In this letter, we propose a control scheme for rigid bodies designed to optimise transient behaviors. The search space for the optimal control input is parameterized to yield a passive, specifically lossless, nonlinear feedback controller. As a result, it can be combined with other stabilizing controllers without compromising the stability of the closed-loop system. The controller commands torques generating fictitious gyroscopic effects characteristics of 3D rotational rigid body motions, and as such does not inject nor extract kinetic energy from the system. We validate the controller in simulation using a model predictive control (MPC) scheme, successfully combining stability and performance in a stabilization task with obstacle avoidance constraints.
In this article, we consider the problem of unconstrained time-varying convex optimization, where the cost function changes with time. We provide an in-depth technical analysis of the problem and argue why freezing the cost at each time step and taking finite steps toward the minimizer is not the best tracking solution for this problem. We propose a set of algorithms that by taking into account the temporal variation of the cost aim to reduce the tracking error of the time-varying minimizer of the problem. The main contribution of our work is that our proposed algorithms only require the first-order derivatives of the cost function with respect to the decision variable. This approach significantly reduces computational cost compared to the existing algorithms, which use the inverse of the Hessian of the cost. Specifically, the proposed algorithms reduce the computational cost from $O(n^3)$ to $O(n)$ per timestep, where $n$ is the size of the decision variable. Avoiding the inverse of the Hessian also makes our algorithms applicable to non-convex optimization problems. We refer to these algorithms as $O(n)$-algorithms. These $O(n)$-algorithms are designed to solve the problem for different scenarios based on the available temporal information about the cost. We illustrate our results through various examples, including the solution of a model predictive control problem framed as a convex optimization problem with a streaming time-varying cost function.
Recent efforts in the development of autonomous driving technology have induced great advancements in perception, planning and control systems. Model predictive control is one of the most popular advanced control methods, but its application to nonlinear systems still depends on the development of computationally efficient methods. This work presents a nonlinear model predictive control formulation based on real-time iteration using an implicit discretization of the system's dynamics, with the objective of achieving greater prediction accuracy and lower computational cost when dealing with stiff dynamical systems, as is the case for vehicle dynamics. The proposed method is described and later evaluated on a simulation scenario considering modeling errors and external disturbances. The presented results demonstrate the effectiveness of the method when it comes to tracking a given trajectory and its low computational burden, measured in terms of execution time.
This paper presents a comprehensive approach to nonlinear dynamics identification for UAVs using a combination of data-driven techniques and theoretical modeling. Two key methodologies are explored: Proportional-Derivative (PD) approximation and Sparse Identification of Nonlinear Dynamics (SINDy). The UAV dynamics are first modeled using the Euler-Lagrange formulation, providing a set of generalized coordinates. However, platform constraints limit the control inputs to attitude angles, and linear and angular velocities along the z-axis. To accommodate these limitations, thrust and torque inputs are approximated using a PD controller, serving as the foundation for nonlinear system identification. In parallel, SINDy, a data-driven method, is employed to derive a compact and interpretable model of the UAV dynamics from experimental data. Both identified models are then integrated into a Model Predictive Control (MPC) framework for accurate trajectory tracking, where model accuracy, informed by data-driven insights, plays a critical role in optimizing control performance. This fusion of data-driven approaches and theoretical modeling enhances the system's robustness and adaptability in real-world conditions, offering a detailed analysis of the UAV's dynamic behavior.
In this paper, we introduce a nonlinear distributed model predictive control (DMPC) algorithm, which allows for dissimilar and time-varying control horizons among agents, thereby addressing a common limitation in current DMPC schemes. We consider cooperative agents with varying computational capabilities and operational objectives, each willing to manage varying numbers of optimization variables at each time step. Recursive feasibility and a non-increasing evolution of the optimal cost are proven for the proposed algorithm. Through numerical simulations on systems with three agents, we show that our approach effectively approximates the performance of traditional DMPC, while reducing the number of variables to be optimized. This advancement paves the way for a more decentralized yet coordinated control strategy in various applications, including power systems and traffic management.
Flying quadrotors in tight formations is a challenging problem. It is known that in the near-field airflow of a quadrotor, the aerodynamic effects induced by the propellers are complex and difficult to characterize. Although machine learning tools can potentially be used to derive models that capture these effects, these data-driven approaches can be sample inefficient and the resulting models often do not generalize as well as their first-principles counterparts. In this work, we propose a framework that combines the benefits of first-principles modeling and data-driven approaches to construct an accurate and sample efficient representation of the complex aerodynamic effects resulting from quadrotors flying in formation. The data-driven component within our model is lightweight, making it amenable for optimization-based control design. Through simulations and physical experiments, we show that incorporating the model into a novel learning-based nonlinear model predictive control (MPC) framework results in substantial performance improvements in terms of trajectory tracking and disturbance rejection. In particular, our framework significantly outperforms nominal MPC in physical experiments, achieving a 40.1% improvement in the average trajectory tracking errors and a 57.5% reduction in the maximum vertical separation errors. Our framework also achieves exceptional sample efficiency, using only a total of 46 seconds of flight data for training across both simulations and physical experiments. Furthermore, with our proposed framework, the quadrotors achieve an exceptionally tight formation, flying with an average separation of less than 1.5 body lengths throughout the flight. A video illustrating our framework and physical experiments is given here: https://youtu.be/Hv-0JiVoJGo
How can a robot safely navigate around people with complex motion patterns? Deep Reinforcement Learning (DRL) in simulation holds some promise, but much prior work relies on simulators that fail to capture the nuances of real human motion. Thus, we propose Deep Residual Model Predictive Control (DR-MPC) to enable robots to quickly and safely perform DRL from real-world crowd navigation data. By blending MPC with model-free DRL, DR-MPC overcomes the DRL challenges of large data requirements and unsafe initial behavior. DR-MPC is initialized with MPC-based path tracking, and gradually learns to interact more effectively with humans. To further accelerate learning, a safety component estimates out-of-distribution states to guide the robot away from likely collisions. In simulation, we show that DR-MPC substantially outperforms prior work, including traditional DRL and residual DRL models. Hardware experiments show our approach successfully enables a robot to navigate a variety of crowded situations with few errors using less than 4 hours of training data.
The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments benefiting from real-time feedback mechanisms. Inspired by the feedback philosophy, we present feedback neural networks, showing that a feedback loop can flexibly correct the learned latent dynamics of neural ordinary differential equations (neural ODEs), leading to a prominent generalization improvement. The feedback neural network is a novel two-DOF neural network, which possesses robust performance in unseen scenarios with no loss of accuracy performance on previous tasks.} A linear feedback form is presented to correct the learned latent dynamics firstly, with a convergence guarantee. Then, domain randomization is utilized to learn a nonlinear neural feedback form. Finally, extensive tests including trajectory prediction of a real irregular object and model predictive control of a quadrotor with various uncertainties, are implemented, indicating significant improvements over state-of-the-art model-based and learning-based methods.
This paper presents a novel robust variable-horizon model predictive control scheme designed to intercept a target moving along a known trajectory, in finite time. Linear discrete-time systems affected by bounded process disturbances are considered and a tube-based MPC approach is adopted. The main contribution is an adaptive mechanism for choosing the terminal constraint set sequence in the MPC optimization problem. This mechanism is designed to ensure recursive feasibility while promoting minimization of the final distance to the target. Finite-time convergence of the proposed control scheme is proven. In order to evaluate its effectiveness, the designed control law is tested through numerical simulations, including a case study involving orbital rendezvous of a satellite with a tumbling object. The results indicate a significant reduction in conservatism compared to existing state-of-the-art methods using a fixed terminal set sequence.
Employing model predictive control to systems with unbounded, stochastic disturbances poses the challenge of guaranteeing safety, i.e., repeated feasibility and stability of the closed-loop system. Especially, there are no strict repeated feasibility guarantees for standard stochastic MPC formulations. Thus, traditional stability proofs are not straightforwardly applicable. We exploit the concept of input-to-state stability in probability and outline how it can be used to provide stability guarantees, circumventing the requirement for strict repeated feasibility guarantees. Loss of feasibility is captured by a back-up controller, which is explicitly taken into account in the stability analysis. We illustrate our findings using a numeric example.
Can large language models (LLMs) directly serve as powerful world models for model-based agents? While the gaps between the prior knowledge of LLMs and the specified environment's dynamics do exist, our study reveals that the gaps can be bridged by aligning an LLM with its deployed environment and such "world alignment" can be efficiently achieved by rule learning on LLMs. Given the rich prior knowledge of LLMs, only a few additional rules suffice to align LLM predictions with the specified environment dynamics. To this end, we propose a neurosymbolic approach to learn these rules gradient-free through LLMs, by inducing, updating, and pruning rules based on comparisons of agent-explored trajectories and world model predictions. The resulting world model is composed of the LLM and the learned rules. Our embodied LLM agent "WALL-E" is built upon model-predictive control (MPC). By optimizing look-ahead actions based on the precise world model, MPC significantly improves exploration and learning efficiency. Compared to existing LLM agents, WALL-E's reasoning only requires a few principal rules rather than verbose buffered trajectories being included in the LLM input. On open-world challenges in Minecraft and ALFWorld, WALL-E achieves higher success rates than existing methods, with lower costs on replanning time and the number of tokens used for reasoning. In Minecraft, WALL-E exceeds baselines by 15-30% in success rate while costing 8-20 fewer replanning rounds and only 60-80% of tokens. In ALFWorld, its success rate surges to a new record high of 95% only after 6 iterations.
We propose Diffusion Model Predictive Control (D-MPC), a novel MPC approach that learns a multi-step action proposal and a multi-step dynamics model, both using diffusion models, and combines them for use in online MPC. On the popular D4RL benchmark, we show performance that is significantly better than existing model-based offline planning methods using MPC and competitive with state-of-the-art (SOTA) model-based and model-free reinforcement learning methods. We additionally illustrate D-MPC's ability to optimize novel reward functions at run time and adapt to novel dynamics, and highlight its advantages compared to existing diffusion-based planning baselines.
Model predictive control (MPC) is a powerful control technique for online optimization using system model-based predictions over a finite time horizon. However, the computational cost MPC requires can be prohibitive in resource-constrained computer systems. This paper presents a fuzzy controller synthesis framework guided by MPC. In the proposed framework, training data is obtained from MPC closed-loop simulations and is used to optimize a low computational complexity controller to emulate the response of MPC. In particular, autoregressive moving average (ARMA) controllers are trained using data obtained from MPC closed-loop simulations, such that each ARMA controller emulates the response of the MPC controller under particular desired conditions. Using a Takagi-Sugeno (T-S) fuzzy system, the responses of all the trained ARMA controllers are then weighted depending on the measured system conditions, resulting in the Fuzzy-Autoregressive Moving Average (F-ARMA) controller. The effectiveness of the trained F-ARMA controllers is illustrated via numerical examples.
Privacy is a major concern when computing-as-a-service (CaaS) platforms, e.g., cloud-computing platforms, are utilized for building automation, as CaaS platforms can infer sensitive information, such as occupancy, using the sensor measurements of a building. Although the existing encrypted model-based control algorithms can ensure the security and privacy of sensor measurements, they are highly complex to implement and require high computational resources, which result in a high cost of using CaaS platforms. To address these issues, in this paper, we propose an encrypted fully model-free event-triggered cloud-based HVAC control framework that ensures the privacy of occupancy information and minimizes the communication and computation overhead associated with encrypted HVAC control. To this end, we first develop a model-free controller for regulating indoor temperature and CO2 levels. We then design a model-free event-triggering unit which reduces the communication and computation costs of encrypted HVAC control using an optimal triggering policy. Finally, we evaluate the performance of the proposed encrypted fully model-free event-triggered cloud-based HVAC control framework using the TRNSYS simulator, comparing it to an encrypted model-based event-triggered control framework, which uses model predictive control to regulate the indoor climate. Our numerical results demonstrate that, compared to the encrypted model-based method, the proposed fully model-free framework improves the control performance while reducing the communication and computation costs. More specifically, it reduces the communication between the system and the CaaS platform by 64% amount, and its computation time is 75% less than that of the model-based control.
Extreme cornering in racing often leads to large sideslip angles, presenting a significant challenge for vehicle control. Conventional vehicle controllers struggle to manage this scenario, necessitating the use of a drifting controller. However, the large sideslip angle in drift conditions introduces model mismatch, which in turn affects control precision. To address this issue, we propose a model correction drift controller that integrates Model Predictive Control (MPC) with Gaussian Process Regression (GPR). GPR is employed to correct vehicle model mismatches during both drift equilibrium solving and the MPC optimization process. Additionally, the variance from GPR is utilized to actively explore different cornering drifting velocities, aiming to minimize trajectory tracking errors. The proposed algorithm is validated through simulations on the Simulink-Carsim platform and experiments with a 1:10 scale RC vehicle. In the simulation, the average lateral error with GPR is reduced by 52.8% compared to the non-GPR case. Incorporating exploration further decreases this error by 27.1%. The velocity tracking Root Mean Square Error (RMSE) also decreases by 10.6% with exploration. In the RC car experiment, the average lateral error with GPR is 36.7% lower, and exploration further leads to a 29.0% reduction. Moreover, the velocity tracking RMSE decreases by 7.2% with the inclusion of exploration.
The cause of the speed-accuracy tradeoff (typically quantified via Fitts' Law) is a debated topic of interest in motor neuroscience, and is commonly studied using tools from control theory. Two prominent theories involve the presence of signal dependent motor noise and planning variability -- these factors are generally incorporated separately. In this work, we study how well the simultaneous presence of both factors explains the speed-accuracy tradeoff. A human arm reaching model is developed with bio-realistic signal dependent motor noise, and a Gaussian noise model is used to deterministically approximate the motor noise. Both offline trajectory optimization and online model predictive control are used to simulate the planning and execution of several different reaching tasks with varying target sizes and movement durations. These reaching trajectories are then compared to experimental human reaching data, revealing that both models produce behavior consistent with humans, and the speed-accuracy tradeoff is present in both online and offline control. These results suggest the speed-accuracy tradeoff is likely caused by a combination of these two factors, and also that it plays a role in both offline and online computation.
We consider the discrete time infinite horizon average reward restless markovian bandit (RMAB) problem. We propose a \emph{model predictive control} based non-stationary policy with a rolling computational horizon $\tau$. At each time-slot, this policy solves a $\tau$ horizon linear program whose first control value is kept as a control for the RMAB. Our solution requires minimal assumptions and quantifies the loss in optimality in terms of $\tau$ and the number of arms, $N$. We show that its sub-optimality gap is $O(1/\sqrt{N})$ in general, and $\exp(-\Omega(N))$ under a local-stability condition. Our proof is based on a framework from dynamic control known as \emph{dissipativity}. Our solution easy to implement and performs very well in practice when compared to the state of the art. Further, both our solution and our proof methodology can easily be generalized to more general constrained MDP settings and should thus, be of great interest to the burgeoning RMAB community.
We address a task of local trajectory planning for the mobile robot in the presence of static and dynamic obstacles. Local trajectory is obtained as a numerical solution of the Model Predictive Control (MPC) problem. Collision avoidance may be provided by adding repulsive potential of the obstacles to the cost function of MPC. We develop an approach, where repulsive potential is estimated by the neural model. We propose and explore three possible strategies of handling dynamic obstacles. First, environment with dynamic obstacles is considered as a sequence of static environments. Second, the neural model predict a sequence of repulsive potential at once. Third, the neural model predict future repulsive potential step by step in autoregressive mode. We implement these strategies and compare it with CIAO* and MPPI using BenchMR framework. First two strategies showed higher performance than CIAO* and MPPI while preserving safety constraints. The third strategy was a bit slower, however it still satisfy time limits. We deploy our approach on Husky UGV mobile platform, which move through the office corridors under proposed MPC local trajectory planner. The code and trained models are available at \url{https://github.com/CognitiveAISystems/Dynamic-Neural-Potential-Field}.
Commercial buildings account for 17% of U.S. carbon emissions, with roughly half of that from Heating, Ventilation, and Air Conditioning (HVAC). HVAC devices form a complex thermodynamic system, and while Model Predictive Control and Reinforcement Learning have been used to optimize control policies, scaling to thousands of buildings remains a significant unsolved challenge. Most current algorithms are over-optimized for specific buildings and rely on proprietary data or hard-to-configure simulations. We present the Smart Buildings Control Suite, the first open source interactive HVAC control benchmark with a focus on solutions that scale. It consists of 3 components: real-world telemetric data extracted from 11 buildings over 6 years, a lightweight data-driven simulator for each building, and a modular Physically Informed Neural Network (PINN) building model as a simulator alternative. The buildings span a variety of climates, management systems, and sizes, and both the simulator and PINN easily scale to new buildings, ensuring solutions using this benchmark are robust to these factors and only reliant on fully scalable building models. This represents a major step towards scaling HVAC optimization from the lab to buildings everywhere. To facilitate use, our benchmark is compatible with the Gym standard, and our data is part of TensorFlow Datasets.
Model predictive control (MPC) is a powerful tool for controlling complex nonlinear systems under constraints, but often struggles with model uncertainties and the design of suitable cost functions. To address these challenges, we discuss an approach that integrates MPC with safe Bayesian optimization to optimize long-term closed-loop performance despite significant model-plant mismatches. By parameterizing the MPC stage cost function using a radial basis function network, we employ Bayesian optimization as a multi-episode learning strategy to tune the controller without relying on precise system models. This method mitigates conservativeness introduced by overly cautious soft constraints in the MPC cost function and provides probabilistic safety guarantees during learning, ensuring that safety-critical constraints are met with high probability. As a practical application, we apply our approach to fast charging of lithium-ion batteries, a challenging task due to the complicated battery dynamics and strict safety requirements, subject to the requirement to be implementable in real time. Simulation results demonstrate that, in the context of model-plant mismatch, our method reduces charging times compared to traditional MPC methods while maintaining safety. This work extends previous research by emphasizing closed-loop constraint satisfaction and offers a promising solution for enhancing performance in systems where model uncertainties and safety are critical concerns.