FATROP : A Fast Constrained Optimal Control Problem Solver for Robot Trajectory Optimization and Control

Trajectory optimization is a powerful tool for robot motion planning and control. State-of-the-art general-purpose nonlinear programming solvers are versatile, handle constraints in an effective way and provide a high numerical robustness, but they are slow because they do not fully exploit the optimal control problem structure at hand. Existing structure-exploiting solvers are fast but they often lack techniques to deal with nonlinearity or rely on penalty methods to enforce (equality or inequality) path constraints. This works presents FATROP: a trajectory optimization solver that is fast and benefits from the salient features of general-purpose nonlinear optimization solvers. The speed-up is mainly achieved through the use of a specialized linear solver, based on a Riccati recursion that is generalized to also support stagewise equality constraints. To demonstrate the algorithm's potential, it is benchmarked on a set of robot problems that are challenging from a numerical perspective, including problems with a minimum-time objective and no-collision constraints. The solver is shown to solve problems for trajectory generation of a quadrotor, a robot manipulator and a truck-trailer problem in a few tens of milliseconds. The algorithm's C++-code implementation accompanies this work as open source software, released under the GNU Lesser General Public License (LGPL). This software framework may encourage and enable the robotics community to use trajectory optimization in more challenging applications

Tight Collision Probability for UAV Motion Planning in Uncertain Environment

Operating unmanned aerial vehicles (UAVs) in complex environments that feature dynamic obstacles and external disturbances poses significant challenges, primarily due to the inherent uncertainty in such scenarios. Additionally, inaccurate robot localization and modeling errors further exacerbate these challenges. Recent research on UAV motion planning in static environments has been unable to cope with the rapidly changing surroundings, resulting in trajectories that may not be feasible. Moreover, previous approaches that have addressed dynamic obstacles or external disturbances in isolation are insufficient to handle the complexities of such environments. This paper proposes a reliable motion planning framework for UAVs, integrating various uncertainties into a chance constraint that characterizes the uncertainty in a probabilistic manner. The chance constraint provides a probabilistic safety certificate by calculating the collision probability between the robot's Gaussian-distributed forward reachable set and states of obstacles. To reduce the conservatism of the planned trajectory, we propose a tight upper bound of the collision probability and evaluate it both exactly and approximately. The approximated solution is used to generate motion primitives as a reference trajectory, while the exact solution is leveraged to iteratively optimize the trajectory for better results. Our method is thoroughly tested in simulation and real-world experiments, verifying its reliability and effectiveness in uncertain environments.Comment: Paper Accepted by IROS 202

Game-Theoretic Safety Assurance for Human-Centered Robotic Systems

In order for autonomous systems like robots, drones, and self-driving cars to be reliably introduced into our society, they must have the ability to actively account for safety during their operation. While safety analysis has traditionally been conducted offline for controlled environments like cages on factory floors, the much higher complexity of open, human-populated spaces like our homes, cities, and roads makes it unviable to rely on common design-time assumptions, since these may be violated once the system is deployed. Instead, the next generation of robotic technologies will need to reason about safety online, constructing high-confidence assurances informed by ongoing observations of the environment and other agents, in spite of models of them being necessarily fallible.This dissertation aims to lay down the necessary foundations to enable autonomous systems to ensure their own safety in complex, changing, and uncertain environments, by explicitly reasoning about the gap between their models and the real world. It first introduces a suite of novel robust optimal control formulations and algorithmic tools that permit tractable safety analysis in time-varying, multi-agent systems, as well as safe real-time robotic navigation in partially unknown environments; these approaches are demonstrated on large-scale unmanned air traffic simulation and physical quadrotor platforms. After this, it draws on Bayesian machine learning methods to translate model-based guarantees into high-confidence assurances, monitoring the reliability of predictive models in light of changing evidence about the physical system and surrounding agents. This principle is first applied to a general safety framework allowing the use of learning-based control (e.g. reinforcement learning) for safety-critical robotic systems such as drones, and then combined with insights from cognitive science and dynamic game theory to enable safe human-centered navigation and interaction; these techniques are showcased on physical quadrotors—flying in unmodeled wind and among human pedestrians—and simulated highway driving. The dissertation ends with a discussion of challenges and opportunities ahead, including the bridging of safety analysis and reinforcement learning and the need to ``close the loop'' around learning and adaptation in order to deploy increasingly advanced autonomous systems with confidence

Augmented Lagrangian Methods as Layered Control Architectures

For optimal control problems that involve planning and following a trajectory, two degree of freedom (2DOF) controllers are a ubiquitously used control architecture that decomposes the problem into a trajectory generation layer and a feedback control layer. However, despite the broad use and practical success of this layered control architecture, it remains a design choice that must be imposed $a\ priori$ on the control policy. To address this gap, this paper seeks to initiate a principled study of the design of layered control architectures, with an initial focus on the 2DOF controller. We show that applying the Alternating Direction Method of Multipliers (ADMM) algorithm to solve a strategically rewritten optimal control problem results in solutions that are naturally layered, and composed of a trajectory generation layer and a feedback control layer. Furthermore, these layers are coupled via Lagrange multipliers that ensure dynamic feasibility of the planned trajectory. We instantiate this framework in the context of deterministic and stochastic linear optimal control problems, and show how our approach automatically yields a feedforward/feedback-based control policy that exactly solves the original problem. We then show that the simplicity of the resulting controller structure suggests natural heuristic algorithms for approximately solving nonlinear optimal control problems. We empirically demonstrate improved performance of these layered nonlinear optimal controllers as compared to iLQR, and highlight their flexibility by incorporating both convex and nonconvex constraints