Matthew D. Berkemeier

Tracking fast inverted trajectories of the underactuated Acrobot

The Acrobot is a simple underactuated system consisting of a double pendulum with an actuator at the second joint only. We derive a set of exact trajectories of the nonlinear equations of motion, which involve inverted periodic motions. The trajectories can be made arbitrarily fast by an appropriate choice of the Acrobot mass and length parameters. Next, we present a nonlinear control law and show how it can be applied to the Acrobot to track these trajectories. In simulations we compare tracking results for our controller and one based on pseudo-linearization. The pseudo-linearizing controller produces significant error for a 1 Hz trajectory, while ours produces none. Finally, we present experimental results which demonstrate that the assumptions of the theory were not overly restrictive. In particular, peak-to-peak oscillations of joints as large as 850 were obtained, despite real-world effects, such as joint friction, inexact parameter values, and noisy and delayed joint velocity data.

Modeling the dynamics of spring-driven oscillating-foil propulsion

In this paper we present a model for oscillating-foil propulsion in which springs are used to transmit forces from the actuators to the foil. The expressions for hydrodynamic force and moment on the foil come from classical, linear, unsteady aerodynamics, and these are coupled to linearized rigid-body mechanics to obtain the complete model for swimming. The model is presented as a low-order set of ordinary differential equations, which makes it suitable for the application of techniques from systems and control theory. The springs serve to reduce energy costs, and we derive explicit expressions for spring constants which are optimal in this sense. However, the use of springs can potentially lead to unstable dynamics. Therefore, we also derive a set of necessary and sufficient conditions for stability. A detailed example is presented in which energy costs for one actuator are reduced by 33%.

Sliding and hopping gaits for the underactuated Acrobot

An example of a planar hopping robot is considered, which has only one actuated joint. Simulations demonstrate that the robot can perform both sliding and hopping gaits, despite the fact that almost all other hopping robots have at least two actuated joints.

Passive dynamic quadrupedal walking

It has been shown that a suitably designed biped will walk passively, i.e., without actuation or control, down a shallow slope. This paper extends the concept from bipedal to quadrupedal locomotion. A simple rimless-wheel model is analyzed first to provide a few basic insights, followed by a more complex model with freely-swinging legs. The gaits found for the quadruped are similar to, but more efficient than, those of the biped. However, for any reasonable choice of physical parameters for the system, quadrupedal walking is unstable.

Control of a two-link robot to achieve sliding and hopping gaits

A new example of a hopping robot is considered, consisting simply of two links (the end of one link acts as the foot) joined by an actuated, revolute joint. For the stance phase a nonlinear controller is derived that maintains the balance of the robot and periodically accelerates the center of mass vertically. For large enough oscillations the robot can slide or take off. If flight is achieved, the drift caused by non-zero angular momentum can typically be cancelled by rotating the actuated joint an integral number of times, and the robot can land in the same configuration in which it took off. This is due to the holonomy of a single rotation of the actuated joint. Results of simulations are presented in which the robot achieves both sliding and hopping gaits.<<ETX>>

Design of a robot leg with elastic energy storage, comparison to biology, and preliminary experimental results

This paper presents a novel robot leg design. The leg is powered by a DC motor which drives elastic tendons to turn a foot. The tendons store elastic energy just as in nature. Preliminary experimental results show the leg has a well-defined resonance which can be exploited to produce hopping. We also offer a comparison of our leg with the cat hindlimb. Eventually, the leg will be part of a quadrupedal robot.

Control of hopping height in legged robots using a neural-mechanical approach

We compare two previous approaches for hopping height control to the new scheme proposed in this paper. This new approach is an example of work in the developing area of neural-mechanical systems and has some very simplified versions of building blocks observed in nature, including a central pattern generator. Explicit formulas for hopping height and conditions for stability were obtained for all three approaches based on approximate Poincare return maps (not included). We also present a novel robot leg design and experimental data which supports our analysis. Our adaptive periodic forcing approach is shown to be comparable or out-perform the other two methods in terms of bandwidth requirement, hopping height, and stability properties.

The motion of a finite-width rimless wheel in 3D

We consider a new model for human (or biped robot) locomotion, consisting of a spoked rimless wheel of finite width rolling down a slope. In our model, consecutive spokes are on alternate sides of the wheel, and this models the finite leg separation in humans or robots. Full 3D motion is considered, in contrast to McGeers 2D model. Numerical studies indicate that for a given slope, a single steady-state solution exists, and this corresponds to rolling straight down the slope at a particular average speed. Moreover, this equilibrium solution is asymptotically stable.

Low-energy control of a one-legged robot with 2 degrees of freedom

We consider the dynamics of forward motion for a one-legged hopping robot. We analyze the passive dynamics of the leg and find the necessary initial conditions which produce forward hopping. An approximate Poincare return map is derived using perturbation theory, and a control system designed to consume a small amount of energy is applied. Numerical simulations indicate that a moderate range of stable forward speeds may be achieved. The control strategy applied allows a steady-state hopping motion to be maintained using low-bandwidth sensory feedback while introducing little energy into the system.

Visual servoing of an omni-directional mobile robot for alignment with parking lot lines

ODIS is an omni-directional mobile robot designed to autonomously or semi-autonomously inspect automobiles in a parking lot. Periodically, its position and orientation references need to be reset. This paper considers visual servoing to parking lot lines as one possible approach. Analysis and simulations demonstrate that a surprisingly simple proportional controller in the image coordinates can accomplish position and orientation alignment with parking lot lines. Unlike previous work, no image Jacobian matrix is necessary. Knowledge of the camera focal length is not required, but the camera and vehicle axes are assumed to be aligned, and the vehicle is assumed to rotate about the camera frames y-axis.