Optimization-based Constrained Trajectory Generation for Autonomous Vehicles

Abstract

In this thesis, we study problems in constrained trajectory generation for autonomous vehicles with a focus on designing optimization-based algorithms.

First, we investigate the problem of designing trajectories required to satisfy signal temporal logic specifications for non-holonomic car-like robots. Autonomous mobile robots are actively applied to execute complex tasks, such as package delivery, autonomous taxiing, and search-and-rescue. Signal Temporal Logic (STL) offers a powerful formalism for such complex tasks. We formulate the problem as a nonlinear program to generate trajectories for a multi-robot system with car-like robots to perform complex tasks specified with STL grammar. The proposed approach uses an exact closed-form nonlinear parameterization of the kinematics to evaluate the STL grammar in the NLP. We demonstrate the effectiveness and scalability of our algorithm in practice compared to a state-of-the-art baseline.

Second, we also investigate the problem of designing trajectories with obstacle avoidance constraints for quadcopters. Often robots operate in obstacle-free spaces that can be approximated by orthogonal polytopes. We leverage this problem structure and design an algorithm that is massively scalable in practice. Initially, we study the combinatorial optimization problem of decomposing orthogonal polytopes into a minimum number of boxes. We design a novel integer linear program to solve the problem exactly and show that a simple rounding scheme recovers near-optimal solutions from the relaxed linear program in practice. Next, we heuristically select a subset of the boxes to traverse in and then study the continuous problem of generating piecewise trajectories constrained to stay within the selected subset of boxes. We formulate a biconvex optimization program by parametrizing the trajectory and design an algorithm to recover a locally optimal solution using convex alternating minimizations. Finally, we demonstrate that our algorithms are significantly faster than existing baselines and are scalable for large-scale real-world quadcopter scenarios.

Our solution approaches focus on generating trajectories that are provably correct with optimization-based techniques. We demonstrate our algorithms on real world platforms to show that our formulation is tractable for robots in practice.