Multi-Agent Exploration under Sparsity Constraints

Abstract

The operation of robotic systems on extraterrestrial missions involves long distance communications, which have large delays and make the control of any agent complicated. This problem becomes even more dominant if multiple robotic systems are used. One solution to this problem is to increase the autonomy of each robotic system such that each robot can decide what to do according to its’ current task and previous measurements. Furthermore, by utilizing cooperation between each robotic system, a task might even be solved more time efficiently.
Hence, this thesis considers the problem of using a spatially distributed robotic system for exploratory tasks such as mapping of an unknown process in the context of space exploration. This thesis therefore presents an information driven approach for exploration – based on the theory of optimal experiment design – to estimate new measurement locations that increase the accuracy of the used model. As many natural processes can be represented in a sparse basis, this thesis additionally assumes that the underlying model can be considered as sparse. Furthermore, the influence of a sparse model on the exploration phase is also examined. In general, this thesis studies how to do the estimation and exploration cooperatively by information exchange.
This thesis looks at two different estimation frameworks – the frequentist framework and the Bayesian framework – combined with two conceptually different distribution paradigms. Multiple distributed versions of a sparse Bayesian learning algorithm are developed for each distributed paradigm. Then, the estimation results are exploited to derive an information metric that is suited to estimate new measurement locations. Here, the D-optimality criterion is utilized and this thesis presents how to estimate the D-optimality criterion for the considered distributed settings and the different frameworks. Furthermore, the influence of the sparsity assumption is analyzed. For the frequentist framework, the sparsity inducing cost-function is altered into a ridge-regression based on the sparse parameter estimates, in order to approximate a Hessian matrix of the nonzero parameter estimates. For the Bayesian methods the covariance of the posterior probability density function (PDF) is used for the D-optimality criterion.
Next, the estimation of the model parameters and the estimation of the new measurement locations are formulated into multiple exploration algorithms for all frameworks and distribution paradigms. The thesis evaluates multiple optimization strategies of the exploration criteria, in order to figure out which are a better fit for a multi-agent system.
After the analysis of the building blocks of this work – the distributed parameter weight estimation and the distributed exploration – experimental validations demonstrate how the proposed system works in reality. The results show that the exploration algorithms are able to work in real-time and they indicate that the estimated covariance based on the Bayesian framework leads to better performances although the Bayesian methods are computationally more complex.