Duane W. Marhefka

A compliant contact model with nonlinear damping for simulation of robotic systems

Contact modeling is an important aspect of simulation of many robotic tasks. In the paper, a compliant contact model with nonlinear damping is investigated, and many previously unknown characteristics of the model are developed. Compliance is used to eliminate many of the problems associated with using rigid body models with Coulomb friction, while the use of nonlinear damping eliminates the discontinuous impact forces and most sticky tensile forces which arise in Kelvin-Voigt linear models. Two of the most important characteristics of the model are the dependence of the coefficient of restitution on velocity and damping in a physically meaningful manner, and its computational simplicity. A full mathematical development for an impact response is given, along with the effects of the system and model parameters on energy loss. A quasistatic analysis gives results which are consistent with energy loss characteristics of a more complex distributed foundation model under sustained contact conditions. A foot contact example for a walking machine is given which demonstrates the applicability of the model for impact on foot placement, sustained contact during the support phase, and the breaking of the contact upon liftoff of the foot.

Simulation of contact using a nonlinear damping model

In this paper, a simple nonlinear contact model is presented for use in computer simulation. The nonlinear model is shown to maintain the computational simplicity of the linear model while addressing many of its deficiencies. One such advantage is that contact forces vary continuously over time. A new phase plane solution for the nonlinear model is obtained which reveals many previously unnoted properties. These include proper variation of the coefficient of restitution with impact velocity over a wide range of impact velocities, independence of model parameters, and lack of tensile (sticking) forces in simple impacts. An example is presented which demonstrates the use of the contact model in simulating the foot-ground interaction during the locomotion cycle of a walking machine.

Intelligent control of quadruped gallops

In this paper, a new intelligent control approach for high-speed quadruped bounding and galloping gaits is presented. The controller is capable of learning the leg touchdown angles and leg thrusts required to track the desired running height and velocity of a quadruped in only one stride. Training of the controller is accomplished not with a mathematical model, but with simple rules based on a heuristic knowledge of the quadruped mechanics. The result is a controller that produces better velocity and height tracking characteristics than a Raibert-based controller and is robust to modeling errors. Additionally, by making use of the natural dynamics of the system, gait characteristics comparable to biological quadrupeds result. The status of a legged machine being constructed for demonstration of the control approach and further study of the characteristics of galloping is also presented.

Gait planning for energy efficiency in walking machines

This paper addresses the problem of achieving energy efficiency in statically stable walking machines without mechanically constraining the system. In contrast to previous work, power is minimized over an entire locomotion cycle, through optimal selection of walking parameters, rather than for a fixed instant of time only. Dynamic simulation experiments of a hexapod with full three degree-of-freedom legs are used to develop a set of 5 rules for setting velocity, footholds, body height, duty factor, and stroke to achieve maximum energy efficiency. Optimization of walking parameters alone was found to reduce power consumption by up to 50% over a reasonable first set of parameters. The rules presented may be used as the basis for development of energy-efficient behaviors or other intelligent control schemes for walking machines.

Intelligent control of an experimental articulated leg for a galloping machine

Intelligent controllers are being used with increasing effectiveness on complex systems. This work verifies the effectiveness of fuzzy control, an intelligent method, on a single, articulated-leg that was designed to be used on a high-speed galloping quadruped. Intelligent methods are compared to other control methods in simulation and on the OSU DASH (Dynamic Articulated Structure for High-performance) leg. It is shown that the intelligent controllers outperform non-learning methods. Using fuzzy control, the OSU DASH leg performs stable hopping on a treadmill moving at 2.0 m/s.

Quadratic optimization of force distribution in walking machines

Energy efficiency remains a problem in walking machines. One approach to improving energy efficiency involves solving for an optimal set of foot forces which minimizes the power supplied to DC motor actuators at each instant. Energy regenerated by the motors, which may be significant, is generally lost and should be explicitly taken into account to produce the optimal force distribution. A method to produce this optimal solution using quadratic programming is developed in this paper. The results are compared to three suboptimal quadratic programming approaches which minimize internal forces, a weighted norm of joint torques, and finally power without accounting for regeneration, all on a simulated hexapod. It is found that the common approach of minimizing internal forces may often result in poor energy efficiency.

Fuzzy control of quadrupedal running

In this paper, a new fuzzy systems approach to the control of quadrupedal running is presented. The fuzzy controller is capable of learning the necessary leg touchdown angles and leg thrusts required to track the desired running height and velocity of a bounding quadruped in only one stride. This is accomplished through an adaptation mechanism which is based on heuristics similar to those used by Raibert (1986) to design his controllers. The performance of the fuzzy controller is compared to that of a modified Raibert controller and shows better tracking characteristics. The fuzzy controllers ability to respond to significant modeling errors in the quadruped is demonstrated with an example.

Hybrid kinematic and dynamic simulation of running machines

Dynamic simulation requires the computationally expensive calculation of joint accelerations, while in kinematic simulation these accelerations are known based on a given trajectory. This paper describes a hybrid kinematic and dynamic simulation method that can be applied to the simulation of running machines to speed up the computations over that of a dynamic simulation. This is possible because much of the time the legs of a running machine are in the air and their trajectories are directly specified and tightly controlled. The method is more flexible than dynamic simulation alone because it allows joints to be either motion-controlled or force-controlled. It is general to all robotic systems with tree structures, and fully motion-controlled or force-controlled kinematic loops. It should work best for machines with appendages that are motion-controlled, such as those encountered in underwater and space manipulation.

XAnimate: an educational tool for robot graphical simulation

XAnimate has been developed at The Ohio State University to provide portable graphical simulation capabilities at no cost. XAnimates graphical user interface, C library of functions, and a set of predefined objects enable users to easily display animated wireframe images or solid color objects for robotics systems of any topological structure. The use of X Windows and C allows the package to be ported to almost any Unix system.

Teaching future verification engineers: the forgotten side of logic design

This paper describes a senior/graduate level course in hardware logic verification being offered by The Ohio State University in cooperation with IBM. The need for the course is established through the growing importance of logic verification to users of custom logic designs. We discuss the short-term and long-term goals for the course, and describe the course content and format. The course relies heavily on lab projects to illustrate the main concepts. Three projects and a final project review are described.