Controlling a walking biped robot is a challenging problem due to the robot's complex and uncertain dynamics. In order to tackle this problem, we propose a sliding mode controller based on a dynamic model that we obtained using the conformal geometric algebra (CGA) approach. An important contribution of this paper is the development of algorithms using the CGA framework. The CGA framework permits us to use lines, points, and other geometric entities to obtain the Lagrange equations of the system. The references for the joints of the robot were obtained in a bio-inspired way following the kinematics of a walking human body. The first and second derivatives of the reference signal were obtained via an exact robust differentiator based on a high-order sliding mode. We analyzed the performance of the proposed control schemes by using bio-inspired walking patterns and simulations.

The automatic landmark identification is very important in autonomous robotnavigation tasks. In this paper, we use a monocular omnidirectional visionsystem to extract the image features and the conformal geometric algebra tocompute the projective invariants from such features. We show how these featurescan be used to compute projective and permutationp2-invariants from any kind ofomnidirectional vision system. Thep2-invariants represent scenesublandmarks, and a set of them characterize a landmark. The advantage of thisrepresentation is that the landmarks are more robust than the singlecross-ratio.

The research, described in this paper, concerns the robot indoor navigation, emphasizing the aspects of sensor model and calibration, environment representation, and self-localization. The main point is that combining all of these aspects, an effective navigation system is obtained. We present a model of the catadioptric image formation process. Our model simplifies the operations needed in the catadioptric image process. Once we know the model of the catadioptric sensor, we have to calibrate it with respect to the other sensors of the robot, in order to be able to fuse their information. When the sensors are mounted on a robot arm, we can use the hand-eye calibration algorithm to calibrate them. In our case the sensors are mounted on a mobile robot that moves over a flat floor, thus the sensors have less degrees of freedom. For this reason we develop a calibration algorithm for sensors mounted on a mobile robot. Finally, combining all the previous results and a scan matching algorithm that we develop, we build 3D maps of the environment. These maps are used for the self-localization of the robot and to carry out path following tasks. In this work we present experiments which show the effectiveness of the proposed algorithms.