For various typical cases and situations where the formulation results in an optimal control problem, the linear quadratic regulator (LQR) approach and its variants continue to be highly attractive. In certain scenarios, it can happen that some prescribed structural constraints on the gain matrix would arise. Consequently then, the algebraic Riccati equation (ARE) is no longer applicable in a straightforward way to obtain the optimal solution. This work presents a rather effective alternative optimization approach based on gradient projection. The utilized gradient is obtained through a data-driven methodology, and then projected onto applicable constrained hyperplanes. Essentially, this projection gradient determines a direction of progression and computation for the gain matrix update with a decreasing functional cost; and then the gain matrix is further refined in an iterative framework. With this formulation, a data-driven optimization algorithm is summarized for controller synthesis with structural constraints. This data-driven approach has the key advantage that it avoids the necessity of precise modeling which is always required in the classical model-based counterpart; and thus the approach can additionally accommodate various model uncertainties. Illustrative examples are also provided in the work to validate the theoretical results.

Trajectory planning is one of the indispensable and critical components in robotics and autonomous systems. As an efficient indirect method to deal with the nonlinear system dynamics in trajectory planning tasks over the unconstrained state and control space, the iterative linear quadratic regulator (iLQR) has demonstrated noteworthy outcomes. In this article, a local-learning-enabled constrained iLQR algorithm is herein presented for trajectory planning based on hybrid dynamic optimization and machine learning. Rather importantly, this algorithm attains the key advantage of circumventing the requirement of system identification, and the trajectory planning task is achieved with a simultaneous refinement of the optimal policy and the neural network system in an iterative framework. The neural network can be designed to represent the local system model with a simple architecture, and thus it leads to a sample-efficient training pipeline. In addition, in this learning paradigm, the constraints of the general form that are typically encountered in trajectory planning tasks are preserved. Several illustrative examples on trajectory planning are scheduled as part of the test itinerary to demonstrate the effectiveness and significance of this work.

This article involves the innovative development of a symmetric Gauss–Seidel ADMM algorithm to solve the$\mathcal {H}_{\infty }$guaranteed cost control problem. In the presence of parametric uncertainties, the$\mathcal {H}_{\infty }$guaranteed cost control problem generally leads to the large-scale optimization. This is due to the exponential growth of the number of the extreme systems involved with respect to the number of parametric uncertainties. In this work, through a variant of the Youla–Kucera parameterization, the stabilizing controllers are parameterized in a convex set; yielding the outcome that the$\mathcal {H}_{\infty }$guaranteed cost control problem is converted to a convex optimization problem. Based on an appropriate reformulation using the Schur complement, it then renders possible the use of the ADMM algorithm with symmetric Gauss–Seidel backward and forward sweeps. Significantly, this approach alleviates the often-times prohibitively heavy computational burden typical in many$\mathcal H_{\infty }$optimization problems while exhibiting good convergence guarantees, which is particularly essential for the related large-scale optimization procedures involved. With this approach, the desired robust stability is ensured, and the disturbance attenuation is maintained at the minimum level in the presence of parametric uncertainties. Rather importantly too, with the attained effectiveness, the methodology thus evidently possesses extensive applicability in various important controller synthesis problems, such as decentralized control, sparse control, and output feedback control problems.

In the context of autonomous driving, the iterative linear quadratic regulator (iLQR) is known to be an efficient approach to deal with the nonlinear vehicle model in motion planning problems. Particularly, the constrained iLQR algorithm has shown noteworthy advantageous outcomes of computation efficiency in achieving motion planning tasks under general constraints of different types. However, the constrained iLQR methodology requires a feasible trajectory at the first iteration as a prerequisite when the logarithmic barrier function is used. Also, the methodology leaves open the possibility for incorporation of fast, efficient, and effective optimization methods (i.e., fast-solvers) to further speed up the optimization process such that the requirements of real-time implementation can be successfully fulfilled. In this paper, a well-defined and commonly-encountered motion planning problem is formulated under nonlinear vehicle dynamics and various constraints, and the alternating direction method of multipliers (ADMM) is utilized to determine the optimal control actions leveraging the iLQR. With this development, the approach is able to circumvent the feasibility requirement of the trajectory at the first iteration. An illustrative example of motion planning for autonomous vehicles is then investigated with different driving scenarios taken into consideration, and a noteworthy achievement of high computation efficiency is attained with the proposed development. Comparing with the constrained iLQR algorithm based on the logarithmic barrier function, our proposed method reduces the average computation time by 31.93%, 38.52%, and 44.57% in the three scenarios; compared with the optimization solver IPOPT, our proposed method reduces the average computation time by 46.02%, 53.26%, and 88.43% in the three scenarios. As a result, real-time computation and implementation can be realized through our proposed framework, and thus it provides additional safety to the on-road driving tasks.

This paper investigates the cooperative planning and control problem for multiple connected autonomous vehicles (CAVs) in different scenarios. In the existing literature, most of the methods suffer from significant problems in computational efficiency. Furthermore, as the optimization problem is nonlinear and nonconvex, it typically poses great difficulty in determining the optimal solution. To address this issue, this work proposes a novel and completely parallel computation framework by leveraging the alternating direction method of multipliers (ADMM). The nonlinear and nonconvex optimization problem in the autonomous driving problem can be divided into two manageable sub-problems; and the resulting sub-problems can be solved by using effective optimization methods in a parallel framework. Here, the differential dynamic programming (DDP) algorithm is capable of addressing the nonlinearity of the system dynamics rather effectively; and the nonconvex coupling constraints with small dimensions can be resolved by invoking the notion of semi-definite relaxation (SDR), which can also be solved in a very short time. Due to the parallel computation and efficient relaxation of nonconvex constraints, our proposed approach effectively realizes real-time implementation; and thus extra assurance of driving safety is provided. In addition, two transportation scenarios for multiple CAVs are used to illustrate the effectiveness and efficiency of the proposed method.

In this work, an adaptive iterative sliding mode control method is proposed for multi-axis mechatronic systems. Commonly, the multi-axis mechatronic systems are applied in high-speed and high-precision contouring tasks. For such contouring tasks, the multi-axis coordination is a main issue. As an inevitable challenge, several factors affect the multi-axis coordinate and diminish the contouring performance. Also, some special mechanical structure brings strong coupling to the system, which makes the system identification rather difficult. To solve these problems, this work proposes a learning-based totally model-free control approach for contouring tasks in application to such multi-axis motion stages. With this approach, all the coupling, disturbance, nonlinearity, and other unknown dynamics are regarded as lumped uncertainties in each axis. As a result, these uncertainties can be attenuated and compensated by the proposed controller. To analyze the contouring performance, a case study of a flexure-linked dual-drive H-gantry system is investigated to illustrate the effectiveness of the proposed method.

Collaborative motion planning for multi-agent systems is a challenging problem because of the existence of highly nonlinear and nonconvex constraints. Such difficulties also lead to inavoidable computational inefficiency, which significantly prohibits applying the existing collaborative motion planning algorithms to complex scenarios. This paper proposes a parallel computational algorithm to achieve collaborative motion planning efficiently, considering the nonlinear dynamics model and the nonconvex collision-avoidance constraints. Specifically, the alternating direction method of multipliers (ADMM) framework is elegantly incorporated to separate the large-scale cooperative nonconvex planning problem as two tractable and manageable subproblems, where the two subproblems handle the dynamics constraints and collision-free constraints, respectively. In the proposed approach, the differential dynamic programming (DDP) method is utilized to effectively solve the nonlinear subproblem with the dynamics constraints; meanwhile, the interior point (IPOPT) method is employed to address the nonconvex subproblem derived from the collision-avoidance constraints. Finally, two simulation scenarios are successfully implemented to illustrate the effectiveness of the proposed algorithm.

A distributed optimization algorithm for a decentralized control problem for uncertain systems is investigated in this paper. Based on ℋ2formulation, the optimal control problem under parameter uncertainties can be reformulated and solved in parameter space. Besides, the stabilizing controller gains of the decentralized control system with parameter uncertainties can be parameterized in a convex set; thus, the decentralized control problem can be reformulated as a conic optimization problem, which can be solved by using the symmetric Gauss-Seidel (sGS) semi-proximal augmented Lagrangian method (sPALM) efficiently. Then, a comprehensive analysis is provided to employ the sGS-sPALM to find the optimal solution of the decentralized control problem under parameter uncertainties. Robust performance and robust stability can be guaranteed using this methodology while satisfying the sparsity constraints resulting from the decentralized structure. Two examples are used to illustrate the effectiveness of the proposed method.

For a specific class of under-actuated mechanical systems, non-holonomic servo constraints and model uncertainties are usually encountered. For such systems, this paper investigates the design of an adaptive robust controller with parameter optimization. A tighter link between the fuzzy set theory and the control of UMSs is bridged appropriately. Based on the UMSs with fuzzy information, an adaptive robust control method is then designed, and an analytical solution of the control input is determined, even if the servo constraints are non-holonomic. Furthermore, a concomitant parameter in the designed controller is analyzed, and a feasible controller admitting the optimal performance can be determined by minimizing a predefined performance index, such that the deterministic system performance can be ensured to be at a satisfying level. As supported by rigorous proofs, the existence and the uniqueness of the global solution to the optimization problem are presented. Finally, a numerical experiment is implemented to demonstrate the effectiveness of the proposed control design methodology.

A two-degree-of-freedom (2-DoF) flexure-based nanopositioner is investigated for the planar scanning tasks, and a robust controller design scheme based on the convex inner approximation method is proposed. In practice, a flexure-based mechanism is usually represented by a second-order dynamic model. However, the second-order dynamic model cannot precisely fit the real system dynamics, and the model mismatch renders it difficult to achieve satisfying system performance in applications. Such a mismatch includes the parameter uncertainties caused by inaccurate model identification, different motion conditions, as well as high-order resonances. Note that if the controller is not well designed, the high-order resonances can be frequently activated, especially when the system input variation is significant. Therefore, to deal with the above impediments, a novel scheme for the robust controller design is proposed, with the variation of system input considered. In the proposed scheme, a subset of gains that can stabilize the closed-loop system is characterized elegantly via an inner approximation method considering the model uncertainties, and the formulated optimization problem regarding the determination of the controller parameters can be efficiently solved. Furthermore, the proposed scheme guarantees the performance regarding the H2-norm level and limits the H∞-norm level in a designated range. Finally, numerical optimization and comparative experiments are carried out, and the results evidently show the effectiveness of the proposed method.

Continued great efforts have been dedicated toward high-quality trajectory generation based on optimization methods; however, most of them do not suitably and effectively consider the situation with moving obstacles; and more particularly, the future position of these moving obstacles in the presence of uncertainty within some possible prescribed prediction horizon. To cater to this rather major shortcoming, this work shows how a variational Bayesian Gaussian mixture model (vBGMM) framework can be employed to predict the future trajectory of moving obstacles; and then with this methodology, a trajectory generation framework is proposed which will efficiently and effectively address trajectory generation in the presence of moving obstacles, and incorporate the presence of uncertainty within a prediction horizon. In this work, the full predictive conditional probability density function (PDF) with mean and covariance is obtained and, thus, a future trajectory with uncertainty is formulated as a collision region represented by a confidence ellipsoid. To avoid the collision region, chance constraints are imposed to restrict the collision probability, and subsequently, a nonlinear model predictive control problem is constructed with these chance constraints. It is shown that the proposed approach is able to predict the future position of the moving obstacles effectively; and, thus, based on the environmental information of the probabilistic prediction, it is also shown that the timing of collision avoidance can be earlier than the method without prediction. The tracking error and distance to obstacles of the trajectory with prediction are smaller compared with the method without prediction.

Data-driven control methods for modern controller design are becoming popular recently. However, the traditional Proportional-Integral-Derivative (PID) controller is still the most widely used controller to the industrial preference. To tune the parameters of the PID controller, optimal PID tuning approaches such as solving the Riccati equation of the Linear Quadratic Regulator (LQR) provide the optimal solution. The disadvantages of the LQR are that an accurate model of the system is required, and the high-order system must be reduced to the second-order system so that the Riccati equation can be solved. In this paper, a novel data-driven method is proposed to cope with these problems. For the system which is difficult to be identified accurately, the proposed data-driven method can skip the procedure of system identification and tune the parameters of the PID controller directly with the experimental data instead of solving the Riccati equation. This data-driven tuning method also ensures that the parameters of the PID controller for the high-order system are optimized without using the reduced-order model of the system. Simulations are conducted on a tray indexing system with the second-order model and the full-order model demonstrating high applicability and accuracy of the proposed method.

Even though path planning is a well-studied problem in 2D environment, finding an optimal or near-optimal path in a complex and unknown 3D environment has great prospect, but it is hard to find the optimal path quickly. In this paper, we propose a new algorithm called Hierarchical Lazy Theta* (HLT*), which can plan the near-optimal path efficiently for real-time operation based on the heuristic-based path-finding algorithm Lazy Theta* with a hierarchical path planning approach. Path refinement, smoothing, and polishing are used to refine the path to ensure the feasibility of computed path. Its computation time and path quality are dependent on parameters, such as map size, environment complexity, sensor detection range, refinement range, computation time limits, and any restriction on planning time. Simulation experiments are used to assess the performance, and the simulation results show that HLT* algorithm is capable of planning a high-quality path in a shorter time.