Robust Tracking of Bio-Inspired References for a Biped Robot Using Geometric Algebra and Sliding Modes

Controlling walking biped robots is a challenging problem due to its complex and uncertain dynamics. In order to tackle this, we propose a sliding mode controller based on a dynamic model which was obtained using the conformal geometric algebra approach (CGA). 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 bio-inspired in the kinematics of a walking human body. The first and second derivatives of the reference signal were obtained through an exact robust differentiator based on high order sliding modes. The performance of the proposed control scheme is illustrated through simulation.CINVESTA

Visual Servoing and Robust Object Manipulation Using Symmetries and Conformal Geometric Algebra

Object tracking and manipulation is an important process for many applications in robotics and computer vision. A novel 3D pose estimation of objects using reflectionally symmetry formulated in Conformal Geometric Algebra (CGA) is proposed in this work. The synthesis of the kinematics model for robots and a sliding mode controller using the CGA approach is described. Real time implementation results are presented for the pose estimation of object using a stereo vision system.ITESO, A.C.CINVESTA

Adaptive land classification and new class generation by unsupervised double-stage learning in Poincare sphere space for polarimetric synthetic aperture radars

Polarimetric satellite-borne synthetic aperture radar (PolSAR) is expected to provide land usage information globally and precisely. In this paper, we propose a unsupervised double-stage learning land state classification system using a self-organizing map (SOM) that utilizes ensemble variation vectors. We find that the Poincare sphere parameters representing the polarization state of scattered wave have specific features of the land state, in particular, in their ensemble variation rather than spatial variation. Experiments demonstrate that the proposed PolSAR double-stage SOM system generate new classes appropriately, resulting in successful fine land classification and/or appropriate new class generation

Contributions to automated realtime underwater navigation

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2012This dissertation presents three separate–but related–contributions to the art of underwater navigation. These methods may be used in postprocessing with a human in the loop, but the overarching goal is to enhance vehicle autonomy, so the emphasis is on automated approaches that can be used in realtime. The three research threads are: i) in situ navigation sensor alignment, ii) dead reckoning through the water column, and iii) model-driven delayed measurement fusion. Contributions to each of these areas have been demonstrated in simulation, with laboratory data, or in the field–some have been demonstrated in all three arenas. The solution to the in situ navigation sensor alignment problem is an asymptotically stable adaptive identifier formulated using rotors in Geometric Algebra. This identifier is applied to precisely estimate the unknown alignment between a gyrocompass and Doppler velocity log, with the goal of improving realtime dead reckoning navigation. Laboratory and field results show the identifier performs comparably to previously reported methods using rotation matrices, providing an alignment estimate that reduces the position residuals between dead reckoning and an external acoustic positioning system. The Geometric Algebra formulation also encourages a straightforward interpretation of the identifier as a proportional feedback regulator on the observable output error. Future applications of the identifier may include alignment between inertial, visual, and acoustic sensors. The ability to link the Global Positioning System at the surface to precision dead reckoning near the seafloor might enable new kinds of missions for autonomous underwater vehicles. This research introduces a method for dead reckoning through the water column using water current profile data collected by an onboard acoustic Doppler current profiler. Overlapping relative current profiles provide information to simultaneously estimate the vehicle velocity and local ocean current–the vehicle velocity is then integrated to estimate position. The method is applied to field data using online bin average, weighted least squares, and recursive least squares implementations. This demonstrates an autonomous navigation link between the surface and the seafloor without any dependence on a ship or external acoustic tracking systems. Finally, in many state estimation applications, delayed measurements present an interesting challenge. Underwater navigation is a particularly compelling case because of the relatively long delays inherent in all available position measurements. This research develops a flexible, model-driven approach to delayed measurement fusion in realtime Kalman filters. Using a priori estimates of delayed measurements as augmented states minimizes the computational cost of the delay treatment. Managing the augmented states with time-varying conditional process and measurement models ensures the approach works within the proven Kalman filter framework–without altering the filter structure or requiring any ad-hoc adjustments. The end result is a mathematically principled treatment of the delay that leads to more consistent estimates with lower error and uncertainty. Field results from dead reckoning aided by acoustic positioning systems demonstrate the applicability of this approach to real-world problems in underwater navigation.I have been financially supported by: the National Defense Science and Engineering Graduate (NDSEG) Fellowship administered by the American Society for Engineering Education, the Edwin A. Link Foundation Ocean Engineering and Instrumentation Fellowship, and WHOI Academic Programs office

Articulating Space: Geometric Algebra for Parametric Design -- Symmetry, Kinematics, and Curvature

To advance the use of geometric algebra in practice, we develop computational methods for parameterizing spatial structures with the conformal model. Three discrete parameterizations – symmetric, kinematic, and curvilinear – are employed to generate space groups, linkage mechanisms, and rationalized surfaces. In the process we illustrate techniques that directly benefit from the underlying mathematics, and demonstrate how they might be applied to various scenarios. Each technique engages the versor – as opposed to matrix – representation of transformations, which allows for structure-preserving operations on geometric primitives. This covariant methodology facilitates constructive design through geometric reasoning: incidence and movement are expressed in terms of spatial variables such as lines, circles and spheres. In addition to providing a toolset for generating forms and transformations in computer graphics, the resulting expressions could be used in the design and fabrication of machine parts, tensegrity systems, robot manipulators, deployable structures, and freeform architectures. Building upon existing algorithms, these methods participate in the advancement of geometric thinking, developing an intuitive spatial articulation that can be creatively applied across disciplines, ranging from time-based media to mechanical and structural engineering, or reformulated in higher dimensions