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We consider the problem of safe multi-agent motion planning for drones in uncertain, cluttered workspaces. For this problem, we present a tractable motion planner that builds upon the strengths of reinforcement learning and constrained-control-based trajectory planning. First, we use single-agent reinforcement learning to learn motion plans from data that reach the target but may not be collision-free. Next, we use a convex optimization, chance constraints, and set-based methods for constrained control to ensure safety, despite the uncertainty in the workspace, agent motion, and sensing. The proposed approach can handle state and control constraints on the agents, and enforce collision avoidance among themselves and with static obstacles in the workspace with high probability. The proposed approach yields a safe, real-time implementable, multi-agent motion planner that is simpler to train than methods based solely on learning. Numerical simulations and experiments show the efficacy of the approach.

Safety is a core challenge of autonomous robot motion planning, especially in the presence of dynamic and uncertain obstacles. Many recent results use learning and deep learning-based motion planners and prediction modules to predict multiple possible obstacle trajectories and generate obstacle-aware ego robot plans. However, planners that ignore the inherent uncertainties in such predictions incur collision risks and lack formal safety guarantees. In this paper, we present a computationally efficient safety filtering solution to reduce the collision risk of ego robot motion plans using multiple samples of obstacle trajectory predictions. The proposed approach reformulates the collision avoidance problem by computing safe halfspaces based on obstacle sample trajectories using distributionally robust optimization (DRO) techniques. The safe halfspaces are used in a model predictive control (MPC)-like safety filter to apply corrections to the reference ego trajectory thereby promoting safer planning. The efficacy and computational efficiency of our approach are demonstrated through numerical simulations.

We develop a real-time feasible mixed-integer programming-based decision making (MIP-DM) system for automated driving. Using a linear vehicle model in a road-aligned coordinate frame, the lane change constraints, collision avoidance and traffic rules can be formulated as mixed-integer inequalities, resulting in a mixed-integer quadratic program (MIQP). The proposed MIP-DM simultaneously performs maneuver selection and trajectory generation by solving the MIQP at each sampling time instant. While solving MIQPs in real time has been considered intractable in the past, we show that our recently developed solver BB-ASIPM is capable of solving MIP-DM problems on embedded hardware in real time. The performance of this approach is illustrated in simulations in various scenarios including merging points and traffic intersections, and hardware-in-the-loop simulations on dSPACE Scalexio and MicroAutoBox-III. Finally, we present results from hardware experiments on small-scale automated vehicles., Comment: 14 pages, 11 figures, 3 tables, submitted to IEEE Transactions on Control Systems Technology

Motivated by the recent interest in risk-aware control, we study a continuous-time control synthesis problem to bound the risk that a stochastic linear system violates a given specification. We use risk signal temporal logic as a specification formalism in which distributionally robust risk predicates are considered and equipped with the usual Boolean and temporal operators. Our control approach relies on reformulating these risk predicates as deterministic predicates over mean and covariance states of the system. We then obtain a timed sequence of sets of mean and covariance states from the timed automata representation of the specification. To avoid an explosion in the number of automata states, we propose heuristics to find candidate sequences effectively. To execute and check dynamic feasibility of these sequences, we present a sampled-data control technique based on time discretization and constraint tightening that allows to perform timed transitions while satisfying the continuous-time constraints., Comment: 8 pages, 4 figures, contributed paper at the 2022 American Control Conference (ACC) in Atlanta, GA

Robust autonomy stacks require tight integration of perception, motion planning, and control layers, but these layers often inadequately incorporate inherent perception and prediction uncertainties, either ignoring them altogether or making questionable assumptions of Gaussianity. Robots with nonlinear dynamics and complex sensing modalities operating in an uncertain environment demand more careful consideration of how uncertainties propagate across stack layers. We propose a framework to integrate perception, motion planning, and control by explicitly incorporating perception and prediction uncertainties into planning so that risks of constraint violation can be mitigated. Specifically, we use a nonlinear model predictive control based steering law coupled with a decorrelation scheme based Unscented Kalman Filter for state and environment estimation to propagate the robot state and environment uncertainties. Subsequently, we use distributionally robust risk constraints to limit the risk in the presence of these uncertainties. Finally, we present a layered autonomy stack consisting of a nonlinear steering-based distributionally robust motion planning module and a reference trajectory tracking module. Our numerical experiments with nonlinear robot models and an urban driving simulator show the effectiveness of our proposed approaches., Comment: arXiv admin note: text overlap with arXiv:2002.02928

We propose a two-phase risk-averse architecture for controlling stochastic nonlinear robotic systems. We present Risk-Averse Nonlinear Steering RRT* (RANS-RRT*) as an RRT* variant that incorporates nonlinear dynamics by solving a nonlinear program (NLP) and accounts for risk by approximating the state distribution and performing a distributionally robust (DR) collision check to promote safe planning. The generated plan is used as a reference for a low-level tracking controller. We demonstrate three controllers: finite horizon linear quadratic regulator (LQR) with linearized dynamics around the reference trajectory, LQR with robustness-promoting multiplicative noise terms, and a nonlinear model predictive control law (NMPC). We demonstrate the effectiveness of our algorithm using unicycle dynamics under heavy-tailed Laplace process noise in a cluttered environment., Comment: First three authors contributed equally

We present a general framework for risk semantics on Signal Temporal Logic (STL) specifications for stochastic dynamical systems using axiomatic risk theory. We show that under our recursive risk semantics, risk constraints on STL formulas can be expressed in terms of risk constraints on atomic predicates. We then show how this allows a (stochastic) STL risk constraint to be transformed into a risk-tightened deterministic STL constraint on a related deterministic nominal system, enabling the application of existing STL methods. For affine predicate functions and a (coherent) Distributionally Robust Value at Risk measure, we show how risk constraints on atomic predicates can be reformulated as tightened deterministic affine constraints. We demonstrate the framework using a Model Predictive Control (MPC) design with an STL risk constraint., Comment: 6 pages, 1 figure, to be published in IEEE L-CSS

We present a distributed control strategy for a team of quadrotors to autonomously achieve a desired 3D formation. Our approach is based on local relative position measurements and does not require global position information or inter-vehicle communication. We assume that quadrotors have a common sense of direction, which is chosen as the direction of gravitational force measured by their onboard IMU sensors. However, this assumption is not crucial, and our approach is robust to inaccuracies and effects of acceleration on gravitational measurements. In particular, converge to the desired formation is unaffected if each quadrotor has a velocity vector that projects positively onto the desired velocity vector provided by the formation control strategy. We demonstrate the validity of proposed approach in an experimental setup and show that a team of quadrotors achieve a desired 3D formation., Comment: Extended abstract

We present a distributed formation control strategy for agents with a variety of dynamics to achieve a desired planar formation. Our approach is based on the barycentric-coordinate-based (BCB) control, which is fully distributed, does not require inter-agent communication or a common sense of orientation, and can be implemented using relative position measurements acquired by agents in their local coordinate frames. This removes the need for global positioning or alignment of local coordinate frames, which are required across several existing strategies. We show how the BCB control for agents with the simplest dynamical model, i.e., the single-integrator dynamics, can be extended to agents with higher-order dynamics such as quadrotors, and nonholonomic agents such as unicycles and cars. Specifically, our extension preserves the desired convergence and robustness guarantees of the BCB approach and is provably robust to saturations in the input and unmodeled linear actuator dynamics for unicycle and car agents. We further show that under our proposed BCB control design, the agents can move along a rotated and scaled control direction without affecting the convergence to the desired formation. This observation is used to design a fully distributed collision avoidance strategy, which is often not considered in the formation control literature. We demonstrate the proposed approach in simulations and further present a distributed robotic platform to test the strategy experimentally. Our experimental platform consists of off-the-shelf equipment that can be used to test and validate other multi-agent algorithms. The code and implementation instructions for this platform are available online.