The performance of robots in high-level tasks depends on the quality of their lower-level controller, which requires fine-tuning. However, the intrinsically nonlinear dynamics and controllers make tuning a challenging task when it is done by hand. In this paper, we present DiffTune, a novel, gradient-based automatic tuning framework. We formulate the controller tuning as a parameter optimization problem. Our method unrolls the dynamical system and controller as a computational graph and updates the controller parameters through gradient-based optimization. The gradient is obtained using sensitivity propagation, which is the only method for gradient computation when tuning for a physical system instead of its simulated counterpart. Furthermore, we use $\mathcal{L}_1$ adaptive control to compensate for the uncertainties (that unavoidably exist in a physical system) such that the gradient is not biased by the unmodelled uncertainties. We validate the DiffTune on a Dubin's car and a quadrotor in challenging simulation environments. In comparison with state-of-the-art auto-tuning methods, DiffTune achieves the best performance in a more efficient manner owing to its effective usage of the first-order information of the system. Experiments on tuning a nonlinear controller for quadrotor show promising results, where DiffTune achieves 3.5x tracking error reduction on an aggressive trajectory in only 10 trials over a 12-dimensional controller parameter space.

L-1 adaptive control (L(1)AC) theory gives uniform steady-state and transient performance bounds on state variables and control inputs and delay margin guarantees. These guarantees are strict and can be conservative as they are derived from the small gain theorem. On the other hand, a recently-developed verification tool - Verse [1] computes over-approximations of reachable sets from simulation data for particular problem instances and can provide more realistic and less conservative performance bounds. Prior work on the verification and validation (V&V) of control design specifications and performance metrics primarily centered on optimizing design parameters through optimization or parameter variable space exploration. However, analyzing highly nonlinear systems poses challenges in mathematical analysis and performance-bound quantification, leading to a case-by-case approach to observing the design guidelines. In this paper, we propose a general framework that leverages Verse to establish verification for L(1)AC design specifications. Furthermore, design guidelines for closed-loop nonlinear systems with L(1)AC are observed from the verification results and can be instructive for control development.

$\mathcal{L}_1$ adaptive control ($\mathcal{L}_1$AC) theory gives uniform steady-state and transient performance bounds on state variables and control inputs and delay margin guarantees. These guarantees are strict and can be conservative as they are derived from the small gain theorem. On the other hand, a recently-developed verification tool -- Verse~\cite{li2023verse} computes over-approximations of reachable sets from simulation data, for particular problem instances, and can provide more realistic and less conservative performance bounds. Prior work on the verification and validation (V&V) of control design specifications and performance metrics primarily centered on optimizing design parameters through optimization or parameter variable space exploration. However, analyzing highly nonlinear systems poses challenges in mathematical analysis and performance-bound quantification, leading to a case-by-case approach to observing the design guidelines. In this paper, we propose a general framework that leverages Verse to establish verification for $\mathcal{L}_1$AC design specifications. Furthermore, design guidelines for closed-loop nonlinear systems with $\mathcal{L}_1$AC are observed from the verification results and can be instructive for control development.

This paper introduces a novel numerical approach to achieving smooth lane-change trajectories in autonomous driving scenarios. Our trajectory generation approach leverages particle swarm optimization (PSO) techniques, incorporating Neural Network (NN) predictions for trajectory refinement. The generation of smooth and dynamically feasible trajectories for the lane change maneuver is facilitated by combining polynomial curve fitting with particle propagation, which can account for vehicle dynamics. The proposed planning algorithm is capable of determining feasible trajectories with real-time computation capability. We conduct comparative analyses with two baseline methods for lane changing, involving analytic solutions and heuristic techniques in numerical simulations. The simulation results validate the efficacy and effectiveness of our proposed approach.

This paper presents a novel approach for achieving safe stochastic optimal control in networked multi-agent systems (MASs). The proposed method incorporates barrier states (BaSs) into the system dynamics to embed safety constraints. To accomplish this, the networked MAS is factorized into multiple subsystems, and each one is augmented with BaSs for the central agent. The optimal control law is obtained by solving the joint Hamilton-Jacobi-Bellman (HJB) equation on the augmented subsystem, which guarantees safety via the boundedness of the BaSs. The BaS-based optimal control technique yields safe control actions while maintaining optimality. The safe optimal control solution is approximated using path integrals. To validate the effectiveness of the proposed approach, numerical simulations are conducted on a cooperative UAV team in two different scenarios.

In this article, we propose a unified framework to instantly generate a safe optimal control action for a new task from existing controllers on multiagent systems. The control action composition is achieved by taking a weighted mixture of the existing controllers according to the contribution of each component task. Instead of sophisticatedly tuning the cost parameters and other hyperparameters for safe and reliable behavior in the optimal control framework, the safety of each single-task solution is guaranteed using the control barrier functions (CBFs) for high relative degree stochastic systems, which constrains the system state within a known safe operation region where it originates from. Linearity of CBF constraints in control ensures the feasibility of safe control action composition. The discussed framework can immediately provide reliable solutions to new tasks by taking a weighted mixture of solved component-task actions and satisfying some CBF constraints, instead of performing an extensive sampling to compute a new controller. Our results are verified and demonstrated on both a single unmanned aerial vehicle (UAV) and two cooperative UAV teams in an environment with obstacles.

Controller tuning is a vital step to ensure the controller delivers its designed performance. DiffTune has been proposed as an automatic tuning method that unrolls the dynamical system and controller into a computational graph and uses auto-differentiation to obtain the gradient for the controller's parameter update. However, DiffTune uses the vanilla gradient descent to iteratively update the parameter, in which the performance largely depends on the choice of the learning rate (as a hyperparameter). In this paper, we propose to use hyperparameter-free methods to update the controller parameters. We find the optimal parameter update by maximizing the loss reduction, where a predicted loss based on the approximated state and control is used for the maximization. Two methods are proposed to optimally update the parameters and are compared with related variants in simulations on a Dubin's car and a quadrotor. Simulation experiments show that the proposed first-order method outperforms the hyperparameter-based methods and is more robust than the second-order hyperparameter-free methods.

This paper proposes a safe and optimal control framework using waypoints and associated reference trajectories as guidance. The waypoints are obtained by efficiently solving satisfiability problems over linear constraints. The waypoint synthesis formulation can incorporate control errors and ensure that the computed reference trajectory still satisfies given specifications even in the presence of error. We further use the optimal control framework with an augmented tracking-error-minimization objective to closely follow the reference trajectory. Since the reference trajectory is safe by design, the ideal tracking performance of the reference also implies the safety of the closed-loop state trajectory, which eliminates the need for additional safety constraints that may hinder solution optimality. We compute the optimal control law for stochastic systems using a path-integral reformulation. Our approach outperforms the optimal control framework without a synthesized reference trajectory in terms of trajectory optimality and goal-reach accuracy, as validated by numerical simulations on a UAV model passing through an obstacle-cluttered environment.

L_1 adaptive control (L_1AC) is a control design technique that can handle a broad class of system uncertainties and provide transient performance guarantees. In this work-in-progress abstract, we discuss how existing formal verification tools can be applied to check the performance of L_1AC systems. We show that the theoretical transient performance and robustness guarantees of an L_1 adaptive controller for an 18-dimensional quadrotor system can be verified using the recently developed Verse reachability analysis tool. We will further consider the performance verification of L_1AC on systems with learning-enabled components.

A simplified analysis is performed on the Bode-type filtering sensitivity trade-off integrals, which capture the sensitivity characteristics of the estimate and estimation error with respect to the process input and estimated signal in continuous- and discrete-time linear time-invariant filtering systems. Compared with the previous analyses based on complex analysis and Cauchy's residue theorem, the analysis results derived from the simplified method are more explicit, thorough, and require less restrictive assumptions. For continuous-time filtering systems, our simplified analysis reveals that apart from the non-minimum phase zero sets reported in the previous literature, the value and boundedness of filtering sensitivity integrals are also determined by the leading coefficients, relative degrees, minimum phase zeros, and poles of plants and filters. By invoking the simplified method, a comprehensive analysis on the discrete-time filtering sensitivity integrals is conducted for the first time. Numerical examples are provided to verify the validity and correctness of the simplified analysis.

We present a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based L-1-adaptive (CL1) control and Bayesian learning in the form of Gaussian process (GP) regression. The CL1 controller ensures that control objectives are met while providing safety certificates. Furthermore, the controller incorporates any available data into GP models of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients.

In this paper, we discuss the methodology of generalizing the optimal control law from learned component tasks to unlearned composite tasks on Multi-Agent Systems (MASs), by using the linearity composition principle of linearly solvable optimal control (LSOC) problems. The proposed approach achieves both the compositionality and optimality of control actions simultaneously within the cooperative MAS framework in both discrete- and continuous-time in a sample-efficient manner, which reduces the burden of re-computation of the optimal control solutions for the new task on the MASs. We investigate the application of the proposed approach on the MAS with coordination between agents. The experiments show feasible results in investigated scenarios, including both discrete and continuous dynamical systems for task generalization without resampling.

We present $\mathcal{RL}_1$-$\mathcal{GP}$, a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are Riemannian energy $\mathcal{L}_1$ ($\mathcal{RL}_1$) control and Bayesian learning in the form of Gaussian process (GP) regression. The $\mathcal{RL}_1$ controller ensures that control objectives are met while providing safety certificates. Furthermore, $\mathcal{RL}_1$-$\mathcal{GP}$ incorporates any available data into a GP model of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients. We provide a few illustrative examples for the safe learning and control of planar quadrotor systems in a variety of environments.

We present $\mathcal{CL}_1$-$\mathcal{GP}$, a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based $\mathcal{L}_1$ ($\mathcal{CL}_1$) control and Bayesian learning in the form of Gaussian process (GP) regression. The $\mathcal{CL}_1$ controller ensures that control objectives are met while providing safety certificates. Furthermore, $\mathcal{CL}_1$-$\mathcal{GP}$ incorporates any available data into a GP model of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients. We provide a few illustrative examples for the safe learning and control of planar quadrotor systems in a variety of environments.

In this paper, we investigate using Ultra-Wideband (UWB) technology in vehicles for localization as well as other possible infrastructure-free applications.To that end, we first introduce the on-vehicle UWB anchor system configuration, then conduct a theoretical analysis to shed light on the capabilities and limitations of using UWB anchors with this configuration. Extensive field trials performed verified the validity of the analysis conducted.Finally, Virtual Pedestrian Traffic Light (VPTL), an infrastructure-free pedestrian traffic light system is introduced as an example application of the presented approach.