Preliminary results of a new computational approach to generate aggressive trajectories in real-time for constrained mechanical systems are presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that real-time trajectory generation for constrained mechanical systems is possible by mapping the problem to one of finding trajectory curves in a lower dimensional space. Performance of the algorithm is compared with existing optimal trajectory generation techniques. Numerical results are reported using the NTG software package. Keywords: Real-time optimization, nonlinear control design, optimal control, constrained trajectory generation, guidance. 1

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this paper show the success of this choice for V for stabilization. An inner-loop PD controller on #, # is implemented to stabilize to the receding horizon states # # T , # # T . The # dynamics are the fastest for this system and although most receding horizon controllers were found to be nominally stable without this inner-loop controller, small disturbances could lead to instability

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We consider the control of interacting subsystems whose dynamics and constraints are uncoupled, but whose state vectors are coupled non-separably in a single centralized cost function of a finite horizon optimal control problem. For a given centralized cost structure, we generate distributed optimal control problems for each subsystem and establish that the distributed receding horizon implementation is asymptotically stabilizing. The communication requirements between subsystems with coupling in the cost function are that each subsystem obtain the previous optimal control trajectory of those subsystems at each receding horizon update. The key requirements for stability are that each distributed optimal control not deviate too far from the previous optimal control, and that the receding horizon updates happen su#ciently fast. The theory is applied in simulation for stabilization of a formation of vehicles.

We introduce a class of triangulated graphs for algebraic representation of formations that allows us to specify a mission cost for a group of vehicles. This representation plus the navigational information allows us to formally specify and solve tracking problems for groups of vehicles in formations using an optimizationbased approach. The approach is illustrated using a collection of six underactuated vehicles that track a desired trajectory in formation.

In this paper we propose extensions to trust-region algorithms in which the classical step is augmented with a second step that we insist yields a decrease in the value of the objective function. The classical convergence theory for trust-region algorithms is adapted to this class of two-step algorithms. The algorithms can be applied to any problem with variable(s) whose contribution to the objective function is a known functional form. In the nonlinear programming package LANCELOT, they have been applied to update slack variables and variables introduced to solve minimax problems, leading to enhanced optimization eciency. Extensive numerical results are presented to show the eectiveness of these techniques. Keywords. Trust regions, line searches, two-step algorithms, spacer steps, slack variables, LANCELOT, minimax problems, expensive function evaluations, circuit optimization. AMS subject classications. 49M37, 90C06, 90C30 1 Introduction In nonlinear optimization proble...

Model predictive control (MPC) is applied to the Caltech ducted fan, a thrust-vectored flight experiment. A real-time trajectory generation software based on spline theory and sequential quadratic programming is used to implement the MPC controllers. Timing issues related to the computation and implementation of repeatedly updated optimal trajectories are discussed. Results show computational speeds greater than 10 Hz, 2.5 times that of the actuator dynamics. The MPC controllers successfully stabilize a step disturbance applied to the ducted fan and compare favorably to LQR methods.

Station-keeping and reorientation control of a cluster of fully-actuated low-thrust micro-satellites is considered in this paper. We propose a very general optimization based control methodology to solve constrained trajectory generation problems for stationkeeping and reorientation. By taking advantage of the fully-actuated structure of the micro-satellite, it is possible to compute the control on-board the micro-satellites. Performance of this methodology is reported for a typical micro-satellite formation flying space mission using the Nonlinear Trajectory Generation software package.

overview of an inversion based methodology applied to a shuttle atmospheric reentry problem. The proposed method originates in the search for computationally efficient trajectory optimization as an enabling technology for versatile real-time trajectory generation. The technique is based on the nonlinear control theory notion of inversion and flatness. This point of view allows to map the system dynamics, objective, and constraints to a lower dimensional space. The optimization problem is then solved in the lower dimensional space. Eventually the optimal states and inputs are recovered from the inverse mapping.