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1. Trajectory Generation on SE(3) for an Underactuated Vehicle with Pointing Direction Constraints

   https://doi.org/10.23919/ACC.2019.8815238  

   Dhullipalla, Mani H.; Hamrah, Reza; Warier, Rakesh R.; Sanyal, Amit K. (July 2019, 2019 American Control Conference (ACC))

   This paper addresses the problem of generating a position trajectory with pointing direction constraints at given waypoints for underactuated unmanned vehicles. The problem is initially posed on the configuration space ℝ 3 × ℝ 2 and thereafter, upon suitable modifications, is re-posed as a problem on the Lie group SE(3). This is done by determining a vector orthogonal to the pointing direction and using it as the vehicle's thrust direction. This translates to converting reduced attitude constraints to full attitude constraints at the waypoints. For the position trajectory, in addition to position constraints, this modification adds acceleration constraints at the waypoints. For real-time implementation with low computational expenses, a linear-quadratic regulator (LQR) approach is adopted to determine the position trajectory with smoothness upto the fourth time derivative of position (snap). For the attitude trajectory, the thrust direction extracted from the position trajectory is used to first propagate the attitude to the subsequent waypoint and then correct it over time to achieve the desired attitude at this waypoint. Finally, numerical simulation results are presented to validate the trajectory generation scheme. 

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2. A Data-driven Approach for Constrained Infinite-Horizon Linear Quadratic Regulation

   https://doi.org/10.1109/CDC42340.2020.9304046  

   Pang, Bo; Jiang, Zhong-Ping (December 2020, Proc. 59th IEEE Conference on Decision and Control)

   null (Ed.)

   This paper presents a data-driven algorithm to solve the problem of infinite-horizon linear quadratic regulation (LQR), for a class of discrete-time linear time-invariant systems subjected to state and control constraints. The problem is divided into a constrained finite-horizon LQR subproblem and an unconstrained infinite-horizon LQR subproblem, which can be solved directly from collected input/state data, separately. Under certain conditions, the combination of the solutions of the subproblems converges to the optimal solution of the original problem. The effectiveness of the proposed approach is validated by a numerical example. 

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3. 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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4. Convergent iLQR for Safe Trajectory Planning and Control of Legged Robots

   Zhu, James; Payne, J Joe; Johnson, Aaron M (May 2024, IEEE International Conference on Robotics and Automation)

   In order to perform highly dynamic and agile maneuvers, legged robots typically spend time in underactuated domains (e.g. with feet off the ground) where the system has limited command of its acceleration and a constrained amount of time before transitioning to a new domain (e.g. foot touchdown). Meanwhile, these transitions can instantaneously change the system’s state, possibly causing perturbations to be mapped arbitrarily far away from the target trajectory. These properties make it difficult for local feedback controllers to effectively recover from disturbances as the system evolves through underactuated domains and hybrid impact events. To address this, we utilize the fundamental solution matrix that characterizes the evolution of perturbations through a hybrid trajectory and its 2-norm, which represents the worst-case growth of perturbations. In this paper, the worst-case perturbation analysis is used to explicitly reason about the tracking performance of a hybrid trajectory and is incorporated in an iLQR framework to optimize a trajectory while taking into account the closed-loop convergence of the trajectory under an LQR tracking controller. The generated convergent trajectories recover more effectively from perturbations, are more robust to large disturbances, and use less feedback control effort than trajectories generated with traditional methods. 

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5. Augmented Physics-Based Models for High-Order Markov Filtering

   https://doi.org/10.3390/s24186132  

   Tang, Shuo; Imbiriba, Tales; Duník, Jindřich; Straka, Ondřej; Closas, Pau (September 2024, Sensors)

   Hybrid physics-based data-driven models, namely, augmented physics-based models (APBMs), are capable of learning complex state dynamics while maintaining some level of model interpretability that can be controlled through appropriate regularizations of the data-driven component. In this article, we extend the APBM formulation for high-order Markov models, where the state space is further augmented with past states (AG-APBM). Typically, state augmentation is a powerful method for state estimation for a high-order Markov model, but it requires the exact knowledge of the system dynamics. The proposed approach, however, does not require full knowledge of dynamics, especially the Markovity order. To mitigate the extra computational burden of such augmentation we propose an approximated-state APBM (AP-APBM) implementation leveraging summaries from past time steps. We demonstrate the performance of AG- and AP-APBMs in an autoregressive model and a target-tracking scenario based on the trajectory of a controlled aircraft with delay-feedback control. The experiments showed that both proposed strategies outperformed the standard APBM approach in terms of estimation error and that the AP-APBM only degraded slightly when compared to AG-APBM. For example, the autoregressive (AR) model simulation in our settings showed that AG-APBM and AP-APBM reduced the estimate error by 31.1% and 26.7%. The time cost and memory usage were reduced by 37.5% and 20% by AP-APBM compared to AG-APBM. 

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