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1. Implicit Trajectory Planning for Feedback Linearizable Systems: A Time-varying Optimization Approach

   https://doi.org/10.23919/ACC45564.2020.9147997  

   Zheng, Tianqi; Simpson-Porco, John; Mallada, Enrique (July 2020, American Control Conference)

   We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints. 

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2. Density-Driven Multi-Agent Swarm Control with Potential Field Based Collision Avoidance

   https://doi.org/10.1109/UEMCON59035.2023.10316140  

   Seo, Sungjun; Lee, Kooktae (October 2023, IEEE)

   In this paper, a density-driven multi-agent swarm control problem is investigated. Robot swarms can provide a great benefit, especially for applications where a single robot cannot effectively achieve a given task. For large spatial-scale applications such as search and rescue, environmental monitoring, and surveillance, a new multi-agent swarm control strategy is necessary because of physical constraints including a robot number and operation time. This paper provides a novel density-driven swarm control strategy for multi-agent systems based on the Optimal Transport theory, to cover a spacious domain with limited resources. In such a scenario, \textit{efficiency} will likely be a key point in achieving an efficient robot swarm behavior rather than uniform coverage that might be infeasible. With the given reference density, pre-constructed from available information, the proposed swarm control method will drive the multi-agent system such that their time-averaged behavior becomes similar to the reference density. In this way, density-driven swarm control will enable the multiple agents to spend most of their time on high-priority regions that are reflected in the reference density, leading to efficiency. To protect the agents from collisions, the Artificial Potential Field method is employed and combined with the proposed density-driven swarm control scheme. Simulations are conducted to validate density-driven swarm control as well as to test collision avoidance. Also, the swarm performance is analyzed by varying the agent number in the simulation. 

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3. Robust Trajectory Execution for Multi-robot Teams Using Distributed Real-time Replanning

   https://doi.org/10.1007/978-3-030-05816-6_12  

   Şenbaşlar, Baskın; Hönig, Wolfgang; Ayanian, Nora (October 2018, Distributed Autonomous Robotic Systems)

   Robust trajectory execution is an extension of cooperative collision avoidance that takes pre-planned trajectories directly into account. We propose an algorithm for robust trajectory execution that compensates for a variety of dynamic changes, including newly appearing obstacles, robots breaking down, imperfect motion execution, and external disturbances. Robots do not communicate with each other and only sense other robots’ positions and the obstacles around them. At the high-level we use a hybrid planning strategy employing both discrete planning and trajectory optimization with a dynamic receding horizon approach. The discrete planner helps to avoid local minima, adjusts the planning horizon, and provides good initial guesses for the optimization stage. Trajectory optimization uses a quadratic programming formulation, where all safety-critical parts are formulated as hard constraints. At the low-level, we use buffered Voronoi cells as a multi-robot collision avoidance strategy. Compared to ORCA, our approach supports higher-order dynamic limits and avoids deadlocks better. We demonstrate our approach in simulation and on physical robots, showing that it can operate in real time. 

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4. Robust Trajectory Execution for Multi-Robot Teams Using Distributed Real-time Replanning

   Baskın Senbaslar, Wolfgang Hoenig (October 2018, International Symposium on Distributed Autonomous Robotic Systems)

   Robust trajectory execution is an extension of cooperative collision avoidance that takes pre-planned trajectories directly into account. We propose an algorithm for robust trajectory execution that compensates for a variety of dynamic changes, including newly appearing obstacles, robots breaking down, imperfect motion execution, and external disturbances. Robots do not communicate with each other and only sense other robots’ positions and the obstacles around them. At the high-level we use a hybrid planning strategy employing both discrete planning and trajectory optimization with a dynamic receding horizon approach. The discrete planner helps to avoid local minima, adjusts the planning horizon, and provides good initial guesses for the optimization stage. Trajectory optimization uses a quadratic programming formulation, where all safety-critical parts are formulated as hard constraints. At the low-level, we use buffered Voronoi cells as a multi-robot collision avoidance strategy. Compared to ORCA, our approach supports higher-order dynamic limits and avoids deadlocks better. We demonstrate our approach in simulation and on physical robots, showing that it can operate in real time. 

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5. LeTO: Learning Constrained Visuomotor Policy With Differentiable Trajectory Optimization

   https://doi.org/10.1109/TASE.2024.3486542  

   Xu, Zhengtong; She, Yu (March 2025, IEEE Transactions on Automation Science and Engineering)

   This paper introduces LeTO, a method for learning constrained visuomotor policy with differentiable trajectory optimization. Our approach integrates a differentiable optimization layer into the neural network. By formulating the optimization layer as a trajectory optimization problem, we enable the model to end-to-end generate actions in a safe and constraint-controlled fashion without extra modules. Our method allows for the introduction of constraint information during the training process, thereby balancing the training objectives of satisfying constraints, smoothing the trajectories, and minimizing errors with demonstrations. This “gray box” method marries optimization-based safety and interpretability with powerful representational abilities of neural networks. We quantitatively evaluate LeTO in simulation and in the real robot. The results demonstrate that LeTO performs well in both simulated and real-world tasks. In addition, it is capable of generating trajectories that are less uncertain, higher quality, and smoother compared to existing imitation learning methods. Therefore, it is shown that LeTO provides a practical example of how to achieve the integration of neural networks with trajectory optimization. We release our code at https://github.com/ZhengtongXu/LeTO. 

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