Optimal Motion Planning for Object Interception and Capture

The work presented in this thesis is motivated by the great strength of optimal control and numerical optimization in generating feasible and optimal trajectories for complex robot trajectory planning problems. The task of interest is the interception and capture of free-flying objects, to include the interception with a flying object on ground by means of a fixed-based robot and the capture of a free-tumbling satellite in orbit by means of a space robot. In the first application, dynamic constraints play an important role in the optimal solutions, which need to be computed in a short time. In the second application, the optimal motion planning is characterized by multiple motion and sensor-based constraints, as well as by the non-holonomic dynamics of the robot. The stringent safety requirements in the remote orbital operational environment call for methods which can provide guarantees of feasibility with respect to the constraints at hand. Given the non-convex and highly constrained nature of these planning problems, the performance of trajectory optimization methods heavily depends on the provided trajectory initialization and they are generally not guaranteed to find a feasible solution. This motivates generating solutions offline and retrieving them online with the aid of generalization via regression. A series of regression methods are applied and compared to the first problem, namely the interception with a flying object on ground, for purpose of analysis. The optimal solutions generated offline build a training set for the regression methods, which construct a mapping function between a suitable task space and the optimization parameter solution space. This mapping is then used in an online setting, to quickly provide an initial guess for warm starting an online planner. Statistical simulation results show a very high rate of convergence of the online planner, and give insight into the relation between the optimality of the solutions and the size of the training data set. For the second task, namely the robot trajectory planning for the capture of a freetumbling satellite in orbit, knowledge of the satellite motion in future time is required. The dynamics of a free-tumbling satellite in orbit can be modelled as a free rigid body. The rotational dynamics however still presents some challenges, when wanting to propagate the body’s orientation for a sufficient time, for planning purposes. These challenges are addressed here in detail, proposing a method to identify the state and inertial parameters necessary for a robust motion prediction, accounting for measurement noise, modelling errors and other dynamical effects pertinent to the free-body dynamics. Furthermore, a statistical propagation method is presented which provides an estimate of the dispersion of the motion prediction, which results from the same disturbances. This information is intended as input to robust control methods, which account for the given uncertainty. The OOS-SIM robotic experimental facility at the DLR reproduces orbital dynamic and illumination conditions on ground, and was used to validate the proposed methods. A complex trajectory planner is then presented for the task of capturing the free-tumbling satellite by means of a free-floating robot in a realistic operational scenario. Due to the long computation times necessary for generating a training data set, an initialization method was developed based on a look-up table combined with a motion propagation of the target satellite. A statistical simulation analysis shows a satisfactory convergence behavior of the online planner. Furthermore, in order to make use of the motion planning solutions for control purposes, a tracking controller is presented which combines the planner’s input to sensor feedback. This controller was also implemented and tested on the OOS-SIM facility. The methods presented in this thesis for the satellite capture task describe an autonomous operational strategy. The motion planning is combined with target satellite motion prediction and robot tracking control functionalities in a new fashion. The use of numerical trajectory optimization for control purposes is as such demonstrated for this application. The effectiveness of using an experimental facility on ground for validation purposes is also demonstrated. More generally, the results for the two addressed interception and capture tasks have shown that generalization via regression of feasible and optimal solutions generated offline has great potential for efficiently solving complex trajectory planning problems online. This potential is also recognizable from the described possible improvements of the adopted methods, as well as from the possible use of GPU and cluster technologies. A reference trajectory is argued to be necessary to provide guarantees of feasibility for a given task. However, its intrinsic uncertainty calls for methods which provide the same guarantees, in view of the necessary trajectory deviations in the tracking phase