Discrete and Continuous Trajectory Optimization Methods for Complex Robot Systems

Abstract

Path planning for autonomous systems is a fundamental problem in robotics, especially when the task assigned to a robot is heavily dependent on the motion of one or more of its constituent parts. Efficient path planning requires fast adaptation to changes in the environment and generalizability to a variety of tasks while being intricately linked with a motion planner that handles the kinematic and dynamic constraints of the robot and its workspace. Present-day planning algorithms for robots fail to achieve real-time performance for robot systems with complex kinematics and heavy interactions such as multi-robot systems and robot manipulators. In fact, the motion planning objectives for these complex systems often present mathematical infeasibilities when posed as an optimization problem or become computationally cumbersome to compute by pure sampling. Further, these algorithms do not generalize to the task of collision avoidance against different types of obstacles for multi-robot systems or different types of end-effectors in robots with high-dimensional articulation. The primary focus of this dissertation is to present computationally-tractable solutions to the trajectory optimization problem for both multi-robot systems and manipulators. We explore gradient-based and stochastic optimization techniques and perform mathematical reformulations to adapt them to a wide variety of applications. First, we provide the requisite background in robot path planning and motion planning, including robot kinematics, trajectory representation methods, and collision-avoidance techniques. We also discuss state-of-the-art methods in gradient-based trajectory optimization and stochastic trajectory optimization. Next, we present a distributed GPU-based multi-agent trajectory optimizer that first converts the gradientbased multi-agent trajectory optimization problem into a set of simple matrix-matrix products and then leverages parallel computations over GPUs to accelerate these computations. We demonstrate through a large number of qualitative and quantitative experiments in simulation that our distributed algorithm outperforms existing sequential trajectory optimizers or sampling-based methods for multi-robot planning. Next, we design a collision-aware path planner for robot manipulators operating in the high-dimensional joint space and demonstrate its application across scenes with different types and numbers of obstacles. We finally couple this stochastic optimization-based path planner with a low-level motion planner for the task of pushing objects on a table using a robot manipulator. We also make our software for multi-agent path planning public for open-source development so that our algorithm can be used for further research in this domain