The integration of Unmanned Aircraft Systems (UAS) into civil, nonsegregated airspace remains an open problem for which many distinct proposals have been made. One of the fundamental ingredients for a viable system is the facilitation of the communication of an aircraft’s trajectory among the airspace stakeholders so as to introduce a necessary degree of predictability into the system. This is essential for the coordination of aircraft in a densely populated airspace and, in particular, to be prepared for potential time-critical contingencies. The Aircraft Intent Description Language (AIDL) has been proposed in the past to efficiently represent an aircraft’s trajectory. It consists of describing the aircraft’s flight intent into several parallel sequences of instructions, which are intuitive and easily interpretable, and can be translated into a high resolution flight trajectory which takes into account the aircraft performance model and environmental conditions. The benefits of this representation is that its information content is minimal suitable for reduced bandwidth communications, and it is independent of the aircraft’s performance model and environmental conditions, both of which may vary over time, or for which certain stakeholders may later dispose of improved information. Nevertheless, a potential hindrance in the implementation of this trajectory representation consists in the trajectory reconstruction process. A system of differential-algebraic equations (DAE) of possibly high index must be solved. Numerical tools to date have required the consideration of numerous special use cases such as to condition the numerical solution problem accordingly. This paper presents a generic approach by which this trajectory reconstruction process is performed making use of the object-oriented modeling language Modelica and associated tools. Efficient embeddable code can Michael Hardt Boeing Research & Technology Europe, Avenida Sur del Aeropuerto de Barajas 38, Floor 4, Madrid, Spain, e-mail: michael.w.hardt@boeing.com Robert Höpler Campus Burghausen, Technische Hochschule Rosenheim, Marktler Strasse 50, 84489 Burghausen, Germany e-mail: robert.hoepler@th-rosenheim.de

The validation campaign results are presented for the European International Berthing and Docking Mechanism (IBDM) intended for space vehicle docking. The validation was performed using the first prototype of this mechanism together with a KUKA robot manipulator carrying as payload the passive IBDM counterpart. The docking of the ATV with the ISS was very closely emulated as was demonstrated by the high correlation of representative contact forces measured during the tests and those contact forces predicted by high fidelity simulations. Furthermore, the IBDM control was also successfully validated in its capability to align itself with the passive counterpart while experiencing large relative kinematic initial configuration errors near its capture envelope and representative approach velocities. 1. IBDM REQUIREMENTS & DESIGN The International Berthing and Docking Mechanism (IBDM) is a c ontact force sensing, magnetically latched for capture, low impact docking system, capable of docking and berthing large and small vehicles. Mechanically, it is an actively controlled 6DOF parallel manipulator powered by six linear actuators. Functionally, the IBDM consists of two systems, the soft docking system and the hard docking system. The soft docking system captures and actively damps the two spacecraft. The hard docking system makes the structural pressurized connection between the two spacecraft and is responsible for the service connections and the nominal and emergency separation functions. The IBDM was initiated as a j oint development programme by ESA and NASA JSC, with the purpose of enabling the berthing/docking and attachment of the CRV to the ISS. Since the cancellation of the CRV program, ESA has progressed on the IBDM alone developing a prototype mechanism and accompanying avionics with SENER Ingeniería y Sistemas S.A. and Verhaert Space. The validation of this first prototype is consequently presented here. The IBDM is conceived to have the capability to perform docking for a wide range of vehicles as well as being more robust with respect to the relative docking kinematic alignment errors than if it were purely passive. The active IBDM system drives the actuators to move the guiding ring in order to align the active IBDM and passive IBDM systems. The 21 ton ATV has been selected as the baseline docking vehicle together with the 400t ISS. For this purpose, the linear electro-mechanical actuators designed by SENER supporting the top ring must deliver linear forces up to 650N in order to achieve the necessary contact forces required to dampen and halt the opposing docking vehicle, while achieving linear velocities of 170mm/s to match the maximum potential relative approach velocity. Equally important is the long available stroke length of 290mm for each actuator granting the mechanism the available workspace to manoeuvre sufficiently given the maximum kinematic configuration errors between the docking vehicles. The permitted kinematic configuration errors which define the capture envelope of the mechanism are listed in Table 1 below. Note that the Z-axis is aligned with the principal direction of docking. The variables Vx, Vy, Vz are the time derivatives of the X, Y, Z position of the passive IBDM docking platform. Table 1. Docking misalignment and velocity tolerances. minimum maximum units

The complete development process for achieving walking motion with a recently constructed humanoid robot is discussed. The desired motion is based on the solution of an optimal control problem whose constraints depend upon the high-dimensional nonlinear multibody system dynamics of a 17 DoF humanoid and physical contact constraints with the environment. On-line control strategies are developed for tracking the precalculated trajectories. Experimental walking results with the humanoid robot are presented.

Numerical simulation and optimization of gaits for quadruped robots based on nonlinear multi-body dynamics models of legged locomotion have made progress recently. A fully three-dimensional dynamical model of Sony's four-legged robot is used to state an optimal control problem for a symmetric, dynamically stable gait. The optimal control problem is solved by a sparse direct collocation method. Numerical problems related to the high-index differential algebraic equations of motion are avoided by substituting the differential algebraic equations by an equivalent set of reduced dynamics ordinary differential equations. Numerical and experimental results validate the model and the methods used for gait generation.

Fundamental principles and recent methods for investigating the nonlinear dynamics of legged robot motions with respect to control, stability, and design are discussed. One of them is the still challenging problem of producing dynamically stable gaits. The generation of fast walking or running motions requires methods and algorithms adept at handling the nonlinear dynamical effects and stability issues which arise. Reduced, recursive multibody algorithms, a numerical optimal control method, and new stability and energy performance indices are presented which are well-suited for this purpose. Difficulties and open problems are discussed along with numerical investigations into the proposed gait generation scheme. Our analysis considers both bipedal and quadrupedal gaits. (C) 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Multibody systems such as legged robots require sophisticated and efficient methods for their modeling, control and simulation. This paper discusses the development of a software library based on modern tools such as C++, OpenGL and XML for highly efficient dynamics modeling. A primary focus lies on modularity permitting its easy extensibility in connection with different actuation and contact models, optimization algorithms, localized and centralized on‐line control schemes as well as animation and simulation environments.

Methods for modeling, simulation and optimization of the dynamics, stability, and performance of humanoid robots are presented in this paper. Optimal control trajectory following by joint-level control combined with an online compensation method using Jacobians is proposed. The kinematic design, dynamic properties, hard- and software architecture for an autonomous biped, and experimental results are presented.

Fundamental principles and recent methods for investigating the nonlinear dynamics of legged robot motions with respect to control, stability and design are discussed. One of them is the still challenging problem of producing dynamically stable gaits. The generation of fast walking or running motions require methods and algorithms adept at handling the nonlinear dynamical effects and stability issues which arise. Reduced, recursive multibody algorithms, a numerical optimal control package, and new stability and energy performance indices are presented which are well-suited for this purpose. Difficulties and open problems are discussed along with numerical investigations into the proposed gait generation scheme. Our analysis considers both biped and quadrupedal gaits with particular reference to the problems arising in soccer-playing tasks encountered at the RoboCup where our team, the Darmstadt Dribbling Dackels, participates as part of the German Team in the Sony Legged Robot League.

Methods for modeling, simulating and optimizing the dynamics, stability and performance of legged robot locomotion are discussed in this paper. It is demonstrated how these tools are used in the design, implementation and operation of a humanoid robot. The selection and integration of fundamental hard- and software needed for autonomous operation and high agility is presented for a recently developed fully-actuated 17 DoF humanoid. The results are additionally reported form simulations and gait optimizations completed during its development using a 3D dynamic biped model coupled with multiple physical and stability constraints.

Nonlinear hybrid dynamical systems are the main focus of this paper. A modeling framework is proposed, feedback control strategies and numerical solution methods for optimal control problems in this setting are introduced, and their implementation with various illustrative applications are presented. Hybrid dynamical systems are characterized by discrete event and continuous dynamics which have an interconnected structure and can thus represent an extremely wide range of systems of practical interest. Consequently, many modeling and control methods have surfaced for these problems. This work is particularly focused on systems for which the degree of discrete/continuous interconnection is comparatively strong and the continuous portion of the dynamics may be highly nonlinear and of high dimension. The hybrid optimal control problem is defined and two solution techniques for obtaining suboptimal solutions are presented (both based on numerical direct collocation for continuous dynamic optimization): one fixes interior point constraints on a grid, another uses branch-and-bound. These are applied to a robotic multi-arm transport task, an underactuated robot arm, and a benchmark motorized traveling salesman problem.

Optimal gait planning is applied in this work to the problem of improving stability in quadruped locomotion. In many settings, it is desired to operate legged machines at high performance levels where rapid velocities and a changing environment make stability of utmost concern. Since gait planning still remains a vital component of legged system control design, an efficient method of determining periodic paths is presented which optimize a dynamic stability criterion. Efficient recursive multibody algorithms are used with numerical optimal control software to solve the minimax performance stability criteria.

This paper discusses the design concept and system development of a small and relatively fast walking, autonomous humanoid robot with 17 degrees-of-freedom (DoF). The selection of motor size and gear ratios is based on numerical optimization of detailed multibody dynamics and optimal control corresponding to fast steps of the robot with an envisioned target speed of more than 0.5 m/s. In this paper the design considerations based on numerical optimal control studies and the mechanical realization of the robot are presented including first investigations on the achievable performance of a decentralized, microcontroller-based control architecture.

The design considerations for a small, relatively fast walking, autonomous humanoid robot are presented. The robot must be energy efficient but also produce sufficient torque to reach greater speeds. On the basis of previous investigations into gait optimization for multilegged systems, dynamical modeling and nonlinear optimization tools are used for design optimization and choosing the motor size and gear ratios. Gait trajectories for relatively fast steps and different prototypes were calculated. The design decisions are described for the humanoid robot with 6 degrees-of-freedom (DoF) in each leg and 2 DoF in each arm based on numerical results and preliminary investigations with a 4 DoF test robot.

Numerical solution techniques for a class of hybrid (discrete event / continuous variable) optimal control problems (HOCP) are described, and their potential use in robotic applications is demonstrated. HOCPs are inherently combinatorial due to their discrete event aspect which is one of the main challenges when numerically solving for optimal hybrid trajectories. One may associate a continuous nonlinear multi-phase problem with each possible discrete state sequence. Two solution techniques for obtaining suboptimal solutions are presented (both based on numerical direct collocation): one fixes interior point constraints on a grid, another uses branch-and-bound. Numerical results of a robotic multi-arm transport task and an underactuated robot are presented.

We consider the problem of finding optimal gaits for a quadruped robot. Paths are sought which minimize the actuation energy required for walking in an attempt to approximate natural motion. The number of possible gaits for a quadruped is quite large when one considers varied orders of leg motion, different liftoff times, and various ground contact combinations for the legs. The problem is treated as a fully nonlinear optimal hybrid path planning problem on a 22-dimensional state space. Modeling aspects, our numerical approach, and experimental results are discussed in this paper.