In this paper authors Raibery and Hodgins present a method to animate dynamic legged locomotion. The method is based on the use of control algorithms which transform expressions of desired behavior into actuator control signals to produce motion. The legged systems were all modeled as linked sets of rigid bodies with compliant actuators (an actuated system is one which can power and regulate its own motion - an example is a human being) at the joints (i.e., where the rigid bodies are linked). The models were actually modeled in a tree fashion such that each rigid body was connected to its parent rigid body via some type of joint (e.g., sliding or rotary). The joint were basically modeled as a physical spring and damper systems so we can imagine that one joint may be modeled like a pendulum and another might be modeled like a mass hanging from a spring. By modeling the joints in this fashion, the authors were able to take advantage of the physical properties of the models (e.g., how stiff is the spring, what is the friction inherent in the spring (damping), the potential energy in the compressed spring, the kinetic energy due to the motion of the mass (body)).
The main issues presented by the authors in terms of control were (1) hopping control, (2) speed control and (3) posture control. These are quite important in regards to producing a system that does not "blow up". That is it does "hop to infinity" or "fall", etc.
Some of the assumptions made were (1) the models and control algorithms contained some sort of symmetry, (2) parameters to the system are manually input and (3) the model is initially manually positioned.
The animation process is modeled quite simply. A user supplies input to the system. The control algorithms compute the forces and torques that are applied to the model, the model (consisting of equations of motion for rigid bodies) calculates it behavior and graphics are displayed. The period of the model calculating it behavior (based on the forces and torques from the control algorithms) occurs @ every 0.0004s and the control component calculates new forces and torques to apply to the model @ every few milliseconds.
The actual action is modeled as a finite state machine. The control algorithms sequentially go from one state to the next. The next state depends only on the previous state (Markovian) and transition into the next state has a probability of one (you cannot go to any other state). I would assume that a probability exists to stay in the current state, or to never reach the next state. I suppose this would be an example of the system "blowing up".
It would be interesting to actually see the system working to determine how realistic the locomotion is. Additionally, as stated in the paper, tweaking and/or adding additional constraints to the system could improve realism.
This paper describes physics-based locomotion of computer-generated models and compares the results with physical analogs. At the root of the locomotion are the control mechanisms that control the joints of a system of rigid bodies. Gravity and contact with the ground are the only outside forces accounted for in the simulation. The most interesting physical model is that of the Kangaroo. The authors captured the dynamic of Kangaroo movement and described it in terms of several controls: hopping, speed and posture. The controls are all guided by the equations of motion and are numerically integrated over time. The results are very realistic when compared with experimental data. It turns out that although the results are realistic, the motion may not necessarily look natural. The authors talk about serveral factors like energy efficiency, smoothness and compliance that, if calculated more carefully, might yield a better looking simulation.
Automated Learning of Muscle-Actuated Locomotion Through Control Abstraction Grzeszczuk and Terzopoulos
This is a fascinating paper about physically based models learning to locomote in an optimal way. The models are all highly-elastic models like fish and snakes. The models have "brains" which, through feedback, know their actions and can modify them. The models are mostly made up of springs (muscles) with low-level actuators based on the Lagrangian equation of motion. There is an "Objective Functional" that measures progress of the low-level control. Low-level controllers can be grouped into higher-level controller which can help the models to very impressive "tricks." The paper is impressive and I would be interested in seeing the concepts extended to include interaction among models and maybe competition or cooperation.
While the readings for last week dealt with physically realistic animation of solid deformable objects, those for this week are concerned with the animation of actuated systems, as for example in legged creatures, either bipeds or quadrupeds. Actuated systems are those that use muscles, motors or some other kind of actuator to convert stored energy into time-varying forces that act within the system's mechanical structure. These actuated systems are distinct from passive physical objects in one important respect: they can power and regulate their own motions. Researchers have been very interested in developing control systems for such systems because as new technology has made it increasingly easy to generate complex and realistic models of animals, such as humans, snakes, fish, etc., it is also becoming increasingly difficult to manually control the large numbers of parameters in these models. Hence the need for control systems for such models.
In this paper, Raibert and Hodgins present a control system that generates computer animations of a biped robot, a quadruped robot and a planar kangaroo with one arm, one leg and a tail. The algorithm was able to simulate motion of these models at various gaits, like running, hopping, trotting and galloping. However, a big disadvantage of this technique is that the parameters of the control system had to be "tweaked" for different models and, more importantly, for different gaits of the same model. This is highly undesirable. The authors also report that the simulations of a single creature ran between 7 to 10 times slower than real time on a SUN Sparc2. On the other hand, one very nice thing implemented in this system was dynamic scaling, which allowed the user to scale the size of the model.
This paper overcomes the main problem in the approach of Raibert and Hodgins by intro ducing a learning component in the animal models used. The control system proposed was mainly intended for models of animals with highly flexible bodies with many degrees of freedom and a considerable number of internal muscle actuators, such as snakes and fish. The authors formalize the problem of learning realistic locomotion as one of optimizing a class of objective functions, for which there are various solution techniques, a number of them using neural network methods like genetic algorithms. Because of this kind of learning, the kinds of locomotion that the models may learn to perform are potentially infinite and can be controlled directly by the objective functions. This is obviously very useful.
Considerable effort is currently underway in a few labs at MIT, among other places, to develop a variety of artificial muscle actuator technologies for use in devices such as anthropomorphic robots, micro-robots, micro-surgical robots, prosthetic devices. Nature has developed over several million of years muscle as an actuator. From the elephants to the mice, dinosaurs, fish all use the same basic actuator element: the muscle cell. When we compare nature's actuators to electric, pneumatic, hydraulic or combustion engine, we find these latter all fail in one respect or another to perform as well as muscle would it be because of the force per unit area, efficiency or speed. With the advent of such new technology, each "muscle" in the model would contain a prohibitively large number of degrees of freedom, making manual control of the parameters very difficult. It is likely that the algorithm proposed by Grzeszczuk and Terzopoulos will be very useful for such models.
Stan Sclaroff
Created: Jan 21, 1997
Last Modified: Feb 19, 1997