This paper presents a novel approach for collision avoidance in optimal and model predictive control, in which the environment is represented by a large number of points and the robot as a union of padded polygons. The conditions that none of the points shall collide with the robot can be written in terms of an infinite number of constraints per obstacle point. We show that the resulting semi-infinite programming (SIP) optimal control problem (OCP) can be efficiently tackled through a combination of two methods: local reduction and an external active-set method. Specifically, this involves iteratively identifying the closest point obstacles, determining the lower-level distance minimizer among all feasible robot shape parameters, and solving the upper-level finitely-constrained subproblems. In addition, this paper addresses robust collision avoidance in the presence of ellipsoidal state uncertainties. Enforcing constraint satisfaction over all possible uncertainty realizations extends the dimension of constraint infiniteness. The infinitely many constraints arising from translational uncertainty are handled by local reduction together with the robot shape parameterization, while rotational uncertainty is addressed via a backoff reformulation. A controller implemented based on the proposed method is demonstrated on a real-world robot running at 20 Hz, enabling fast and collision-free navigation in tight spaces. An application to 3D collision avoidance is also demonstrated in simulation.

In today’s industrial solar cell production, laser processing is a standard technology and will remain important for future developments, such as silver-free solar cell concepts. High throughput laser processing of more than 10.000 wafers per hour with a high precision of 10 to 100 μm is required. Current laser systems use complex automation and transport systems for accurate positioning. However, these systems are costly, large, and have limited throughput. On-the-fly laser processing, with wafers processed on a conveyor belt, offers a compact and cost-effective high-throughput approach. However, its accuracy is limited by transport imprecision. To overcome this, we propose a novel system using real-time measurement of speed fluctuations to adjust the beam position via feed-forward control to achieve both high throughput and accuracy. An FPGA-based array of optical tracking sensors was developed and used in an on-the-fly demonstrator setup. The sensor’s accuracy is characterized and demonstrated in a one-dimensional oscillation compensation. Oscillatory deviations of the laser markings are reduced from 82.2 to 13.2 μm (1 σ), a six-fold improvement. Thereby, sampling delay limits the control bandwidth. Offline analysis shows that Kalman filtering could compensate for this, and still reduce the estimation uncertainty by 23%.

Flexible robots may overcome some of the industry’s major challenges, such as enabling intrinsically safe human-robot collaboration and achieving a higher payload-to-mass ratio. However, controlling flexible robots is complicated due to their complex dynamics, which include oscillatory behavior and a high-dimensional state space. Nonlinear model predictive control (NMPC) offers an effective means to control such robots, but its significant computational demand often limits its application in real-time scenarios. To enable fast control of flexible robots, we propose a framework for a safe approximation of NMPC using imitation learning and a predictive safety filter. Our framework significantly reduces computation time while incurring a slight loss in performance. Compared to NMPC, our framework shows more than an eightfold improvement in computation time when controlling a three-dimensional flexible robot arm in simulation, all while guaranteeing safety constraints. Notably, our approach out-performs state-of-the-art reinforcement learning methods. The development of fast and safe approximate NMPC holds the potential to accelerate the adoption of flexible robots in industry. The project code is available at: tinyurl.com/anmpc4fr

This work proposes an optimal control scheme for a trajectory-tracking Automated Guided Vehicle considering motion and collision constraints in a warehouse environment. We outline how the simpler obstacle avoidance constraints in the Cartesian Coordinate Frame (CCF) can be retained, while projecting the tricycle kinematics to the Frenet Coordinate Frame (FCF) for track progress. The Nonlinear Model Predictive Control (NMPC) scheme is subsequently implemented using acados and its real-time feasibility is demonstrated in simulation and aboard a test vehicle at a warehouse.

Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this article, we present a self-supervised learning approach that actively models the dynamics of nonlinear robotic systems. We combineofflinelearning from past experience andonlinelearning from current robot interaction with the unknown environment. These two ingredients enable a highly sample-efficient and adaptive learning process, capable of accurately inferring model dynamics in real-time even in operating regimes that greatly differ from the training distribution. Moreover, we design an uncertainty-aware model predictive controller that is heuristically conditioned to the aleatoric (data) uncertainty of the learned dynamics. This controlleractivelychooses the optimal control actions that i) optimize the control performance, and ii) improve the efficiency of online learning sample collection. We demonstrate the effectiveness of our method through a series of challenging real-world experiments using a quadrotor system. Our approach showcases high resilience and generalization capabilities by consistently adapting to unseen flight conditions, while it significantly outperforms classical and adaptive control baselines.11Video:https://youtu.be/QmEhSTcWob4

Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained mechanical systems, i.e., those whose state coordinates are subject to holonomic or nonholonomic constraints, such as loop-closure or rolling-contact constraints. These constraints confine the robot trajectories to an implicitly-defined manifold, which complicates the computation of accurate solutions. Discretization errors inherent to the transcription of the problem easily make the trajectories drift away from this manifold, which results in physically inconsistent motions that are difficult to track with a controller. This article reviews existing methods to deal with this problem and proposes new ones to overcome their limitations. Current approaches either disregard the kinematic constraints (which leads to drift accumulation) or modify the system dynamics to keep the trajectory close to the manifold (which adds artificial forces or energy dissipation to the system). The methods we propose, in contrast, achieve full drift elimination on the discrete trajectory, or even along the continuous one, without artificial modifications of the system dynamics. We illustrate and compare the methods using various examples of different complexity.

We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex ambiguity sets, which can be generalized to sets based on integral probability metrics and finite-order moment bounds. This perspective unifies multiple existing robust and stochastic optimization methods. We prove a theorem that generalizes the classical duality in the mathematical problem of moments. Enabled by this theorem, we reformulate the maximization with respect to measures in DRO into the dual program that searches for RKHS functions. Using universal RKHSs, the theorem applies to a broad class of loss functions, lifting common limitations such as polynomial losses and knowledge of the Lipschitz constant. We then establish a connection between DRO and stochastic optimization with expectation constraints. Finally, we propose practical algorithms based on both batch convex solvers and stochastic functional gradient, which apply to general optimization and machine learning tasks.

Robust and accurate pose estimation of moving systems is a challenging task that is often tackled by combining information from different sensor subsystems in a multi-sensor fusion setup. To obtain robust and accurate estimates, it is crucial to respect the exact time of each measurement. Data fusion is additionally challenged when the sensors are running at different rates and the information is subject to processing- and transmission delays. In this paper, we present an optimization-based moving horizon estimator which allows to estimate and compensate for time-varying measurement delays without the need for any synchronization signals between the sensors. By adopting a direct collocation approach, we find a continuous-time solution for the navigation states which allows us to incorporate the discrete-time sensor measurements in an optimal way despite the presence of unknown time delays. The presented sensor fusion algorithm is applied to the problem of pose estimation by fusing data of a high-rate inertial measurement unit and a low-rate centimeter-accurate global navigation satellite system receiver using simulated and real-data experiments.

The advances in computer processor technology have enabled the application of nonlinear model predictive control (NMPC) to agile systems, such as quadrotors. These systems are characterized by their underactuation, nonlinearities, bounded inputs, and time-delays. Classical control solutions fall short in overcoming these difficulties and fully exploiting the capabilities offered by such platforms. This paper presents the design and implementation of an efficient position controller for quadrotors based on real-time NMPC with time-delay compensation and bounds enforcement on the actuators. To deal with the limited computational resources onboard, an offboard control architecture is proposed. It is implemented using the high-performance software package acadoff, which solves optimal control problems and implements a real-time iteration (RTI) variant of a sequential quadratic programming (SQP) scheme with Gauss-Newton Hessian approximation. The quadratic subproblems (QP) in the SQP scheme are solved with HPIPM, an interior-point method solver, built on top of the linear algebra library BLASFEO, finely tuned for multiple CPU architectures. Solution times are further reduced by reformulating the QPs using the efficient partial condensing algorithm implemented in HPIPM. We demonstrate the capabilities of our architecture using the Crazyflie 2.1 nano-quadrotor.

Even though mobile robots have been around for decades, trajectory optimization and continuous time collision avoidance remain subject of active research. Existing methods trade off between path quality, computational complexity, and kinodynamic feasibility. This work approaches the problem using a nonlinear model predictive control (NMPC) framework, that is based on a novel convex inner approximation of the collision avoidance constraint. The proposed Convex Inner ApprOximation (CIAO) method finds kinodynamically feasible and continuous time collision free trajectories, in few iterations, typically one. For a feasible initialization, the approach is guaranteed to find a feasible solution, i.e. it preserves feasibility. Our experimental evaluation shows that CIAO outperforms state of the art baselines in terms of planning efficiency and path quality. Experiments show that it also efficiently scales to high-dimensional systems. Furthermore real-world experiments demonstrate its capability of unifying trajectory optimization and tracking for safe motion planning in dynamic environments.

Basic Linear Algebra Subroutines For Embedded Optimization (BLASFEO) is a dense linear algebra library providing high-performance implementations of BLAS- and LAPACK-like routines for use in embedded optimization and other applications targeting relatively small matrices. BLASFEO defines an application programming interface (API) which uses a packed matrix format as its native format. This format is analogous to the internal memory buffers of optimized BLAS, but it is exposed to the user and it removes the packing cost from the routine call. For matrices fitting in cache, BLASFEO outperforms optimized BLAS implementations, both open source and proprietary. This article investigates the addition of a standard BLAS API to the BLASFEO framework, and proposes an implementation switching between two or more algorithms optimized for different matrix sizes. Thanks to the modular assembly framework in BLASFEO, tailored linear algebra kernels with mixed column- and panel-major arguments are easily developed. This BLAS API has lower performance than the BLASFEO API, but it nonetheless outperforms optimized BLAS and especially LAPACK libraries for matrices fitting in cache. Therefore, it can boost a wide range of applications, where standard BLAS and LAPACK libraries are employed and the matrix size is moderate. In particular, this article investigates the benefits in scientific programming languages such as Octave, SciPy, and Julia.

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple shooting variants, combining advantages like straightforward initialization and a closed-loop forward integration. All algorithms have similar computational complexity, i.e. linear complexity in the time horizon, and can be derived in the same computational framework. We compare the full-step variants of our algorithms and present several simulation examples, including a high-dimensional underactuated robot subject to contact switches. Simulation results show that our multiple shooting algorithms can achieve faster convergence, better local contraction rates and much shorter runtimes than classical iLQR, which makes them a superior choice for nonlinear model predictive control applications.

Basic Linear Algebra Subroutines for Embedded Optimization (BLASFEO) is a dense linear algebra library providing high-performance implementations of BLAS- and LAPACK-like routines for use in embedded optimization and small-scale high-performance computing, in general. A key difference with respect to existing high-performance implementations of BLAS is that the computational performance is optimized for small- to medium-scale matrices, i.e., for sizes up to a few hundred. BLASFEO comes with three different implementations: a high-performance implementation aimed at providing the highest performance for matrices fitting in cache, a reference implementation providing portability and embeddability and optimized for very small matrices, and a wrapper to standard BLAS and LAPACK providing high performance on large matrices. The three implementations of BLASFEO together provide high-performance dense linear algebra routines for matrices ranging from very small to large. Compared to both open-source and proprietary highly tuned BLAS libraries, for matrices of size up to about 100, the high-performance implementation of BLASFEO is about 20--30% faster than the corresponding level 3 BLAS routines and two to three times faster than the corresponding LAPACK routines.

This paper presents an embedded-optimization-based loudspeaker precompensation algorithm using a Hammerstein loudspeaker model, i.e. a cascade of a memoryless nonlinearity and a linear finite impulse response filter. The loudspeaker precompensation consists in a per-frame signal optimization. In order to minimize the perceptible distortion incurred in the loudspeaker, a psychoacoustically motivated optimization criterion is proposed. The resulting per-frame signal optimization problems are solved efficiently using first-order optimization methods. Depending on the invertibility and the smoothness of the memoryless nonlinearity, different first-order optimization methods are proposed and their convergence properties are analyzed. Objective evaluation experiments using synthetic loudspeaker models and real loudspeakers show that the proposed loudspeaker precompensation algorithm provides a significant audio quality improvement, especially so at high playback levels.

Path following deals with the problem of following a geometric path with no predefined timing information and constitutes an important step in solving the motion-planning problem. For differentially flat systems, it has been shown that the projection of the dynamics along the geometric path onto a linear single-input system leads to a small dimensional optimal control problem. Although the projection simplifies the problem to great extent, the resulting problem remains difficult to solve, in particular in the case of nonlinear system dynamics and time-optimal problems. This paper proposes a nonlinear change of variables, using a time transformation, to arrive at a fixed end-time optimal control problem. Numerical simulations on a robotic manipulator and a quadrotor reveal that the proposed problem formulation is solved efficiently without requiring an accurate initial guess.

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time. In the case of a robotic manipulator a convex reformulation of this optimal control problem has been derived previously [1]. However, the bang-bang nature of the time-optimal trajectories results in near-infinite jerks in joint space and operational (Cartesian) space. For systems with un-modeled flexibilities, this usually results in excitation of the resonant frequencies, hence in unwanted vibrations and acceleration peaks, contributing to a tracking error. These vibrations can be reduced by imposing jerk constraints on the trajectory [2]. However, these jerk constraints destroy the convexity of the time-optimal control problem. The present paper proposes an efficient sequential convex programming (SCP) approach to solve the corresponding non-convex optimal control problem by writing the non-convex jerk constraints as a difference of convex (DC) functions. We illustrate the developed approach by means of experiments with a seven d.o.f. robot. Furthermore, numerical simulations illustrate the fast convergence of the proposed method in only a few SCP iterations, confirming the efficiency and practicality of the proposed framework.

The restoration of clipped audio signals, commonly known as declipping, is important to achieve an improved level of audio quality in many audio applications. In this paper, a novel declipping algorithm is presented, jointly based on the theory of compressed sensing (CS) and on well-established properties of human auditory perception. Declipping is formulated as a sparse signal recovery problem using the CS framework. By additionally exploiting knowledge of human auditory perception, a novel perceptual compressed sensing (PCS) framework is devised. A PCS-based declipping algorithm is proposed which uses ℓ1-norm type reconstruction. Comparative objective and subjective evaluation experiments reveal a significant audio quality increase for the proposed PCS-based declipping algorithm compared to CS-based declipping algorithms.

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time. In the case of a robotic manipulator with simplified constraints, a convex reformulation of this optimal control problem has been derived previously. However, many applications in robotics feature constraints such as velocity-dependent torque constraints or torque rate constraints that destroy the convexity. The present paper proposes an efficient sequential convex programming (SCP) approach to solve the corresponding nonconvex optimal control problems by writing the nonconvex constraints as a difference of convex (DC) functions, resulting in convex-concave constraints. We consider seven practical applications that fit into the proposed framework even when mutually combined, illustrating the flexibility and practicality of the proposed framework. Furthermore, numerical simulations for some typical applications illustrate the fast convergence of the proposed method in only a few SCP iterations, confirming the efficiency of the proposed framework.

The aim of this paper is to improve the performance of existing speech distortion weighted multi-channel Wiener filter (SDW-MWFμ) based noise reduction (NR) algorithms. It is well known that for the SDW-MWFμthe improved NR performance comes at the cost of higher speech distortion when a fixed speech distortion weighting factor is used. In this paper we propose two psychoacoustically motivated weighting factor selection strategies, devised to exploit masking properties of the human ear. Experimental results based on PESQ scores, SNR improvement, and signal distortion confirm that both proposed psychoacoustically motivated weighting factor selection strategies do improve the NR performance compared to using a fixed weighting factor. In some of the analyzed scenarios, the fixed weighting factor approach is even seen to degrade the PESQ scores, while the psychoacoustically motivated approaches are seen to significantly improve the PESQ scores in all of the analyzed scenarios.

Clipping is an essential signal processing operation in many real-time audio applications, yet the use of existing clipping techniques generally has a detrimental effect on the perceived audio signal quality. In this paper, we present a novel multidisciplinary approach to clipping which aims to explicitly minimize the perceptible clipping-induced distortion by embedding a convex optimization criterion and a psychoacoustic model into a frame-based algorithm. The core of this perception-based clipping algorithm consists in solving a convex optimization problem for each time frame in a fast and reliable way. To this end, three different structure-exploiting optimization methods are derived in the common mathematical framework of convex optimization, and corresponding theoretical complexity bounds are provided. From comparative audio quality evaluation experiments, it is concluded that the perception-based clipping algorithm results in significantly higher objective audio quality scores than existing clipping techniques. Moreover, the algorithm is shown to be capable to adhere to real-time deadlines without making a sacrifice in terms of audio quality.

Clipping is a necessary signal processing operation in many real time audio applications, yet it often reduces the sound quality of the signal. The recently proposed perception-based clipping algorithm has been shown to significantly outperform other clipping techniques in terms of objective sound quality scores. However, the real-time solution of the optimization problems that form the core of this algorithm, poses a challenge. In this paper, a fast gradient projection optimization method is proposed and incorporated into the perception based clipping algorithm. The optimization method will be shown to have an extremely low computational complexity per iteration, allowing the perception-based clipping algorithm to be applied in real-time for a broad range of clipping factors.

This paper focuses on time-optimal path tracking, which involves planning of robot motions along prescribed geometric paths. Starting from a discretized convex reformulation of time-optimal path tracking problems, a log-barrier based batch solution method is presented which allows to rapidly obtain an approximate solution with smooth actuator torques. Based on this batch method, a recursive variant is derived for on-line path tracking. By means of an experimental test case in which the path data is generated on-line by human demonstration, the results and trade-offs in calculation time, delay and path duration are compared for the batch and recursive variant of the log-barrier method as well as for an exact solution method.

This article addresses the real-time implementation issues of a model predictive control based walking pattern generation for a humanoid robot. We approximate the multibody dynamic model with a linear discrete time system, and at each step solve a quadratic program in order to keep the output within a predefined set of constraints. The focus is on creating an efficient framework for forming and solving the underlying optimization problem. For that purpose we develop: a) a reliable guess for the active constraints at optimality; b) a fast way of generating an initial feasible point with respect to the set of constraints for each preview interval; c) a variable discretization sampling time. A simple implementation of a standard primal active set algorithm which exploits a "hot start" is used to demonstrate the advantages of the first point, while the latter one is verified using an existing dual solver.

Building on previous propositions to generate walking gaits online through the use of linear model predictive control, the goal of this paper is to show that it is possible to allow on top of that a continuous adaptation of the positions of the foot steps, allowing the generation of stable walking gaits even in the presence of strong perturbations, and that this additional adaptation requires only a minimal modification of the previous schemes, especially maintaining the same linear model predictive form. Simulation results are proposed then on the HRP-2 humanoid robot, showing a significant improvement over the previous schemes.