Model Predictive Control

As compared to typical mobile manipulation tasks, sequential mobile manipulation poses a unique challenge -- as the robot operates over extended periods, successful task completion is not solely dependent on consistent motion generation but also on the robot's awareness and adaptivity to changes in the operating environment. While existing motion planners can generate whole-body trajectories to complete sequential tasks, they typically assume that the environment remains static and rely on precomputed maps. This assumption often breaks down during long-term operations, where semi-static changes such as object removal, introduction, or shifts are common. In this work, we propose a novel perceptive hierarchical-task model predictive control (HTMPC) framework for efficient sequential mobile manipulation in unstructured, changing environments. To tackle the challenge, we leverage a Bayesian inference framework to explicitly model object-level changes and thereby maintain a temporally accurate representation of the 3D environment; this up-to-date representation is embedded in a lexicographic optimization framework to enable efficient execution of sequential tasks. We validate our perceptive HTMPC approach through both simulated and real-robot experiments. In contrast to baseline methods, our approach systematically accounts for moved and phantom obstacles, successfully completing sequential tasks with higher efficiency and reactivity, without relying on prior maps or external infrastructure.

High-speed multi-agent autonomous racing demands robust spatiotemporal planning and precise control under strict computational limits. Current methods often oversimplify interactions or abandon strict kinematic constraints. We resolve this by proposing a Topological Gap Identification and Accelerated MPC framework. By predicting opponent behaviors via SGPs, our method constructs dynamic occupancy corridors to robustly select optimal overtaking gaps. We ensure strict kinematic feasibility using a Linear Time-Varying MPC powered by a customized Pseudo-Transient Continuation (PTC) solver for high-frequency execution. Experimental results on the F1TENTH platform show that our method significantly outperforms state-of-the-art baselines: it reduces total maneuver time by 51.6% in sequential scenarios, consistently maintains an overtaking success rate exceeding 81% in dense bottlenecks, and lowers average computational latency by 20.3%, pushing the boundaries of safe and high-speed autonomous racing.

This paper formally develops a novel hierarchical planning and control framework for robust payload transportation by quadrupedal robots, integrating a model predictive control (MPC) algorithm with a gradient-descent-based adaptive updating law. At the framework's high level, an indirect adaptive law estimates the unknown parameters of the reduced-order (template) locomotion model under varying payloads. These estimated parameters feed into an MPC algorithm for real-time trajectory planning, incorporating a convex stability criterion within the MPC constraints to ensure the stability of the template model's estimation error. The optimal reduced-order trajectories generated by the high-level adaptive MPC (AMPC) are then passed to a low-level nonlinear whole-body controller (WBC) for tracking. Extensive numerical investigations validate the framework's capabilities, showcasing the robot's proficiency in transporting unmodeled, unknown static payloads up to 109% in experiments on flat terrains and 91% on rough experimental terrains. The robot also successfully manages dynamic payloads with 73% of its mass on rough terrains. Performance comparisons with a normal MPC and an L1 MPC indicate a significant improvement. Furthermore, comprehensive hardware experiments conducted in indoor and outdoor environments confirm the method's efficacy on rough terrains despite uncertainties such as payload variations, push disturbances, and obstacles.

Brand advertising plays a critical role in building long-term consumer awareness and loyalty, making it a key objective for advertisers across digital platforms. Although real-time bidding has been extensively studied, there is limited literature on algorithms specifically tailored for brand auction ads that fully leverage their unique characteristics. In this paper, we propose a lightweight Model Predictive Control (MPC) framework designed for brand advertising campaigns, exploiting the inherent attributes of brand ads -- such as stable user engagement patterns and fast feedback loops -- to simplify modeling and improve efficiency. Our approach utilizes online isotonic regression to construct monotonic bid-to-spend and bid-to-conversion models directly from streaming data, eliminating the need for complex machine learning models. The algorithm operates fully online with low computational overhead, making it highly practical for real-world deployment. Simulation results demonstrate that our approach significantly improves spend efficiency and cost control compared to baseline strategies, providing a scalable and easily implementable solution for modern brand advertising platforms.

Walking over disconnected footholds requires selecting landing regions while adapting step timing to the robot's motion. We present a perceptive model predictive planner that combines discrete region selection, foot placement, and current-step duration in a mixed-integer quadratic program using step-to-step Divergent Component of Motion (DCM) dynamics. Onboard depth data are fused into a probabilistic heightmap in the stance foot frame. Convex steppable regions are extracted and shrunk by margins that increase with estimated height uncertainty. Linear constraints impose capturability-based bounds on DCM evolution and limit swing-foot retargeting using the remaining commanded swing time. Within-step replanning updates the initial DCM from measurements to respond to model mismatch and disturbances. We evaluate the framework on Digit in simulation over randomized footholds and on hardware over separated plates, with mean planner solve times of 11.4ms and 4.0ms, respectively.

Collaborative transportation of heavy payloads via loco-manipulation is a challenging yet essential capability for legged robots operating in complex, unstructured environments. Centralized planning methods, e.g., holistic trajectory optimization, capture dynamic coupling among robots and payloads but scale poorly with system size, limiting real-time applicability. In contrast, hierarchical and fully decentralized approaches often neglect force and dynamic interactions, leading to conservative behavior. This study proposes an Alternating Direction Method of Multipliers (ADMM)-based distributed model predictive control framework for collaborative loco-manipulation with a team of quadruped robots with manipulators. By exploiting the payload-induced coupling structure, the global optimal control problem is decomposed into parallel individual-robot-level subproblems with consensus constraints. The distributed planner operates in a receding-horizon fashion and achieves fast convergence, requiring only a few ADMM iterations per planning cycle. A wrench-aware whole-body controller executes the planned trajectories, tracking both motion and interaction wrenches. Extensive simulations with up to four robots demonstrate scalability, real-time performance, and robustness to model uncertainty.

Signal Temporal Logic (STL) is expressive formal language that specifies spatio-temporal requirements in robotics. Its quantitative robustness semantics can be easily integrated with optimization-based control frameworks. However, STL specifications may become conflicting in real-world applications, where safety rules, traffic regulations, and task objectives can be cannot be satisfied together. In these situations, traditional STL-constrained Model Predictive Control (MPC) becomes infeasible and default to conservative behaviors such as freezing, which can largely increase risks in safety-critical scenarios. In this paper, we proposes a unified two-stage framework that first restores feasibility via minimal relaxation, then refine the feasible solution by formulating it as a value-aware multi-objective optimization problem. Using $\varepsilon$-constraint method, we approximate the Pareto front of the multi-objective optimization, which allows analysis of tradeoffs among competing objectives and counterfactual analysis of alternative actions. We demonstrate that the proposed approach avoids deadlock under conflicting STL specifications and enables interpretable decision-making in safety-critical applications by conducting a case study in autonomous driving.

Fully actuated omnidirectional UAVs enable independent control of forces and torques along all six degrees of freedom, broadening the operational envelope for agile flight and aerial interaction tasks. However, conventional control allocation methods neglect the asymmetric dynamics of the onboard actuators, which can induce oscillatory motor commands and degrade trajectory tracking during dynamic maneuvers. This work proposes a receding-horizon, actuation-aware allocation strategy that explicitly incorporates asymmetric motor dynamics and exploits the redundancy of over-actuated platforms through nullspace optimization. By forward-simulating the closed-loop system over a prediction horizon, the method anticipates actuator-induced oscillations and suppresses them through smooth redistribution of motor commands, while preserving the desired body wrench exactly. The approach is formulated as a constrained optimal control problem solved online via Constrained iterative LQR. Simulation results on the OmniOcta platform demonstrate that the proposed method significantly reduces motor command oscillations compared to a conventional single-step quadratic programming allocator, yielding improved trajectory tracking in both position and orientation.

Obstacle avoidance of polytopic obstacles by polytopic robots is a challenging problem in optimization-based control and trajectory planning. Many existing methods rely on smooth geometric approximations, such as hyperspheres or ellipsoids, which allow differentiable distance expressions but distort the true geometry and restrict the feasible set. Other approaches integrate exact polytope distances into nonlinear model predictive control (MPC), resulting in nonconvex programs that limit real-time performance. In this paper, we construct linear discrete-time control barrier function (DCBF) constraints by deriving supporting hyperplanes from exact closest-point computations between convex polytopes. We then propose a novel iterative convex MPC-DCBF framework, where local linearization of system dynamics and robot geometry ensures convexity of the finite-horizon optimization at each iteration. The resulting formulation reduces computational complexity and enables fast online implementation for safety-critical control and trajectory planning of general nonlinear dynamics. The framework extends to multi-robot and three-dimensional environments. Numerical experiments demonstrate collision-free navigation in cluttered maze scenarios with millisecond-level solve times.

Contact-rich micromanipulation in microfluidic flow is challenging because small disturbances can break pushing contact and induce large lateral drift. We study planar cell pushing with a magnetic rolling microrobot that tracks a waypoint-sampled reference curve under time-varying Poiseuille flow in simulation. We propose a hybrid controller that augments a nominal MPC with a learned residual policy trained by SAC. The policy outputs a bounded 2D velocity correction that is contact-gated, so residual actions are applied only during robot-cell contact, preserving reliable approach behavior and stabilizing learning. All methods share the same actuation interface and speed envelope for fair comparisons. Simulation results show improved robustness and tracking accuracy over pure MPC and PID under nonstationary flow, with generalization from a clover training curve to unseen circle and square trajectories. A residual-bound sweep identifies an intermediate correction limit as the best trade-off, which we use in all benchmarks.

Magnetically actuated fish-like robots offer promising solutions for underwater exploration due to their miniaturization and agility; however, precise control remains a significant challenge because of nonlinear fluid dynamics, flexible fin hysteresis, and the variable-duration control steps inherent to the actuation mechanism. This paper proposes a comprehensive data-driven control framework to address these complexities without relying on analytical modeling. Our methodology comprises three core components: 1) developing a forward dynamics model (FDM) using a neural network trained on real-world experimental data to capture state transitions under varying time steps; 2) integrating this FDM into a gradient-based model predictive control (G-MPC) architecture to optimize control inputs for path following; and 3) applying imitation learning to approximate the G-MPC policy, thereby reducing the computational cost for real-time implementation. We validate the approach through simulations utilizing the identified dynamics model. The results demonstrate that the G-MPC framework achieves accurate path convergence with minimal root mean square error (RMSE), and the imitation learning controller (ILC) effectively replicates this performance. This study highlights the potential of data-driven control strategies for the precise navigation of miniature, fish-like soft robots.

Model Predictive Control (MPC) is a vital technique for autonomous systems, like Unmanned Aerial Vehicles (UAVs), enabling optimized motion planning. However, traditional MPC struggles to adapt to real-time changes such as dynamic obstacles and shifting system dynamics, lacking inherent mechanisms for self-monitoring and adaptive optimization. Here, we introduce Entanglement Learning (EL), an information-theoretic framework that enhances MPC adaptability through an Information Digital Twin (IDT). The IDT monitors and quantifies, in bits, the information flow between MPC inputs, control actions, and UAV behavior. By introducing new information-theoretic metrics we call entanglement metrics, it tracks variations in these dependencies. These metrics measure the mutual information between the optimizer's input, its control actions, and the resulting UAV dynamics, enabling a deeper understanding of their interrelationships. This allows the IDT to detect performance deviations and generate real-time adaptive signals to recalibrate MPC parameters, preserving stability. Unlike traditional MPC, which relies on error-based feedback, this dual-feedback approach leverages information flow for proactive adaptation to evolving conditions. Scalable and leveraging existing infrastructure, this framework improves MPC reliability and robustness across diverse scenarios, extending beyond UAV control to any MPC implementation requiring adaptive performance.

Navigating social robots in dense, dynamic crowds is challenging due to environmental uncertainty and complex human-robot interactions. While Model Predictive Control (MPC) offers strong real-time performance, its reliance on a fixed prediction horizon limits adaptability to changing environments and social dynamics. Furthermore, most MPC approaches treat pedestrians as homogeneous obstacles, ignoring social heterogeneity and cooperative or adversarial interactions, which often causes the Frozen Robot Problem in partially observable real-world environments. In this paper, we identify the planning horizon as a socially conditioned decision variable rather than a fixed design choice. Building on this insight, we propose an optimal-horizon social navigation framework that optimizes MPC foresight online according to inferred social context. A spatio-temporal Transformer infers pedestrian cooperation attributes from local trajectory observations, which serve as social priors for a reinforcement learning policy that optimally selects the prediction horizon under a task-driven objective. The resulting horizon-aware MPC incorporates socially conditioned safety constraints to balance navigation efficiency and interaction safety. Extensive simulations and real-world robot experiments demonstrate that optimal foresight selection is critical for robust social navigation in partially observable crowds. Compared to state-of-the-art baselines, the proposed approach achieves a 6.8% improvement in success rate, reduces collisions by 50%, and shortens navigation time by 19%, with a low timeout rate of 0.8%, validating the necessity of socially optimal planning horizons for efficient and safe robot navigation in crowded environments. Code and videos are available at Under Review.

With advances in imitation learning (IL) and large-scale driving datasets, end-to-end autonomous driving (E2E-AD) has made great progress recently. Currently, IL-based methods have become a mainstream paradigm: models rely on standard driving behaviors given by experts, and learn to minimize the discrepancy between their actions and expert actions. However, this objective of "only driving like the expert" suffers from limited generalization: when encountering rare or unseen long-tail scenarios outside the distribution of expert demonstrations, models tend to produce unsafe decisions in the absence of prior experience. This raises a fundamental question: Can an E2E-AD system make reliable decisions without any expert action supervision? Motivated by this, we propose a unified framework named Risk-aware World Model Predictive Control (RaWMPC) to address this generalization dilemma through robust control, without reliance on expert demonstrations. Practically, RaWMPC leverages a world model to predict the consequences of multiple candidate actions and selects low-risk actions through explicit risk evaluation. To endow the world model with the ability to predict the outcomes of risky driving behaviors, we design a risk-aware interaction strategy that systematically exposes the world model to hazardous behaviors, making catastrophic outcomes predictable and thus avoidable. Furthermore, to generate low-risk candidate actions at test time, we introduce a self-evaluation distillation method to distill riskavoidance capabilities from the well-trained world model into a generative action proposal network without any expert demonstration. Extensive experiments show that RaWMPC outperforms state-of-the-art methods in both in-distribution and out-of-distribution scenarios, while providing superior decision interpretability.

We present a runtime efficient algorithm for autonomous helicopter landings on moving ship decks based on Shrinking-Horizon Model Predictive Control (SHMPC). First, a suitable planning model capturing the relevant aspects of the full nonlinear helicopter dynamics is derived. Next, we use the SHMPC together with a touchdown controller stage to ensure a pre-specified maneuver time and an associated landing time window despite the presence of disturbances. A high disturbance rejection performance is achieved by designing an ancillary controller with disturbance feedback. Thus, given a target position and time, a safe landing with suitable terminal conditions is be guaranteed if the initial optimization problem is feasible. The efficacy of our approach is shown in simulation where all maneuvers achieve a high landing precision in strong winds while satisfying timing and operational constraints with maximum computation times in the millisecond range.

The control of high-dimensional systems, such as soft robots, requires models that faithfully capture complex dynamics while remaining computationally tractable. This work presents a framework that integrates Graph Neural Network (GNN)-based dynamics models with structure-exploiting Model Predictive Control to enable real-time control of high-dimensional systems. By representing the system as a graph with localized interactions, the GNN preserves sparsity, while a tailored condensing algorithm eliminates state variables from the control problem, ensuring efficient computation. The complexity of our condensing algorithm scales linearly with the number of system nodes, and leverages Graphics Processing Unit (GPU) parallelization to achieve real-time performance. The proposed approach is validated in simulation and experimentally on a physical soft robotic trunk. Results show that our method scales to systems with up to 1,000 nodes at 100 Hz in closed-loop, and demonstrates real-time reference tracking on hardware with sub-centimeter accuracy, outperforming baselines by 63.6%. Finally, we show the capability of our method to achieve effective full-body obstacle avoidance.

The sudden appearance of a static obstacle on the road, i.e. the moose test, is a well-known emergency scenario in collision avoidance for automated driving. Model Predictive Control (MPC) has long been employed for planning and control of automated vehicles in the state of the art. However, real-time implementation of automated collision avoidance in emergency scenarios such as the moose test remains unaddressed due to the high computational demand of MPC for evasive action in such hazardous scenarios. This paper offers new insights into real-time collision avoidance via the experimental imple- mentation of MPC for motion planning after a sudden and unexpected appearance of a static obstacle. As the state-of-the-art nonlinear MPC shows limited capability to provide an acceptable solution in real-time, we propose a human-like feed-forward planner to assist when the MPC optimization problem is either infeasible or unable to find a suitable solution due to the poor quality of its initial guess. We introduce the concept of maximum steering maneuver to design the feed-forward planner and mimic a human-like reaction after detecting the static obstacle on the road. Real-life experiments are conducted across various speeds and level of emergency using FPEV2-Kanon electric vehicle. Moreover, we demonstrate the effectiveness of our planning strategy via comparison with the state-of- the-art MPC motion planner.

SLOT (Soft Legged Omnidirectional Tetrapod), a tendon-driven soft quadruped robot with 3D-printed TPU legs, is presented to study physics-informed modeling and control of compliant legged locomotion using only four actuators. Each leg is modeled as a deformable continuum using discrete Cosserat rod theory, enabling the capture of large bending deformations, distributed elasticity, tendon actuation, and ground contact interactions. A modular whole-body modeling framework is introduced, in which compliant leg dynamics are represented through physically consistent reaction forces applied to a rigid torso, providing a scalable interface between continuum soft limbs and rigid-body locomotion dynamics. This formulation allows efficient whole-body simulation and real-time control without sacrificing physical fidelity. The proposed model is embedded into a convex model predictive control framework that optimizes ground reaction forces over a 0.495 s prediction horizon and maps them to tendon actuation through a physics-informed force-angle relationship. The resulting controller achieves asymptotic stability under diverse perturbations. The framework is experimentally validated on a physical prototype during crawling and walking gaits, achieving high accuracy with less than 5 mm RMSE in center of mass trajectories. These results demonstrate a generalizable approach for integrating continuum soft legs into model-based locomotion control, advancing scalable and reusable modeling and control methods for soft quadruped robots.

This paper proposes a nonplanar model predictive control (MPC) framework for autonomous vehicles operating on nonplanar terrain. To approximate complex vehicle dynamics in such environments, we develop a geometry-aware modeling approach that learns a residual Gaussian Process (GP). By utilizing a recursive sparse GP, the framework enables real-time adaptation to varying terrain geometry. The effectiveness of the learned model is demonstrated in a reference-tracking task using a Model Predictive Path Integral (MPPI) controller. Validation within a custom Isaac Sim environment confirms the framework's capability to maintain high tracking accuracy on challenging 3D surfaces.

Robots executing iterative tasks in complex, uncertain environments require control strategies that balance robustness, safety, and high performance. This paper introduces a safe information-theoretic learning model predictive control (SIT-LMPC) algorithm for iterative tasks. Specifically, we design an iterative control framework based on an information-theoretic model predictive control algorithm to address a constrained infinite-horizon optimal control problem for discrete-time nonlinear stochastic systems. An adaptive penalty method is developed to ensure safety while balancing optimality. Trajectories from previous iterations are utilized to learn a value function using normalizing flows, which enables richer uncertainty modeling compared to Gaussian priors. SIT-LMPC is designed for highly parallel execution on graphics processing units, allowing efficient real-time optimization. Benchmark simulations and hardware experiments demonstrate that SIT-LMPC iteratively improves system performance while robustly satisfying system constraints.

Reliable spacecraft attitude control depends on accurate prediction of attitude dynamics, particularly when model-based strategies such as Model Predictive Control (MPC) are employed, where performance is limited by the quality of the internal system model. For spacecraft with complex dynamics, obtaining accurate physics-based models can be difficult, time-consuming, or computationally heavy. Learning-based system identification presents a compelling alternative; however, models trained exclusively on data frequently exhibit fragile stability properties and limited extrapolation capability. This work explores Physics-Informed Neural Networks (PINNs) for modeling spacecraft attitude dynamics and contrasts it with a conventional data-driven approach. A comprehensive dataset is generated using high-fidelity numerical simulations, and two learning methodologies are investigated: a purely data-driven pipeline and a physics-regularized approach that incorporates prior knowledge into the optimization process. The results indicate that embedding physical constraints during training leads to substantial improvements in predictive reliability, achieving a 68.17% decrease in mean relative error relative. When deployed within an MPC architecture, the physics-informed models yield superior closed-loop tracking performance and improved robustness to uncertainty. Furthermore, a hybrid control formulation that merges the learned nonlinear dynamics with a nominal linear model enables consistent steady-state convergence and significantly faster response, reducing settling times by 61.52%-76.42% under measurement noise and reaction wheel friction.

Autonomous landing of Uncrewed Aerial Vehicles (UAVs) on oscillating marine platforms is severely constrained by wave-induced multi-frequency oscillations, wind disturbances, and prediction phase lags in motion prediction. Existing methods either treat platform motion as a general random process or lack explicit modeling of wave spectral characteristics, leading to suboptimal performance under dynamic sea conditions. To address these limitations, we propose SpecFuse: a novel spectral-temporal fusion predictive control framework that integrates frequency-domain wave decomposition with time-domain recursive state estimation for high-precision 6-DoF motion forecasting of Uncrewed Surface Vehicles (USVs). The framework explicitly models dominant wave harmonics to mitigate phase lags, refining predictions in real time via IMU data without relying on complex calibration. Additionally, we design a hierarchical control architecture featuring a sampling-based HPO-RRT* algorithm for dynamic trajectory planning under non-convex constraints and a learning-augmented predictive controller that fuses data-driven disturbance compensation with optimization-based execution. Extensive validations (2,000 simulations + 8 lake experiments) show our approach achieves a 3.2 cm prediction error, 4.46 cm landing deviation, 98.7% / 87.5% success rates (simulation / real-world), and 82 ms latency on embedded hardware, outperforming state-of-the-art methods by 44%-48% in accuracy. Its robustness to wave-wind coupling disturbances supports critical maritime missions such as search and rescue and environmental monitoring. All code, experimental configurations, and datasets will be released as open-source to facilitate reproducibility.

Continuum soft robots are inherently underactuated and subject to intrinsic input constraints, making dynamic control particularly challenging, especially in hybrid rigid-soft robots. While most existing methods focus on quasi-static behaviors, dynamic tasks such as swing-up require accurate exploitation of continuum dynamics. This has led to studies on simple low-order template systems that often fail to capture the complexity of real continuum deformations. Model-based optimal control offers a systematic solution; however, its application to rigid-soft robots is often limited by the computational cost and inaccuracy of numerical differentiation for high-dimensional models. Building on recent advances in the Geometric Variable Strain model that enable analytical derivatives, this work investigates three optimal control strategies for underactuated soft systems -- Direct Collocation, Differential Dynamic Programming, and Nonlinear Model Predictive Control -- to perform dynamic swing-up tasks. To address stiff continuum dynamics and constrained actuation, implicit integration schemes and warm-start strategies are employed to improve numerical robustness and computational efficiency. The methods are evaluated in simulation on three Rigid-Soft and high-order soft benchmark systems -- the Soft Cart-Pole, the Soft Pendubot, and the Soft Furuta Pendulum -- highlighting their performance and computational trade-offs.

A key challenge in contact-rich dexterous manipulation is the need to jointly reason over global geometry and nonsmooth contact dynamics. End-to-end policies bypass this complexity, but often require large amounts of data and transfer poorly from simulation to reality. We address the limitations with a simple insight: dexterous manipulation is inherently hierarchical--at a high level, a robot decides where to touch (geometry); at a low level it determines how to move the object through contact dynamics. Building on this insight, we propose a hierarchical RL--MPC framework in which a high-level reinforcement learning (RL) policy predicts a contact intention, a novel object-centric interface that specifies (i) an object-surface contact location and (ii) a post-contact object subgoal pose. Conditioned on the contact intention, a low-level contact-implicit model predictive control (MPC) optimizes local contact modes and real-time (re)plans through contact dynamics to generate robot actions that robustly move the object toward each subgoal. We evaluate the framework on non-prehensile tasks, including geometry-generalized pushing across diverse object shapes, pivoting/flipping-based object reorientation, and environment-assisted object repositioning. It achieves high success rate with substantially reduced data (10 times less than end-to-end baselines), highly robust performance, and zero-shot sim-to-real transfer.

MuJoCo is a powerful and efficient physics simulator widely used in robotics. One common way it is applied in practice is through Model Predictive Control (MPC), which uses repeated rollouts of the simulator to optimize future actions and generate responsive control policies in real time. To make this process more accessible, the open source library MuJoCo MPC (MJPC) provides ready-to-use MPC algorithms and implementations built directly on top of the MuJoCo simulator. However, MJPC relies on finite differencing (FD) to compute derivatives through the underlying MuJoCo simulator, which is often a key bottleneck that can make it prohibitively costly for time-sensitive tasks, especially in high-DOF systems or complex scenes. In this paper, we introduce the use of Web of Affine Spaces (WASP) derivatives within MJPC as a drop-in replacement for FD. WASP is a recently developed approach for efficiently computing sequences of accurate derivative approximations. By reusing information from prior, related derivative calculations, WASP accelerates and stabilizes the computation of new derivatives, making it especially well suited for MPC's iterative, fine-grained updates over time. We evaluate WASP across a diverse suite of MJPC tasks spanning multiple robot embodiments. Our results suggest that WASP derivatives are particularly effective in MJPC: it integrates seamlessly across tasks, delivers consistently robust performance, and achieves up to a 2$\mathsf{x}$ speedup compared to an FD backend when used with derivative-based planners, such as iLQG. In addition, WASP-based MPC outperforms MJPC's stochastic sampling-based planners on our evaluation tasks, offering both greater efficiency and reliability. To support adoption and future research, we release an open-source implementation of MJPC with WASP derivatives fully integrated.

Autonomous driving requires reliable collision avoidance in dynamic environments. Nonlinear Model Predictive Controllers (NMPCs) are suitable for this task, but struggle in time-critical scenarios requiring high frequency. To meet this demand, optimization problems are often simplified via linearization, narrowing the horizon window, or reduced temporal nodes, each compromising accuracy or reliability. This work presents the first general convex obstacle avoidance formulation, enabled by a novel approach to integrating logic. This facilitates the incorporation of an obstacle avoidance formulation into convex MPC schemes, enabling a convex optimization framework with substantially improved computational efficiency relative to conventional nonconvex methods. A key property of the formulation is that obstacle avoidance remains effective even when obstacles lie outside the prediction horizon, allowing shorter horizons for real-time deployment. In scenarios where nonconvex formulations are unavoidable, the proposed method meets or exceeds the performance of representative nonconvex alternatives. The method is evaluated in autonomous vehicle applications, where system dynamics are highly nonlinear.

Many aerial tasks involving quadrotors demand both instant reactivity and long-horizon planning for obstacle avoidance, energy efficiency, or trajectory tracking. High-fidelity models enable accurate control but are too slow for long horizons. Low-fidelity planners scale but cannot directly control the system, necessitating cascaded architectures. Prevailing hierarchical approaches plan with a simplified model and use a high-fidelity controller for tracking, yet this decomposition is inherently suboptimal. The controller is limited by the coarse plan, and conventional MPC alternatives shorten the horizon to stay real-time feasible. We present UNIQUE, an MPC architecture that replaces this hierarchical stacking with temporal cascading. The planning problem is formulated as the second-tail horizon of a single multi-phase MPC, rather than being solved separately. We align costs across horizons, derive feasibility constraints for the point-mass planning model, and introduce transition constraints that convert high-fidelity states into meaningful low-fidelity states. Parallel point-mass and mixed-integer solvers address nonconvexities while incorporating progressive 3D obstacle smoothing over the planning horizon. In simulations and real flights, under equal computational budgets, UNIQUE improves closed-loop tracking by up to 75% compared with standard MPC and hierarchical baselines. Ablations and Pareto analyses confirm performance gains across variations in horizon, constraint approximations, and smoothing schedules.

This paper presents an approach to mutual collision avoidance based on Nonlinear Model Predictive Control (NMPC) with time-dependent Reciprocal Velocity Constraints (RVCs). Unlike most existing methods, the proposed approach relies solely on observable information about other robots, eliminating the need for excessive communication. The computationally efficient algorithm for computing RVCs, together with the direct integration of these constraints into the NMPC problem formulation at the controller level, allows the whole pipeline to run at 100 Hz. This high processing rate, combined with modeled nonlinear dynamics of the controlled Uncrewed Aerial Vehicles (UAVs), is a key feature that facilitates the use of the proposed approach for agile UAV flight. The proposed approach was evaluated through extensive simulations emulating real-world conditions in scenarios involving up to 10 UAVs and velocities of up to 25 m/s, and in real-world experiments with accelerations up to 30 m/s$^2$. Comparison with the state of the art shows 31% improvement in terms of flight time reduction in challenging scenarios, while maintaining a collision-free navigation in all trials.

High-altitude balloons (HABs) are common in scientific research due to their wide range of applications and low cost. Because of their nonlinear, underactuated dynamics and the partial observability of wind fields, prior work has largely relied on model-free reinforcement learning (RL) methods to design near-optimal control schemes for station-keeping. These methods often compare only against hand-crafted heuristics, dismissing model-based approaches as impractical given the system complexity and uncertain wind forecasts. We revisit this assumption about the efficacy of model-based control for station-keeping by developing First-Order Model Predictive Control (FOMPC). By implementing the wind and balloon dynamics as differentiable functions in JAX, we enable gradient-based trajectory optimization for online planning. FOMPC outperforms a state-of-the-art RL policy, achieving a 24% improvement in time-within-radius (TWR) without requiring offline training, though at the cost of greater online computation per control step. Through systematic ablations of modeling assumptions and control factors, we show that online planning is effective across many configurations, including under simplified wind and dynamics models.

Safe and efficient robotic navigation among humans is essential for integrating robots into everyday environments. Most existing approaches focus on simplified 2D crowd navigation and fail to account for the full complexity of human body dynamics beyond root motion. We present HumanHalo, an MPC framework for 3D MAV navigation among humans that combines theoretical safety guarantees with data-driven models for realistic human motion forecasting. Our approach introduces a novel reachability-based safety formulation that constrains only the initial control input for safety while modeling its effects over the entire planning horizon, enabling safe yet efficient navigation. We validate HumanHalo in both simulated experiments using real human trajectories and in the real world, demonstrating its effectiveness across tasks ranging from goal-directed navigation to visual servoing for human tracking. While we apply our method to MAV in this work, it is generic and can be adapted to other platforms. Our results show that the method preserves safety without excessive conservatism, even under imperfect human prediction and in constrained workspaces, while remaining efficient enough for real-time onboard execution.