Inge Spangelo

Trajectory planning and collision avoidance for underwater vehicles using optimal control

Energy-optimal trajectories for underwater vehicles be computed using a numerical solution of the optimal control problem. A performance index consisting of a weighted combination of energy and time consumption is proposed. Collision avoidance is solved by including path constraints. Control vector parameterization with direct single shooting is used in this study. The vehicle is modeled with six-dimensional nonlinear and coupled equations of motion. Optimal trajectories are computed for a vehicle controlled in all six degrees of freedom by dc-motor-driven thrusters. Good numerical results are achieved. >

A damped least-squares solution to redundancy resolution

Singularity robust redundancy resolution with task priority can be implemented using the extended Jacobian technique with weighted damped least-squares. The resulting scheme is simple to implement and involves less computation than the task priority scheme. The minimum singular value of the Jacobian can be estimated reliably and accurately with little computation, and this estimate was used to calculate an appropriate damping factor. A constant damping factor was also used with good results. The scheme was successfully implemented in a simulation study with a seven-joint manipulator with a kinematic design derived from the PUMA geometry.<<ETX>>

Generation of energy-optimal trajectories for an autonomous underwater vehicle

Energy-optimal trajectories for an autonomous underwater vehicle can be computed using a numerical solution of the optimal control problem. The vehicle is modeled with the six-dimensional nonlinear and coupled equations of motion, controlled with DC-motors in all degrees of freedom. The actuators are modeled and controlled with velocity loops. The dissipated energy is expressed in terms of the control variables as a nonquadratic function. Two different numerical methods are used in this study, a function space conjugate gradient (CG) method, and a control vector parameterization (CVP) method. Energy-optimal trajectories were computed in simulation experiments. Good results were achieved with the CVP method, which was superior to the CG method.<<ETX>>

Bounds on the largest singular value of the manipulator Jacobian

It is proved that if the manipulator Jacobian is properly scaled, the largest singular value is bounded within a small interval close to unity. In this case, the inverse of the smallest singular value is a good estimate of the condition number. This is useful in singularity analysis. Bounds are derived for a general six-joint manipulator and for the ABB IRb 2000 industrial robot in a case study. >

ROCKET ASCENT WITH HEAT-FLUX AND SPLASHDOWN CONSTRAINTS

Acsent trajectories for the Ariane5 rocket maximizing the payload have been computed using control vector parameterization (CVP) and direct shooting. The rocket has three stages resulting in a three phase optimal control problem. A pitch program at the beginning of the first stage has been introduced for singularity avoidance. The rocket is ascended into a geostationary transfer orbit. Heat-flux and splash-down constraints are necessary and optimal payload for different combinations of these are computed. Minor improvements were observed trying to optimize the thrust-time history. The optimization program package PROMIS was applied.

Rocket Ascent with Heat-Flux and Splash Down Constraints

Abstract Acsent trajectories for the Ariane5 rocket maximizing the payload have been computed using control vector parameterization (CVP) and direct shooting. The rocket has three stages resulting in a three phase optimal control problem. A pitch program at the beginning of the first stage has been introduced for singularity avoidance. The rocket is ascended into a geostationary transfer orbit. Heat-flux and splash-down constraints are necessary and optimal payload for different combinations of these are computed. Minor improvements were observed trying to optimize the thrust-time history. The optimization program package PROMIS was applied.

Thruster Modelling and Energy-Optimization for an Autonomous Underwater Vehicle

Abstract Energy-optimal trajectories for an autonomous underwater vehicle are investigated using control vector parameterization and single shooting. The vehicle has 6 propellers driven by DC-motors. Optimal trajectories are calculated using three different thruster models. The results show that in order to achieve valid trajectories the thrust coefficients linear dependence on the vehicle velocity has to be modelled. Optimal performance index as a function of time consumption is shown.

RESOLVING REDUNDANCY THROUGH A WEIGHTED DAMPED LEAST-SQUARES SOLUTION

Abstract Singularity robust redundancy resolution with task priority can be implemented using the extended Jacobian technique with weighted damped least-squares. The resulting scheme is simple to implement and involves less computation than the task priority scheme. The minimum singular value of the Jacobian can be estimated reliably and accurately with little computation, and this estimate was used to calculate an appropriate damping factor. A constant damping factor was also used with good results. The scheme was successfully implemented in a simulation study with a seven-joint manipulator with a kinematic design derived from the PUMA geometry.