Z. Li | TU Delft Repository

Geometry-Aware Edge-State Tracking for Robust Affine Formation Control

Journal article (2026) - Z. Li, R. T. Rajan

Affine formation control (AFC) is a subset of formation control methods that enables coordinated multiagent movement while preserving affine relationships, and has recently gained increasing popularity due to its utility across diverse applications. AFC is inherently distributed, where each agent's local controller relies on the relative displacements of neighboring agents. The unavailability of these measurements in practice, due to node or communication failures, leads to a change in the underlying graph topology and subsequently causes instability or sub-optimal performance. In this work, each edge in the graph is modeled using a state-space framework, allowing the corresponding edge-states to be estimated with or without up-to-date measurements. We then propose a Kalman-based estimation framework where we fuse both temporal information from agents' dynamics and spatial information, which is derived from the geometry of the affine formations. We give convergence guarantees and optimality analysis on the proposed algorithm, and numerical validations show the enhanced robustness of AFC against these topology changes in several practical scenarios. ...

Reliable Maintenance Policy for Distributed Affine Formation Control of UAVs

Conference paper (2026) - H. Zhou, Z. Li, R. T. Rajan

Distributed affine formation control (AFC) enables unmanned aerial vehicle (UAV) swarms to achieve coordinated motion while maintaining a desired geometric configuration, thereby enhancing their maneuverability. However, conventional leader-follower-based distributed AFC remains vulnerable to dynamic changes in the network topology, where UAVs may be temporarily unavailable due to maintenance in real-world applications. In this work, we propose a reliable maintenance policy that enables individual UAVs to detach from the swarm without compromising the formation stability. Our policy introduces an agent homogenization strategy that replaces the conventional leader UAVs with virtual leaders, thereby ensuring all operational UAVs are followers and thus eligible for maintenance. A relative affine localization (RAL) technique is employed, which allows the remaining UAVs to estimate the relative positions of missing neighbors by leveraging the formation geometry. Our proposed framework is validated through a series of experiments with a swarm of Crazyflie quadrotors in an indoor environment, which demonstrate the effectiveness of our policy that allows individual UAVs to be removed and returned in sequence while the rest of the swarm maintains its target configuration with high accuracy. Our proposed maintenance policy enables robust and long-duration deployments of UAV swarms in inaccessible and harsh environments. ...

Fast Multiagent Formation Stabilization with Sparse Universally Rigid Frameworks

Conference paper (2025) - Z. Li, G.J.T. Leus, R.T. Rajan

Affine formation control (AFC) is a distributed networked control system that has recently received increasing attention in various applications. AFC is typically achieved using a generalized consensus system where the stress matrix, which encodes the graph structure, is used instead of a graph Laplacian. Universally rigid frameworks (URFs) guarantee the existence of the stress matrix and have thus become the guideline for such a network design. In this work, we propose a convex optimization framework to design the stress matrix for AFC without predefining a rigid graph. We aim to find a resulting network with a reduced number of communication links, but still with a fast convergence speed. We show through simulations that our proposed solutions can yield a more sparse graph, while admitting a faster convergence compared to the state-of-the-art solutions. ...

Robust Affine Formation Control of Multiagent Systems

Other (2024) - Z. Li, R.T. Rajan

On the Stability of Consensus Control Under Rotational Ambiguities

Journal article (2024) - Zhonggang Li, Changheng Li, Raj Thilak Rajan

Consensus control of multiagent systems arises in various applications such as rendezvous and formation control. The input to these algorithms, e.g., the (relative) positions of neighboring agents need to be measured using various sensors. Recent works aim to reconstruct these positions, i.e., achieve localization using Euclidean distance measurements instead of displacements, for cost efficiency and scalability. However, this approach inherently introduces ambiguities, such as a rotation or a reflection, which can cause stability issues in practice without corrections by some anchors. In this letter, we conduct a thorough analysis of the stability of consensus control in the presence of localization-induced rotational ambiguities, in several scenarios including, e.g., proper and improper rotation, and the homogeneity of rotations. We give stability criteria and stability margin on the rotations, which are numerically verified with two traditional examples of consensus control. ...

Asymmetrical Modular Multilevel Converter with Sensorless Voltage Control for High-Quality Output

Conference paper (2022) - Zhongxi Li, Zhonggang Li, Nima Tashakor, Angel Peterchev, Stefan M. Goetz

The paper proposes an Asymmetrical Modular Multilevel Converter (AMMC) suitable for low/medium-voltage dc-ac conversions with very high output quality. The modules' dc-links of the AMMC are charged to a binary exponential sequence to produce a large number of output levels using only a few modules.The concept of using asymmetrical dc-links for high-quality output is not entirely new. However, the practicality of existing approaches is relatively low and challenged by the difficulties in maintaining the required dc-link voltages as well as suppressing their interaction with the output, which often requires multiple isolated dc/dc converters. We solve this problem by aligning the modules in the Marquardt MMC inverter module configuration that offers more control freedom, hence the term AMMC. Furthermore, we introduce a highly effective switched-inductor charge transfer and balancing mode between modules and even across arms. We accordingly modify the underlying conventional chopper modules so that the dc-link voltage control can be completely sensorless. The proposed AMMC is tested in a lab setup with four modules per arm reaching 32 output levels. In contrast to the low benefit of an additional module in MMC due to only linear improvement of the output granularity, each further module halves the finest voltage step. The components to maintain the graded voltage sequence and the underlying inductive charge transfer only a fraction (< 10%) of the load current so that relatively low-power devices can be used. ...