent motions in snake robots. To test this hypothesis, we collected shape trajectory data from sidewinder rattlesnakes executing a variety of different behaviors. We then analyze the shape trajectory data in a concise and meaningful way by using a new algorithm, called conditioned basis array factorization, which projects high-dimensional data arrays onto a low-dimensional representation. The low-dimensional representation of the recorded snake motion is able to reproduce the essential features of the recorded biological snake motion on a snake robot, leading to improved agility and maneuverability, confirming our hypothesis. This parameterized representation allows us to search the low-dimensional parameter space to generate behaviors that further improve the performance of snake robots.

Extended gait equation for sidewinding

Sidewinding is an efficient translational gait used by biological snakes to locomote over flat ground. Prior work has identified the fact that it is possible to steer the moving direction of sidewinding. The previously proposed virtual tread model reveals the working principal of sidewinding from a geometric point of view. Unfortunately, the implementation of the virtual tread model relied on a computationally expensive numerical fitting algorithm that impeded online applications. Motivated by this limitation, in this work we propose a novel approach to develop analytical expressions for snake robot gaits based on the study of the corresponding geometric model. This approach is rooted in the identification of dominant frequency components afforded by the two-dimensional Fast Fourier Transformation (FFT). Applying this method to the virtual tread model for conical sidewinding, we derive an analytical expression between the parameters that describe the gaits motion and the turning radius of the system moving in the world. This analytical expression, which we call the extended gait equation, is verified by experimental results.

Proposal of EARLI for the snake robot's obstacle aided locomotion

In this paper, EARLI (Extended Asymmetrical Reverse Lateral Inhibition) is proposed for the snake robots obstacle aided locomotion and behavior. The idea of EARLI starts with an original idea of lateral inhibition; although joints rotate in reverse direction compared with the original lateral inhibition; and information of contact affects not only adjacent joints but also a couple of neighboring joints away from a contacting link. Furthermore, distribution of adding torque is empirically set asymmetrically in order to propel the snake robot forward. The algorithm of EARLI is implemented to ODE (Open Dynamics Engine) to see its behavior in simulation environments and to verify its effectiveness. As a result, a behavior emerges in which the the snake robot is pushing obstacles for longer times and moving greater distances than when using original lateral inhibition. In addition, continuous pushing behavior is also observed when an obstacle is located behind the the snake robot.

Visual sensing for developing autonomous behavior in snake robots

Snake robots are uniquely qualified to investigate a large variety of settings including archaeological sites, natural disaster zones, and nuclear power plants. For these applications, modular snake robots have been tele-operated to perform specific tasks using images returned to it from an onboard camera in the robots head. In order to give the operator an even richer view of the environment and to enable the robot to perform autonomous tasks we developed a structured light sensor that can make three-dimensional maps of the environment. This paper presents a sensor that is uniquely qualified to meet the severe constraints in size, power and computational footprint of snake robots. Using range data, in the form of 3D pointclouds, we show that it is possible to pair high-level planning with mid-level control to accomplish complex tasks without operator intervention.

Using Lie algebra for shape estimation of medical snake robots

Highly articulated robots have the potential to play a key role in minimally invasive surgeries by providing improved access to hard-to-reach anatomy. Estimating their shape inside the body and combining it with 3D preoperative scans of the anatomy enable the surgeon to visualize how the entire robot interacts with the internal organs. As the robot progresses inside the body, the position and orientation of every link comprising the robot, evolves over a coordinate-free Lie algebra, se(3). To capture the full motion and uncertainty of the system, we use an extended Kalman filter where the state vector is defined using elements of se(3). We show that this approach describes the shape of the robot more accurately, than the ones where the state vector is a conventional parametrization, such as Cartesian coordinates and Euler angles. We perform two experiments to demonstrate the effectiveness of this new filtering approach.

Snakeboard Motion Planning With Local Trajectory Information

We address trajectory generation for the snakeboard, a system commonly studied in the geometric mechanics community. Our approach derives a solution using body coordinates and local trajectory information, leading to a more intuitive solution compared to prior work. The simple forms of the solution clearly show how they depend on local curvature and desired velocity profile, allowing for a description of some simple motion primitives. We readily propose techniques to navigate paths, including those with sharp corners, by taking advantage of the snakeboard’s singular configuration, as well as discuss some implications of torque limits.

Impulse optimization for data association

This paper presents a new method that addresses measurement origin uncertainty. Measurement origin uncertainty occurs when the object a measurement originated from is not clear. The systems considered contain multiple bodies which are dynamically indistinguishable other than initial conditions. Each measurement originates from one of the bodies in the system. In the past, recursive data association methods have been used to address problems of this nature. A new technique is presented which treats the measurement association problem as a batch post-processing problem. Reformulating the problem as such, it is possible to transform the data association problem into a trajectory optimization problem. From this point of view it is then possible to solve the measurement association problem using first- and second-order optimization algorithms that rely on having first- and second-order derivatives for cost functions that depend on impulsive trajectories.

Snakeboard motion planning with viscous friction and skidding

The snakeboard is a well-studied example for mechanical systems analysis, largely because of its simultaneous richness in behavior and simplicity in design. However, few snakeboard models incorporate dissipative friction in the traveling direction and skidding as a violation of the rigid nonholonomic constraints. In this paper we investigate these effects on trajectory planning by evaluating a previously proposed friction model as well as a novel skidding model based on the addition of Rayleigh dissipation functions. We show how these additions change the usual behavior of gaits in the forward planning problem, and incorporate the changes into the solutions of the inverse planning problem by utilizing body coordinates along with a curvature parameterization for trajectories.

Use of the nonlinear observability rank condition for improved parametric estimation

The correct way to design controllers for dynamic robots is still very much an open question. This is in a large part due to the complexity and uncertainty in modeling their nonlinear dynamics. In this work, we focus on deriving concise dynamic expressions for a particular class of robots that can be used to better reduce uncertainty with respect to unknown parameters in realtime. We accomplish this by using an extended Kalman filtering framework in conjunction with an online controller that continuously maximizes a local measure of nonlinear observability. The main novel contribution of this work is that we directly use the nonlinear observability rank condition to derive the measure of observability at each time step. We are able to make this extension in part by focusing on serial-chain systems and exploiting the geometric structure in their dynamic models. In particular, we derive concise, closed-form and exact analytical representations for the forward dynamics, linearization, and nonlinear observability rank condition of a fixed-base serial manipulator with actively controlled elastic joints. An example is presented in which the spring constants and damping coefficients for a series-elastic actuated manipulator are estimated using the online observability maximizing techniques we derive.