Nonlinear Model Predictive Control for Constrained Output Path Following

We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following problems. Specifically, we propose a predictive control approach to constrained path-following problems with and without velocity assignments and provide sufficient convergence conditions based on terminal regions and end penalties. Furthermore, we analyze the geometric nature of constrained output path-following problems and thereby provide insight into the computation of suitable terminal control laws and terminal regions. We draw upon an example from robotics to illustrate our findings.Comment: 12 pages, 4 figure

Implementation of Nonlinear Model Predictive Path-Following Control for an Industrial Robot

Many robotic applications, such as milling, gluing, or high precision measurements, require the exact following of a pre-defined geometric path. In this paper, we investigate the real-time feasible implementation of model predictive path-following control for an industrial robot. We consider constrained output path following with and without reference speed assignment. We present results from an implementation of the proposed model predictive path-following controller on a KUKA LWR IV robot.Comment: 8 pages, 3 figures; final revised versio

Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes

This review article provides a pedagogical introduction into various classes of chiral string compactifications to four dimensions with D-branes and fluxes. The main concern is to provide all necessary technical tools to explicitly construct four-dimensional orientifold vacua, with the final aim to come as close as possible to the supersymmetric Standard Model. Furthermore, we outline the available methods to derive the resulting four-dimensional effective action. Finally, we summarize recent attempts to address the string vacuum problem via the statistical approach to D-brane models.Comment: 331 pages, 7 figures, review prepared for Physics Reports, please send constructive comments to: [email protected], v2: refs added, v3: final version to appear in Phys. Rep

Inverse-Dynamics MPC via Nullspace Resolution

Optimal control (OC) using inverse dynamics provides numerical benefits such as coarse optimization, cheaper computation of derivatives, and a high convergence rate. However, in order to take advantage of these benefits in model predictive control (MPC) for legged robots, it is crucial to handle its large number of equality constraints efficiently. To accomplish this, we first (i) propose a novel approach to handle equality constraints based on nullspace parametrization. Our approach balances optimality, and both dynamics and equality-constraint feasibility appropriately, which increases the basin of attraction to good local minima. To do so, we then (ii) adapt our feasibility-driven search by incorporating a merit function. Furthermore, we introduce (iii) a condensed formulation of the inverse dynamics that considers arbitrary actuator models. We also develop (iv) a novel MPC based on inverse dynamics within a perception locomotion framework. Finally, we present (v) a theoretical comparison of optimal control with the forward and inverse dynamics, and evaluate both numerically. Our approach enables the first application of inverse-dynamics MPC on hardware, resulting in state-of-the-art dynamic climbing on the ANYmal robot. We benchmark it over a wide range of robotics problems and generate agile and complex maneuvers. We show the computational reduction of our nullspace resolution and condensed formulation (up to 47.3%). We provide evidence of the benefits of our approach by solving coarse optimization problems with a high convergence rate (up to 10 Hz of discretization). Our algorithm is publicly available inside CROCODDYL.Comment: 17 pages, 14 figures, under-revie

Flux-induced SUSY-breaking soft terms on D7-D3 brane systems

We study the effect of RR and NSNS 3-form fluxes on the effective action of the worldvolume fields of Type IIB D7/D3-brane configurations. The D7-branes wrap 4-cycles on a local Calabi-Yau geometry. This is an extension of previous work on hep-th/0311241, where a similar analysis was applied to the case of D3-branes. Our present analysis is based on the D7- and D3-brane Dirac-Born-Infeld and Chern-Simons actions, and makes full use of the R-symmetries of the system, which allow us to compute explicitly results for the fields lying at the D3-D7 intersections. A number of interesting new properties appear as compared to the simpler case of configurations with only D3-branes. As a general result one finds that fluxes stabilize some or all of the D7-brane moduli. We argue that this is important for the problem of stabilizing Kahler moduli through non-perturbative effects in KKLT-like vacua. We also show that (0,3) imaginary self-dual fluxes, which lead to compactifications with zero vacuum energy, give rise to SUSY-breaking soft terms including gaugino and scalar masses, and trilinear terms. Particular examples of chiral MSSM-like models of this class of vacua, based on D3-D7 brane systems at orbifold singularities are presented.Comment: 58 pages, no figures; v2: numerical factor in section 7.2 correcte

LeggedWalking on Inclined Surfaces

The main contribution of this MS Thesis is centered around taking steps towards successful multi-modal demonstrations using Northeastern's legged-aerial robot, Husky Carbon. This work discusses the challenges involved in achieving multi-modal locomotion such as trotting-hovering and thruster-assisted incline walking and reports progress made towards overcoming these challenges. Animals like birds use a combination of legged and aerial mobility, as seen in Chukars' wing-assisted incline running (WAIR), to achieve multi-modal locomotion. Chukars use forces generated by their flapping wings to manipulate ground contact forces and traverse steep slopes and overhangs. Husky's design takes inspiration from birds such as Chukars. This MS thesis presentation outlines the mechanical and electrical details of Husky's legged and aerial units. The thesis presents simulated incline walking using a high-fidelity model of the Husky Carbon over steep slopes of up to 45 degrees.Comment: Masters thesi

Neuromuscular Control Strategy during Object Transport while Walking: Adaptive Integration of Upper and Lower Limb Movements

When carrying an object while walking, a significant challenge for the central nervous system (CNS) is to preserve the object’s stability against the inter-segmental interaction torques and ground reaction forces. Studies documented several strategies used by the CNS: modulation of grip force (GF), alterations in upper limb kinematics, and gait adaptations. However, the question of how the CNS organizes the multi-segmental joint and muscle coordination patterns to deal with gait-induced perturbations remains poorly understood. This dissertation aimed to explore the neuromuscular control strategy utilized by the CNS to transport an object during walking successfully. Study 1 examined the inter-limb coordination patterns of the upper limbs when carrying a cylinder-shaped object while walking on a treadmill. It was predicted that transporting an object in one hand would affect the movement pattern of the contralateral arm to maintain the overall angular momentum. The results showed that transporting an object caused a decreased anti-phase coordination, but it did not induce significant kinematic and muscle activation changes in the unconstrained arm. Study 2 examined muscle synergy patterns for upper limb damping behavior by using non-negative matrix factorization (NNMF) method. Four synergies were identified, showing a proximal-to-distal pattern of activation preceding heel contacts. Study 3 examined the effect of different precision demands (carrying a cup with or without a ball) and altered visual information (looking forward vs. looking at an object) on the upper limb damping behavior and muscle synergies. Increasing precision demand induced stronger damping behavior and increased the electromyography (EMG) activation of wrist/hand flexors and extensors. The NNMF results replicated Study 2 in that the stabilization of proximal joints occurred before the distal joints. The results indicated that the damping incorporates tonic and phasic muscle activation to ensure object stabilization. Overall, three experiments showed that the CNS adopts a similar synergy pattern regardless of task constraint or altered gaze direction while modulating the amount of muscle activation for object stabilization. Kinematic changes can differ depending on the different levels of constraint, as shown in the smaller movement amplitude of the shoulder joint in the transverse plane during the task with higher precision demand