Lightweight Model Predictive Control for Spacecraft Rendezvous Attitude Synchronization

Peter Stadler; Alexander Meinert; Niklas Baldauf; Alen Turnwald

cs.ROMar 19, 2026

Lightweight Model Predictive Control for Spacecraft Rendezvous Attitude Synchronization

Authors: Peter Stadler, Alexander Meinert, Niklas Baldauf, Alen Turnwald

Organizations: Space Applications Group, e:fs TechHub GmbH, 85080 Gaimersheim, Germany · Faculty of Electrical Engineering and Information Technology, Ingolstadt University of Applied Sciences, Germany

Abstract

This work introduces two lightweight model predictive control (MPC) approaches for attitude tracking with reaction wheels during spacecraft rendezvous synchronization. Both approaches are based on a novel attitude deviation formulation, which enables the use of inherently linear constraints on angular velocity. We develop a single-loop and a dual-loop MPC; the latter embeds a stabilizing feedback controller within the inner loop, yielding a linear time-invariant system. Both controllers are implemented with CasADi - including automatic code generation - evaluated across various solvers, and validated within the Basilisk astrodynamics simulation framework. The experimental results demonstrate improved tracking accuracy alongside reductions in computational effort and memory consumption. Finally, embedded delivery to an ARM Cortex-M7 - representative of commercial off-the-shelf devices used in New Space platforms - confirms the real-time feasibility of these approaches and highlights their suitability for onboard attitude control in resource-constrained spacecraft rendezvous missions.

Figures & tables

Figure 1: Layouts of the Proposed Linear MPCs for Attitude Tracking Both designs use the same reference trajectory, the same constraints, and the proposed error system based on the attitude deviation in reverse order. (a) The single-loop MPC ( 7 ) directly uses the error system linearized at zero: The model for the predictions is a discretization of the affine but parameter-varying (LPV) error system ( 5 ). (b) The dual-loop MPC ( 11 ) linearizes and discretizes an already stable inner loop for the MPC in the outer loop. The inner system is the closed loop of the error system with the stable feedback controller ( 8 ), which also eliminates the parameter variance. The linearization of the inner loop results in the stable and time-invariant (LTI) system ( 10 ).

Figure 2: Attitude Tracking Quality of Different MPCs in Simulation with Basilisk The proposed dual-loop MPC and the single-loop MPC are quite similar and better than the previous MPC from [ 7 ] . For the former two MPCs, the deviations of both attitude and angular speed fall faster with time and the effort measured as accumulated torque is slightly lower. The angular velocity error for the previous MPC must be linearized. This makes it difficult to constrain the angular velocity exactly; here,

\omega_{z}

exceeds the upper bound (highlighted).

Figure 3: Workload of Different MPCs in C++ on Intel i7-11850H The proposed dual-loop MPC is faster than the previous MPC. For horizons less than 20 steps, the single-loop MPC is as slow as the previous MPC. For larger horizons, the runtimes of the single-loop MPC and the proposed dual-loop MPC are similarly low, while the compiled size of the dual-loop MPC is smaller. For each algorithm and horizon, we choose the solver and sparsity pattern yielding the best runtime. The solver switches at 20 steps for the proposed dual-loop MPC and at 40 steps for previous MPC yield visible changes in runtimes distribution and compiled size.

Figure 4: Sparsities of the Dual-Loop MPC with a Horizon of $N=20$ Steps The optimal solution to a quadratic program remains unchanged if we condense some optimization variables. However, the corresponding constraint and cost matrices change in size (gray) and non-zero entries (black). We use any number of blocks that can be generated for a given horizon. The patterns vary from $N$ blocks for the sparse formulation to one block for the dense formulation.

Figure 5: Runtimes of Dual-Loop MPC with CasADi on Intel i7-11850H For each solver and horizon, we selected the sparsity formulation that yields the lowest runtime. We divided the solvers into two plots: those using condensed matrices (solid lines) and those using sparser matrices (dashed lines). In each case, preparation accounts for only a fraction of the total runtime (note the logarithmic scale). DAQP and qpOASES are the fastest for smaller horizons. Yet, the latter exhibits high variation in runtime; computing the initial solution is particularly expensive. ProxQP and OSQP are the fastest for larger horizons, though the runtimes of the former vary less. All of them have lower mean runtimes than HPIPM and HiGHS. However, the former exhibits low variation in runtime, and for larger horizons its maximum runtime is lower than that of qpOASES and OSQP. No violin plots are shown for SuperSCS, QRQP, or ipqp at horizons for which they failed to solve all quadratic programs.

Figure 6: Workload of Dual-Loop MPC in C++ on Intel i7-11850H DAQP is the fastest solver for smaller horizons, where it can benefit from a dense formulation. However, sparser formulations scale better, and OSQP is faster from 20 steps onwards. The runtime of qpOASES falls between the two. Its runtime is slightly higher only at 20 steps, albeit with high variance. QRQP succeeded only for small horizons and was slower than the other solvers. The compiled size for DAQP and qpOASES grows much faster with the horizon than for OSQP. This is particularly relevant for deployment on embedded devices with more restricted memory.

Figure 7: Workload of Dual-Loop MPC in C++ on ARM Cortex M-7 For all selected solvers, the fast memory (RAM1) is the limiting resource for the horizon. The memory consumption is about linear for OSQP, which benefits from a sparser formulation. In contrast, it increases more with the horizon for DAQP and qpOASES as they work with dense matrices. When it has enough memory, DAQP is best suited (up to 20 steps). OSQP works up to 30 steps, where we would expect it to be the fastest solver, too. However, the other solvers cannot run there: QRQP could not solve all arising quadratic programs even for small horizons, and qpOASES runs out of memory after 15 steps. At 15 steps, qpOASES has the lowest mean runtime but with high variation.

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AI-Augmented Model Predictive Control for Safe and Adaptive Rendezvous and Proximity Operations

Luca Sportelli, Tyler Barr, Cagri Kilic, Di Wu

Department of Aerospace Engineering, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114

Spacecraft Rendezvous and Proximity Operations Multi-Agent Control Model Predictive Control Adaptive Control

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Autonomous rendezvous and proximity operations (RPO) in adversarial orbital environments require guidance architectures balancing target pursuit, safety preservation, and real-time adaptability under dynamically evolving interaction conditions. Although learning-based approaches show promise, their application to safety-critical orbital robotics remains limited by concerns regarding interpretability, robustness, and constraint awareness. This work presents an adaptive Model Predictive Control (MPC) framework for autonomous spacecraft RPO in multi-agent adversarial scenarios. The proposed architecture combines a constrained receding-horizon MPC formulation with a data-driven supervisory tuning layer that adjusts controller parameters from offline closed-loop evaluation and online interaction geometry. Relative motion follows Clohessy-Wiltshire (CW) dynamics, enabling computationally efficient finite-horizon prediction and real-time quadratic optimization. The MPC formulation incorporates actuator limits, predictive keep-out-zone constraints, slack-variable feasibility handling, and optional Control Barrier Function (CBF) safety filtering. Rather than generating thrust commands directly, the adaptive layer modifies interpretable MPC parameters, including tracking weights, safety penalties, minimum-separation objectives, and keep-out-zone objectives. The framework was evaluated in the official Kerbal Space Program Differential Game (KSPDG) Capture-the-Satellite environment through Monte Carlo simulations. Results demonstrate improved closed-loop robustness, adaptive maneuvering behavior, and rendezvous performance compared with fixed-parameter MPC while preserving safety-aware operation and real-time feasibility, providing a modular, interpretable foundation for adaptive spacecraft RPO.

Abstract

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