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We consider the problem of synthesizing robust disturbance feedback policiesfor systems performing complex tasks. We formulate the tasks as linear temporallogic specifications and encode them into an optimization framework viamixed-integer constraints. Both the system dynamics and the specifications areknown but affected by uncertainty. The distribution of the uncertainty isunknown, however realizations can be obtained. We introduce a data-drivenapproach where the constraints are fulfilled for a set of realizations andprovide probabilistic generalization guarantees as a function of the number ofconsidered realizations. We use separate chance constraints for thesatisfaction of the specification and operational constraints. This allows usto quantify their violation probabilities independently. We compute disturbancefeedback policies as solutions of mixed-integer linear or quadraticoptimization problems. By using feedback we can exploit information of pastrealizations and provide feasibility for a wider range of situations comparedto static input sequences. We demonstrate the proposed method on two robustmotion-planning case studies for autonomous driving.

From Uncertainty Data to Robust Policies for Temporal Logic Planning