Structure and motion estimation from long image sequences is a an important and difficult problem in computer vision. We propose a novel approach based on nonlinear and adaptive observers based on a dynamic model of the motion. The estimation of the three-dimensional position and velocity of the camera as well as the three-dimensional structure of the scene is done by observing states and parameters of a nonlinear dynamic system, containing a perspective transformation in the output equation, often referred to as a perspective dynamic system. An advantage of the proposed method is that it is filter-based, i.e. it provides an estimate of structure and motion at each time instance, which is then updated based on a novel image in the sequence. The observer demonstrates a trade-off compared to a more computer vision oriented approach, where no specific assumptions regarding the motion dynamics are required, but instead additional feature points are needed. Finally, the performance of the proposed method is shown in simulated experiments.

Estimation of three-dimensional information from two-dimensional images is an important requirement in many computer vision applications. The estimation task can often be formulated as a problem of estimating states and/or parameters in nonlinear dynamic systems. This paper presents an algorithm for recursive state estimation in nonlinear dynamic systems, where the estimated states correspond to three-dimensional positions of feature points on an observed object. The algorithm is designed as a nonlinear observer, with a gain matrix that can be determined using methods from linear control theory. A stability criterion for the resulting nonlinear system is derived, and simulations are presented in order to illustrate the estimation performance.

Fast motion along a predefined path is important in many robot applications, and requires utilization of the maximum allowable torque range. If the torque is at the limit, there is no margin to cope with disturbances or modeling errors, which may result in deviation from the path. A path velocity controller for modification of the velocity along the path when the torques saturate can improve path tracking. The path velocity controller acts as an outer feedback loop outside the ordinary robot controller, and modifies a nominal velocity profile, computed by minimum time optimization using available methods. An experimental evaluation of such a controller is presented. The experiments are done on an industrial robot, where the original robot control system has been replaced by a VME-based computer system. The experimental results demonstrate that the path velocity controller can adjust a nominal minimum time velocity profile, such that the result is good path following and good utilization of the available torque range. It is also demonstrated how the path velocity controller is able to compensate for time variations in the robot dynamics.>

A secondary controller for online time scaling of nominal high-performance trajectories has been proposed to handle path following with torques close to the limits. Such nominal reference trajectories are typically available from an offline optimization. The stability properties of a closed-loop system including a robot, a primary controller, and a new secondary controller are studied. The analysis shows that if the nominal velocity profile is within certain limits, the result is a bounded actual velocity profile. The stability of the closed-loop system is then obtained by requiring a specified tracking performance for the primary controller.>

A feedback scheme for path following by trajectory time scaling is presented. The scheme is used in execution of fast trajectories along a geometric path, where the motion is limited by torque constraints. The time scaling is done by using a secondary controller that modifies a nominal trajectory during motion. The nominal, high-performance trajectory typically leads to torques that are at the limits, which leaves no control authority to compensate for modeling errors and disturbances. By modifying the time scaling of the nominal trajectory when the torques saturate, closed-loop action is possible. A key idea is that a scalar quantity (the path acceleration) is modified, resulting in coordinated adjustment of the individual joint motions. Two algorithms for online trajectory scaling are presented. One is based on online bounds on path acceleration, and one is designed to handle nominal minimum time trajectories. The functionality of the secondary controller is verified by simulations and experiments.>

A feedback scheme for path following by trajectory time scaling is presented. The scheme is used in execution of fast trajectories along a geometric path, where the motion is limited by torque constraints. The time scaling is done by using a secondary controller that modifies a nominal trajectory during motion. The nominal, high-performance trajectory typically leads to torques that are at the limits, hence leaving no control authority to compensate for modeling errors and disturbances. By modifying the time scaling of the nominal trajectory when the torques saturate, closed-loop action is possible. A key idea is that a scalar quantity, the path acceleration, is modified, resulting in coordinated adjustment of the individual joint motions. Two algorithms for online trajectory scaling are presented. One is based on online bounds on path acceleration, and one is designed to handle nominal minimum-time trajectories. The functionality of the secondary controller is verified by simulations and experiments.>