Bipedal walking is one of the most important hallmarks of human that robots have been trying to mimic for many decades. Although previous control methodologies have achieved robot walking on some terrains, there is a need for a framework allowing stable and robust locomotion over a wide range of compliant surfaces. This work proposes a novel biomechanics-inspired controller that adjusts the stiffness of the legs in support for robust and dynamic bipedal locomotion over compliant terrains. First, the 3D Dual-SLIP model is extended to support for the first time locomotion over compliant surfaces with variable stiffness and damping parameters. Then, the proposed controller is compared to a Linear-Quadratic Regulator (LQR) controller, in terms of robustness on stepping on soft terrain. The LQR controller is shown to be robust only up to a moderate ground stiffness level of 174 kN/m, while it fails in lower stiffness levels. On the contrary, the proposed controller can produce stable gait in stiffness levels as low as 30 kN/m, which results in a vertical ground penetration of the leg that is deeper than 10% of its rest length. The proposed framework could advance the field of bipedal walking, by generating stable walking trajectories for a wide range of compliant terrains useful for the control of bipeds and humanoids, as well as by improving controllers for prosthetic devices with tunable stiffness.

This paper explores the application of vision-based system identification techniques in quadrotor modeling and control. Through experiments and analysis, we address the complexities and limitations of quadrotor modeling, particularly in relation to thrust and drag coefficients. Grey-box modeling is employed to mitigate uncertainties, and the effectiveness of an onboard vision system is evaluated. An LQR controller is designed based on a system identification model using data from the onboard vision system. The results demonstrate consistent performance between the models, validating the efficacy of vision based system identification. This study highlights the potential of vision-based techniques in enhancing quadrotor modeling and control, contributing to improved performance and operational capabilities. Our findings provide insights into the usability and consistency of these techniques, paving the way for future research in quadrotor performance enhancement, fault detection, and decision-making processes.

Structural vibrations induced by external excitations pose significant risks, including safety hazards for occupants, structural damage, and increased maintenance costs. While conventional model-based control strategies, such as Linear Quadratic Regulator (LQR), effectively mitigate vibrations, their reliance on accurate system models necessitates tedious system identification. This tedious system identification process can be avoided by using a model-free Reinforcement learning (RL) method. RL controllers derive their policies solely from observed structural behaviour, eliminating the requirement for an explicit structural model. For an RL controller to be truly model-free, its training must occur on the actual physical system rather than in simulation. However, during this training phase, the RL controller lacks prior knowledge and it exerts control force on the structure randomly, which can potentially harm the structure. To mitigate this risk, we propose guiding the RL controller using a Linear Quadratic Regulator (LQR) controller. While LQR control typically relies on an accurate structural model for optimal performance, our observations indicate that even an LQR controller based on an entirely incorrect model outperforms the uncontrolled scenario. Motivated by this finding, we introduce a hybrid control framework that integrates both LQR and RL controllers. In this approach, the LQR policy is derived from a randomly selected model and its parameters. As this LQR policy does not require knowledge of the true or an approximate structural model the overall framework remains model-free. This hybrid approach eliminates dependency on explicit system models while minimizing exploration risks inherent in naive RL implementations. As per our knowledge, this is the first study to address the critical training safety challenge of RL-based vibration control and provide a validated solution.

We present a new approach for designing risk-bounded controllers for Uncrewed Aerial Vehicles (UAVs). Existing frameworks for assessing risk of UAV operations rely on knowing the conditional probability of an incident occurring given different causes. Limited data for computing these probabilities makes real-world implementation of these frameworks difficult. Furthermore, existing frameworks do not include control methods for risk mitigation. Our approach relies on UAV dynamics, and employs reachability analysis for a probabilistic risk assessment over all feasible UAV trajectories. We use this holistic risk assessment to formulate a control optimization problem that minimally changes a UAV's existing control law to be bounded by an accepted risk threshold. We call our approach PRReach. Public and readily available UAV dynamics models and open source spatial data for mapping hazard outcomes enables practical implementation of PRReach for both offline pre-flight and online in-flight risk assessment and mitigation. We evaluate PRReach through simulation experiments on real-world data. Results show that PRReach controllers reduce risk by up to 24% offline, and up to 53% online from classical controllers.

Time-delay embedding is a technique that uses snapshots of state history over time to build a linear state space model of a nonlinear smooth system. We demonstrate that periodic non-smooth or hybrid system can also be modeled as a linear state space system using this approach as long as its behavior is consistent in modes and timings. We extend time-delay embeddings to generate a linear model of two periodic hybrid systems--the bouncing pendulum and the simplest walker--with control inputs. This leads to a state history augmented linear quadratic regulator (LQR) which uses current and past state history for feedback control.

Kinodynamic planning of articulated vehicles in cluttered environments faces additional challenges arising from high-dimensional state space and complex system dynamics. Built upon [1],[2], this work proposes the DE-AGT algorithm that grows a tree using pre-computed motion primitives (MPs) and A* heuristics. The first feature of DE-AGT is a delayed expansion of MPs. In particular, the MPs are divided into different modes, which are ranked online. With the MP classification and prioritization, DE-AGT expands the most promising mode of MPs first, which eliminates unnecessary computation and finds solutions faster. To obtain the cost-to-go heuristic for nonholonomic articulated vehicles, we rely on supervised learning and train neural networks for fast and accurate cost-to-go prediction. The learned heuristic is used for online mode ranking and node selection. Another feature of DE-AGT is the improved goal-reaching. Exactly reaching a goal state usually requires a constant connection checking with the goal by solving steering problems -- non-trivial and time-consuming for articulated vehicles. The proposed termination scheme overcomes this challenge by tightly integrating a light-weight trajectory tracking controller with the search process. DE-AGT is implemented for autonomous parking of a general car-like tractor with 3-trailer. Simulation results show an average of 10x acceleration compared to a previous method.

The control of quadrotor Unmanned Aerial Vehicles (UAVs) presents unique challenges due to their nonlinear dynamics, underactuation, and the need for precise trajectory tracking in dynamic environments. Traditional control techniques often struggle to handle these challenges efficiently while maintaining computational tractability for real-time applications. To address these issues, this work outlines an error-state Linear Quadratic Regulator (LQR) approach, leveraging the compact and singularity-free representation of orientation errors using exponential coordinates. Exponential coordinates provide a robust way to represent orientation errors without the singularities inherent in other parameterizations such as Euler angles. By formulating the controller in terms of error-state dynamics, this approach avoids the complexity of directly controlling the nonlinear dynamics, focusing instead on minimizing deviations from a nominal trajectory. This is achieved by driving the error-state--which includes position, velocity, and orientation errors--toward zero. The proposed controller uses an LQR formulation, a well-established concept in classical control theory for linear systems, to minimize a quadratic cost function balancing state deviations and control effort. Although the quadrotor dynamics are nonlinear, the error-state dynamics can be re-linearized about the current tracking error at a sufficiently high frequency, allowing the LQR controller to operate effectively in real time. This iterative re-linearization ensures that the controller remains responsive to changes in the tracking error while maintaining computational efficiency.

The central element of the paper is a (novel) algorithm that utilizes a convex optimization approach (the so-called System Level Synthesis approach, SLS) for synthesizing LQR controllers using estimated dynamics models. The SLS approach allows for an analysis of how the error in the matrix estimation affects the regret of the LQR controller. Using this controller synthesis, upper bounds on the estimation error of the dynamics matrices as well as upper and lower bounds for the expected loss are provided. The method is compared to existing approaches on a benchmark system. This computational study shows a comparable performance of all methods, with the presented method giving the nicest theoretical guarantees (e.g.

This study presents a machine learning-aided approach to accurately estimate the region of attraction (ROA) of a multi-rotor unmanned aerial vehicle (UAV) controlled using a linear quadratic regulator (LQR) controller. Conventional ROA estimation approaches rely on a nominal dynamic model for ROA calculation, leading to inaccurate estimation due to unknown dynamics and disturbances associated with the physical system. To address this issue, our study utilizes a neural network to predict these unknown disturbances of a planar quadrotor. The nominal model integrated with the learned disturbances is then employed to calculate the ROA of the planer quadrotor using a graphical technique. The estimated ROA is then compared with the ROA calculated using Lyapunov analysis and the graphical approach without incorporating the learned disturbances. The results illustrated that the proposed method provides a more accurate estimation of the ROA, while the conventional Lyapunov-based estimation tends to be more conservative.

Flying insects can perform rapid, sophisticated maneuvers like backflips, sharp banked turns, and in-flight collision recovery. To emulate these in aerial robots weighing less than a gram, known as flying insect robots (FIRs), a fast and responsive control system is essential. To date, these have largely been, at their core, elaborations of proportional-integral-derivative (PID)-type feedback control. Without exception, their gains have been painstakingly tuned by hand. Aggressive maneuvers have further required task-specific tuning. Optimal control has the potential to mitigate these issues, but has to date only been demonstrated using approxiate models and receding horizon controllers (RHC) that are too computationally demanding to be carried out onboard the robot. Here we used a more accurate stroke-averaged model of forces and torques to implement the first demonstration of optimal control on an FIR that is computationally efficient enough to be performed by a microprocessor carried onboard. We took force and torque measurements from a 150 mg FIR, the UW Robofly, using a custom-built sensitive force-torque sensor, and validated them using motion capture data in free flight. We demonstrated stable hovering (RMS error of about 4 cm) and trajectory tracking maneuvers at translational velocities up to 25 cm/s using an optimal linear quadratic regulator (LQR). These results were enabled by a more accurate model and lay the foundation for future work that uses our improved model and optimal controller in conjunction with recent advances in low-power receding horizon control to perform accurate aggressive maneuvers without iterative, task-specific tuning.