Optimal Control of Legged-Robots Subject to Friction Cone Constraints

A hierarchical control architecture is presented for energy-efficient control of legged robots subject to variety of linear/nonlinear inequality constraints such as Coulomb friction cones, switching unilateral contacts, actuator saturation limits, and yet minimizing the power losses in the joint actuators. The control formulation can incorporate the nonlinear friction cone constraints into the control without recourse to the common linear approximation of the constraints or introduction of slack variables. A performance metric is introduced that allows trading-off the multiple constraints when otherwise finding an optimal solution is not feasible. Moreover, the projection-based controller does not require the minimal-order dynamics model and hence allows switching contacts that is particularly appealing for legged robots. The fundamental properties of constrained inertia matrix derived are similar to those of general inertia matrix of the system and subsequently these properties are greatly exploited for control design purposes. The problem of task space control with minimum (point-wise) power dissipation subject to all physical constraints is transcribed into a quadratically constrained quadratic programming (QCQP) that can be solved by barrier methods

Robust Grasp with Compliant Multi-Fingered Hand

As robots find more and more applications in unstructured environments, the need for grippers able to grasp and manipulate a large variety of objects has brought consistent attention to the use of multi-fingered hands. The hardware development and the control of these devices have become one of the most active research subjects in the field of grasping and dexterous manipulation. Despite a large number of publications on grasp planning, grasping frameworks that strongly depend on information collected by touching the object are getting attention only in recent years. The objective of this thesis focuses on the development of a controller for a robotic system composed of a 7-dof collaborative arm + a 16-dof torque-controlled multi-fingered hand to successfully and robustly grasp various objects. The robustness of the grasp is increased through active interaction between the object and the arm/hand robotic system. Algorithms that rely on the kinematic model of the arm/hand system and its compliance characteristics are proposed and tested on real grasping applications. The obtained results underline the importance of taking advantage of information from hand-object contacts, which is necessary to achieve human-like abilities in grasping tasks

Full-Body Torque-Level Non-linear Model Predictive Control for Aerial Manipulation

Non-linear model predictive control (nMPC) is a powerful approach to control complex robots (such as humanoids, quadrupeds, or unmanned aerial manipulators (UAMs)) as it brings important advantages over other existing techniques. The full-body dynamics, along with the prediction capability of the optimal control problem (OCP) solved at the core of the controller, allows to actuate the robot in line with its dynamics. This fact enhances the robot capabilities and allows, e.g., to perform intricate maneuvers at high dynamics while optimizing the amount of energy used. Despite the many similarities between humanoids or quadrupeds and UAMs, full-body torque-level nMPC has rarely been applied to UAMs. This paper provides a thorough description of how to use such techniques in the field of aerial manipulation. We give a detailed explanation of the different parts involved in the OCP, from the UAM dynamical model to the residuals in the cost function. We develop and compare three different nMPC controllers: Weighted MPC, Rail MPC, and Carrot MPC, which differ on the structure of their OCPs and on how these are updated at every time step. To validate the proposed framework, we present a wide variety of simulated case studies. First, we evaluate the trajectory generation problem, i.e., optimal control problems solved offline, involving different kinds of motions (e.g., aggressive maneuvers or contact locomotion) for different types of UAMs. Then, we assess the performance of the three nMPC controllers, i.e., closed-loop controllers solved online, through a variety of realistic simulations. For the benefit of the community, we have made available the source code related to this work.Comment: Submitted to Transactions on Robotics. 17 pages, 16 figure

Trajectory planning of single and dual-arm robots for time-optimal handling of liquids and objects

This Thesis studies the optimal control problem of single-arm and dual-arm serial robots to achieve the time-optimal handling of liquids and objects. The first topic deals with the planning of time-optimal anti-sloshing trajectories of an industrial robot carrying a cylindrical container filled with a liquid, considering 1-dimensional and 2-dimensional planar motions. A technique for the estimation of the sloshing height is presented, together with its extension to 3-dimensional motions. An experimental validation campaign is provided and discussed to assess the thoroughness of such a technique. As far as anti-sloshing trajectories are concerned, 2-dimensional paths are considered and, for each one of them, three constrained optimizations with different values of the sloshing-height thresholds are solved. Experimental results are presented to compare optimized and non-optimized motions. The second part focuses on the time-optimal trajectory planning for dual-arm object handling, employing two collaborative robots (cobots) and adopting an admittance-control strategy. The chosen manipulation approach, known as cooperative grasping, is based on unilateral contact between the cobots and the object, and it may lead to slipping during motion if an internal prestress along the contact-normal direction is not prescribed. Thus, a virtual penetration is considered, aimed at generating the necessary internal prestress. The stability of cooperative grasping is ensured as long as the exerted forces on the object remain inside the static-friction cone. Constrained-optimization problems are solved for 3-dimensional paths: the virtual penetration is chosen among the control inputs of the problem and friction-cone conditions are treated as inequality constraints. Also in this case experiments are presented in order to prove evidence of the firm handling of the object, even for fast motions

Massive Black Holes in Galaxies

After summarizing the current status of black hole related research, I investigate the angular momentum driven flux of stars onto supermassive black hole (SMBH) loss cone orbits by means of direct NBODY6 computations. By performing a large parameter study with different SMBH capture radii and particle numbers ranging from N=1e3 to N=0.5e6, the influence of dynamical effects on the tidal disruption rate of stars is explored. These dynamical effects are the Brownian motion of the SMBH, cusp formation and dynamical heating. Afterwards, the tidal disruption rate is computed by scaling these numerically obtained results to astrophysical galaxies hosting central massive black holes. I found that angular momentum driven diffusion is insufficient to influence the growth of SMBHs which are more massive than 1e6 M_sun. However, the expected rate can be used to unveil black holes in the intermediate black hole mass regime (1e3-1e5 M_sun) owing to a tidal disruption rate which only weakly depends on the black hole mass. In this PhD thesis I also present a new versatile software code (MUESLI) designed for the purpose of computing the evolution of globular cluster systems (GCSs) around elliptical galaxies. MUESLI is based on the self-consistent field method in combination with the time-transformed Leapfrog scheme and applies various internal (e.g. relaxation) and external physical dissolution processes (e.g. triaxial dynamical friction) on each globular cluster. It is found that erosion can explain the absence of globular clusters around the compact elliptical galaxy M32. Furthermore, erosion can explain the transition of a single power law into bell-shaped cluster mass function as well as the observed cores in the number density profiles of globular cluster systems. MUESLI-based computations indicate that the observed core size should depend on the imposed cluster threshold mass/luminosity as long as erosion is the primary process. In principle this allows to discriminate (observationally) between different GCS formation theories. I also found evidence for a new phase in the dynamical evolution of entire globular cluster systems where tidal shocking dominates over other dissolution mechanisms. For this reason I named this phase the tidal disruption dominated phase (TDDP). The TDDP is followed by a less violent relaxation driven mass loss phase. Finally, the implementation of a relativistic black hole into MUESLI is documented and tested. This feature allows to study the growth of SMBHs from cluster debris or stars on centrophilic orbits

Nature’s Optics and Our Understanding of Light

Optical phenomena visible to everyone abundantly illustrate important ideas in science and mathematics. The phenomena considered include rainbows, sparkling reflections on water, green flashes, earthlight on the moon, glories, daylight, crystals, and the squint moon. The concepts include refraction, wave interference, numerical experiments, asymptotics, Regge poles, polarisation singularities, conical intersections, and visual illusions

Modeling of ground excavation with the particle finite element method

The present work introduces a new application of the Particle Finite Element Method (PFEM) for the modeling of excavation problems. PFEM is presented as a very suitable tool for the treatment of excavation problem. The method gives solution for the analysis of all processes that derive from it. The method has a high versatility and a reasonable computational cost. The obtained results are really promising.Postprint (published version