On the one hand, impulsive torque at the beginning and end of the motion and ballistic motion between these two instants give energetically optimal motion for a pendulum. On the other hand many authors suppose that in human walk, muscle activities alternate with some periods of relaxation. From these two arguments, we assume that a motion defined by ballistic motion and impulsive control at double support instant will lead to an energetically economical trajectory.Optimal configurations are defined. Then smooth changes on the reference trajectory are proposed to obtain a trajectory which can be followed with finite torques. The physical constraints on the reaction forces to avoid take off or sliding of the robot, and saturation on the torques produced by the actuators are explicitly taken into account.

This paper investigates ballistic motions in walking quadrupeds on a horizontal plane. The study is carried out on a quadruped consisting of a body and four identical two-link legs. Each leg has a knee joint and is connected to the body by a haunch joint. Three types of quadruped gaits, bound, amble, and trot, are studied. None of these gaits complies with a flight phase, but they all involve simultaneous and identical motion of two legs. Muscle activities are commonly believed to alternate with periods of relaxation. Our study, therefore, assumes that the swing phase is ballistic, i.e., no active control torque is exerted. Ballistic motion is achieved through appropriate initial velocities. These velocities result from impulsive active control torques and ground reactions exerted at the boundary instants of the single support phase. Natural ballistic motions are shown to exist for the three gaits and for each valid walking velocity class. Torque cost analysis shows that amble and trot gaits are more efficient than bound.

The goal of this paper is to define a control law and reference trajectories for a legged robot with feet.We use a computed torque control law associated with a desired motion of the legged robot derived from a ballistic trajectory. This approach leads to the same distribution of the torques as it can be observed for humans, and respects the assumption that muscle activities alternate with some periods of relaxation. Simulations are made on a simple model of quadruped for a dynamically stable planar gait .

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This paper is concerned with learning the canonical gray scale structure of the images of a class of objects. Structure is defined in terms of the geometry and layout of salient image regions that characterize the given views of the objects. The use of such structure based learning of object appearence is motivated by the relative stability of image structure over intensity values. A multiscale segmentation tree description is antomatically extracted for all sample images which are then matched to construct a single canonical representative which serves as the model 0fthe class. Different images are selected as prototypes, and each prototype tree is refined to best match the rest of the class. The model tree for the class is that tree which is best supported over all the initializations with different prototypes.Matching is formulated as a problem of finding the best mapping from regions of example images to those of the model tree, and implemented as a problem in incremental refinement of the model tree using a learning approach. Experiments are reported on a face image database. The results demonstrate that a reasonable model of facial geometry and topology is learnt which includes prominent facial features.