Tony Dear

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.

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.

Kinematic Cartography and the Efficiency of Viscous Swimming

The apparent “distance” between two configurations of a system and the “length” of trajectories through its configuration space can be significantly distorted by plots that use “natural” or intuitively selected coordinates. This effect is similar to the way that a latitude–longitude plot of the Earth distorts the size and shape of the continents. In this paper, we explore how ideas from cartography can be used to identify system parameterizations that better reflect the effort costs of changing configuration. We then apply these new parameters to provide geometric insight about two aspects of moving in dissipative environments such as low Reynolds number fluids: The shape of the optimal gait cycle for a three-link swimmer and the fundamentally superior efficiency of a serpenoid swimmer as compared to the classic three-link system.

Nonlinear dimensionality reduction for kinematic cartography with an application toward robotic locomotion

Planning robot motions often requires a notion of the “distance” between configurations or the “length” of a trajectory connecting them in the configuration space. If these quantities are defined so as to correspond to the effort required to change configurations, then they would likely differ from the Euclidean distance or arclength in the systems configuration parameters, distorting the visual representation of the relative costs of executing the motions. This problem is fundamentally similar to that of producing map projections with minimal distortion in cartography. A separate problem is that of nonlinear dimensionality reduction (NLDR), which, given a set of data, projects it into a lower-dimensional space while seeking to retain the geometric relationship between data points. In this paper, we show that NLDR can be applied to the kinematic cartography problem, allowing us to generate system parameterizations in which distance and arclength correspond to the effort of motion.

MECHANICS AND CONTROL OF A TERRESTRIAL VEHICLE EXPLOITING A NONHOLONOMIC CONSTRAINT FOR FISHLIKE LOCOMOTION

We present a novel mechanical system, the “landfish,” which takes advantage of a combination of articulation and a nonholonomic constraint to exhibit fishlike locomotion. We apply geometric mechanics techniques to establish the equations of motion in terms of the system’s nonholonomic momentum and analyze the system’s equilibrium properties. Finally, we demonstrate its locomotion capabilities under several controllers, including heading and joint velocity control.

Optimal control for geometric motion planning of a robot diver

Inertial reorientation of airborne articulated bodies has been an active area of research in the robotics community, as this behavior can help guide dynamic robots to a safe landing with minimal damage. The main objective of this work is emulating the aggressive and large angle correction maneuvers, like somersaults, that are performed by human divers. To this end, a planar three link robot, called DiverBot, is proposed. By considering a gravity-free scenario, a local connection is obtained between joint angles and the body orientation, resulting in a reduction in the system dynamics. An optimal control policy applied on this reduced configuration space yielded diving maneuvers that are dynamically feasible. Numerical results show that the DiverBot can execute one somersault without drift and multiple somersaults with minimal drift.

The three-link nonholonomic snake as a hybrid kinodynamic system

Motion planners often avoid the so-called singular configurations of a locomoting system because they can change a systems dynamics and cause it to incur unbounded input controller costs. However, such configurations can also allow a system to exhibit new modes of locomotion, which can be incorporated into previously established planning techniques. Here we take a nonholonomic kinematic system and present the formalism for representing it as a hybrid system taking advantage of the singular configuration and the associated dynamics. We show how to achieve the transition maps between the modes of operation by allowing actuated joints to become passive or locked, circumventing problems with unbounded constraint forces. This new model offers a new capability to take advantage of drift dynamics and rolling motions, which we demonstrate using a switching controller involving established kinematic techniques and preliminary dynamic maneuvers.

Motion Planning and Differential Flatness of Mechanical Systems on Principal Bundles

Mechanical systems often exhibit physical symmetries in their configuration variables, allowing for significant reduction of their mathematical complexity arising from characteristics such as underactuation and nonlinearity. In this paper, we exploit the geometric structure of such systems to explore the following motion planning problem: given a desired trajectory in the workspace, can we explicitly solve for the appropriate inputs to follow it? We appeal to results on differential flatness from the nonlinear control literature to develop a general motion planning formulation for systems with symmetries and constraints, which also applies to both fully constrained and unconstrained kinematic systems. We conclude by demonstrating the utility of our results on several canonical mechanical systems found in the locomotion literature.Copyright

Locomotive analysis of a single-input three-link snake robot

When commanding gaits for snake robots and other articulated systems, direct control of all possible joint inputs may not always be necessary or optimal to achieve a locomotive goal. Here we consider a three-link nonholonomic snake robot-an already underactuated system with locomotive capabilities in SE(2)-and reduce its input space to a single actuated joint, replacing the other joints motor with a passive mass-spring-damper system. We show that the modified system can operate dynamically in addition to kinematically, and that it is possible to find gaits that produces locomotion similar to a fully actuated system. In particular, we describe the emergence of a new type of gait that incorporates the systems singular configurations to produce high locomotive efficiency without incurring unbounded constraint forces.

A physical parameter-based skidding model for the snakeboard

The physical violation of a nonholonomic systems idealized constraints in the form of skidding has recently elucidated interest in new models in order to directly incorporate the phenomenon into the system dynamics. However, such models either are too simple to capture physical attributes or have otherwise been tested only on systems with simple behaviors, such as the rolling disk. In this work, we present a novel skidding model, based on physical parameters, for a snakeboard system, which is simultaneously rich in behavior but simple in design. This model extends the systems configuration space and associates traction forces to a skidding angle using an experimentally verified observation from the literature. We validate our model in simulation and discuss its advantages over the Rayleigh dissipation function skidding model. We also show that the model accurately predicts a physical systems behavior in experimentation with tuned parameters and standard controllers.