We present an effective solution for computing locally optimal Reeds-Shepp distances and paths for kinematically-constrained vehicles in environments represented as obstacle-rich 2D Cartesian occupancy grids, addressing the reliance of current methods on discretization and approximation techniques. Our solution leverages a visibility-based marching architecture with continuous analytical expressions for propagating the Reeds-Shepp distance function. We introduce a model to identify reachable and unreachable regions for Reeds-Shepp vehicles, accompanied by a comprehensive representation of the Reeds-Shepp distance function in both cases. Unlike existing approaches, our method computes locally optimal distances and smooth paths globally without discretizing vehicle orientations, motion primitives, or the PDE, and without gradient descent (GD) backtracking, ensuring both accuracy and computational efficiency. Extensive simulations in various environments demonstrate effective improvements over state-of-the-art methods, particularly in complex obstacle-rich scenarios. To facilitate adoption, we provide an open-source solver implemented in C++.

This paper presents a hybrid approach to online controller tuning for systems with structured yet uncertain time-varying dynamics. The method integrates model-based Linear Parameter-Varying (LPV) control design with data-driven Bayesian Optimization (BO) to achieve sample-efficient performance tuning under uncertain plant conditions. A key contribution lies in the development of a problem-specific kernel for Gaussian Process Regression (GPR), which incorporates prior system knowledge derived from an LPV model to accelerate convergence of the BO procedure. The proposed method is experimentally validated on a servo pneumatic system subject to artificial leakages, showing that the custom kernel consistently outperforms standard approaches in convergence speed.

This paper addresses two critical challenges in the application of real-time hybrid-physical-virtual testing (HPVT) to industrial use-cases: test performance monitoring and satisfactory coupling accuracy. For the first challenge, residual energy and power methods are used as performance indicators for co-simulation accuracy and stability. For the second challenge, the assumption is made that the coupling error caused by the co-simulation algorithm is composed of a time delay of one sample. To compensate for the delay, the authors propose Iterative Learning Control (ILC) as a non-causal solution method. The effectiveness of this general approach is validated on an automotive-related use-case. An electric vehicle is represented both in a fully virtual co-simulation environment as well as by a real-time HPVT setup with a physical e-motor and virtual vehicle. Results demonstrate that ILC successfully reduces residual power and energy by several orders of magnitude in both simulated and experimental environments. While sensor noise in the physical setup prevents complete convergence to zero error, the developed method brings significant improvement in co-simulation accuracy.

Safe motion planning is essential for autonomous vessel operations, especially in challenging spaces such as narrow inland waterways. However, conventional motion planning approaches are often computationally intensive or overly conservative. This paper proposes a safe motion planning strategy combining Model Predictive Control (MPC) and Control Barrier Functions (CBFs). We introduce a time-varying inflated ellipse obstacle representation, where the inflation radius is adjusted depending on the relative position and attitude between the vessel and the obstacle. The proposed adaptive inflation reduces the conservativeness of the controller compared to traditional fixed-ellipsoid obstacle formulations. The MPC solution provides an approximate motion plan, and high-order CBFs ensure the vessel’s safety using the varying inflation radius. Simulation and real-world experiments demonstrate that the proposed strategy enables the fully-actuated autonomous robot vessel to navigate through narrow spaces in real time and resolve potential deadlocks, all while ensuring safety.

In this study, we present a simple and intuitive method for accelerating optimal Reeds–Shepp path computation. Our approach uses geometrical reasoning to analyze the behavior of optimal paths, resulting in a new partitioning of the state space and a further reduction in the minimal set of viable paths. We revisit and reimplement classic methodologies from literature, which lack contemporary open-source implementations, to serve as benchmarks for evaluating our method. In addition, we address the underspecified Reeds–Shepp planning problem where the final orientation is unspecified. We perform exhaustive experiments to validate our solutions. Compared to the modern C++ implementation of the original Reeds–Shepp solution in the Open Motion Planning Library, our method demonstrates a$15\times$speedup, while classic methods achieve a$5.79\times$speedup. Both approaches exhibit machine-precision differences in path lengths compared to the original solution. We release our proposed C++ implementations for both the accelerated and underspecified Reeds–Shepp problems as open-source code.

This paper presents a model and parameter estimation methods for an inland cargo catamaran. This model is used in an NMPC scheme to address the path following problem of the vessel in inland waterways. This NMPC scheme derives the control action by minimizing a cost function while meeting constraints. The path consists of waypoints that define safety contours that are derived from IENC. In Addition, circular geometries are used to define safety contours around obstacles along the fairway. The model and NMPC are validated through simulation of a section of Leuven canal.

In autonomous robot navigation, the trajectories from path planners are considered to be safe regions, and deviations could endanger vessels. Model Predictive Control (MPC) stands as a popular choice for trajectory tracking problems as it naturally addresses operational constraints, such as dynamics and control constraints. Nevertheless, achieving robustness in changing environments like oceans and rivers, which are constantly subject to significant external disturbances, remains an ongoing challenge for MPC. It must consistently keep the system within a predefined safe region (such as a reference trajectory) even in the presence of model inaccuracies and perturbations. To address this challenge, we present a robust model predictive control strategy utilizing Control Barrier Functions (CBFs), which increases the disturbance-rejection abilities. We verify our method on an autonomous surface vessel in simulation and natural waters, both with external disturbances. Specifically, compared with the traditional MPC method, our proposed MPC-CBF strategy reduces tracking errors by 17.82% and 40.26% in simulations and field experiments, respectively. Although the control effort slightly increases by 7.78% and 4.20%, respectively, these results clearly demonstrate the enhanced resilience of MPC-CBF to disturbances.

This paper introduces a novel, lightweight method to solve the visibility problem for 2D grids. The proposed method evaluates the existence of lines-of-sight from a source point to all other grid cells in a single pass with no preprocessing and independently of the number and shape of obstacles. It has a compute and memory complexity of $\mathcal{O}(n)$, where n = nx×nyis the size of the grid, and requires at most ten arithmetic operations per grid cell. In the proposed approach, we use a linear first-order hyperbolic partial differential equation to transport the visibility quantity in all directions. In order to accomplish that, we use an entropy-satisfying upwind scheme that converges to the true visibility polygon as the step size goes to zero. This dynamic-programming approach allows the evaluation of visibility for an entire grid orders of magnitude faster than typical ray-casting algorithms. We provide a practical application of our proposed algorithm by posing the visibility quantity as a heuristic and implementing a deterministic, local-minima-free path planner, setting apart the proposed planner from traditional methods. Lastly, we provide necessary algorithms and an open-source implementation of the proposed methods.

This paper presents a robustified time-optimal motion planning approach for navigating an Autonomous Mobile Robot (AMR) from an initial state to a terminal state without colliding with obstacles, even when subjected to disturbances, which are modeled as random process noise and measurement noise. The approach iteratively solves the robustified problem by incorporating updated state-dependent safety margins for collision avoidance, the evolution of which is derived separately from the robustified problem. Additionally, a strategy for selecting an alternative terminal state to reach is introduced, which comes into play when the desired terminal state becomes infeasible considering the disturbances. Both of these contributions are integrated into a robustified motion planning and control pipeline, the efficacy of which is validated through simulation experiments.

This paper proposes DriViDOC: a framework for Driving from Vision through Differentiable Optimal Control, and its application to learn autonomous driving controllers from human demonstrations. DriViDOC combines the automatic inference of relevant features from camera frames with the properties of nonlinear model predictive control (NMPC), such as constraint satisfaction. Our approach leverages the differentiability of parametric NMPC, allowing for end-to-end learning of the driving model from images to control. The model is trained on an offline dataset comprising various human demonstrations collected on a motion-base driving simulator. During online testing, the model demonstrates successful imitation of different driving styles, and the interpreted NMPC parameters provide insights into the achievement of specific driving behaviors. Our experimental results show that DriViDOC outperforms other methods involving NMPC and neural networks, exhibiting an average improvement of 20% in imitation scores.

Accurately predicting deformable linear object (DLO) dynamics is challenging, especially when the task requires a model that is both human-interpretable and computationally efficient. In this work, we draw inspiration from the pseudo-rigid body method (PRB) and model a DLO as a serial chain of rigid bodies whose internal state is unrolled through time by a dynamics network. This dynamics network is trained jointly with a physics-informed encoder that maps observed motion variables to the DLO's hidden state. To encourage the state to acquire a physically meaningful representation, we leverage the forward kinematics of the PRB model as a decoder. We demonstrate in robot experiments that the proposed DLO dynamics model provides physically interpretable predictions from partial observations while being on par with black-box models regarding prediction accuracy. The project code is available at: tinyurl.com/prb-networks

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

Fast and safe manipulation of flexible objects with a robot manipulator necessitates measures to cope with vibrations. Existing approaches either increase the task execution time or require complex models and/or additional instrumentation to measure vibrations. This paper develops a model-based method that overcomes these limitations. It relies on a simple pendulum-like model for modeling the beam, open-loop optimal control for suppressing vibrations, and does not require any exteroceptive sensors. We experimentally show that the proposed method drastically reduces residual vibrations – at least 90% – and outperforms the commonly used input shaping (IS) for trajectories with the same execution time. Besides, our method can also execute the task faster than IS with a minor reduction in vibration suppression performance, thereby facilitating the development of new solutions for flexible object manipulation tasks.

Prioritization of tasks is a common approach to resolve conflicts in instantaneous control of redundant robots. However, the idea of prioritization has not yet been satisfactorily extended to model predictive control (MPC) to allow for real-time robot control. The standard sequential approach for prioritization is unsuitable because of the computational burden involved in solving a nonlinear problem (NLP) at every priority level. We introduce an alternate promising approach of using weighted exact penalties for the MPC stage costs, where a correctly tuned set of weights can introduce strict prioritization. We prove the existence of a set of equivalent weights that provides the same solution as the sequential approach for a local convex approximation of the original NLP and use this insight to design an algorithm to adaptively tune the weights. The weighted method is validated on a dual arm robot task in simulations and also implemented on a physical robot. We report computational times that are fast enough for prioritized MPC of robot manipulators for the first time, to the best of our knowledge.

We present Tasho (Task specification for receding horizon control), an open-source Python toolbox that facilitates systematic programming of optimal control problem (OCP)-based robot motion skills. Separation-of-concerns is followed while designing the components of a motion skill, which promotes their modularity and reusability. This allows us to program complex motion tasks by configuring and composing simpler tasks. We provide templates for several basic tasks like point-to-point and end-effector path-following tasks to speed up prototyping. Internally, the task's symbolic expressions are computed using CasADi and the resulting OCP is transcribed using Rockit. A wide and growing range of mature open-source optimization solvers are supported for solving the OCP. Monitor functions can be easily specified and are automatically deployed with the motion skill, so that the generated motion skills can be easily embedded in a larger control architecture involving higher-level discrete controllers. The motion skills thus programmed can be directly deployed on robot platforms using the C-code generation capabilities of CasADi. The toolbox has been validated through several experiments both in simulation and on physical robot systems. The open-source toolbox can be accessed at: https://gitlab.kuleuven.be/meco-software/tasho

Automated Guided Vehicles (AGVs) are a promising solution to automation in the view of Industry 4.0. The amount of goods that can be automatically transported can be further increased by efficient path planning and tracking methods. The efficiency is always a trade off in terms of cost, accuracy and flexibility, but should never influence safety. This paper proposes a flexible path planning and tracking solution, aiming to be applicable to several application domains, and which is able to dynamically avoid an (unforeseen) obstacle by an overtake manoeuvre. The approach is based on Model Predictive Control (MPC), consisting of multi-domain objectives, applicable to multiple vehicle models and is fast in calculation time due to an adjusted multiple shooting approach, which guarantees constraint satisfaction over the entire time domain. Further, a dynamic maximum velocity approach is proposed, which adapts the maximum velocity constraint to the environmental circumstances, such that an emergency brake can be applied if a human would appear behind a corner or obstacle. These algorithms are implemented on an autonomous forklift. The overall system performance is measured by the time-of-arrival of an obstacle avoidance manoeuvre. To evaluate the influence of usage of a low-cost ultra wideband (UWB) localization technology, the same algorithms and platforms are used in combination with standard off-the-shelf laser based localization technology. The UWB technology does lead to a slightly larger spread in terms of time-of-arrival, but is on average very much comparable to the laser-based setup.

This paper describes two important challenges in the development of an ultra-wideband (UWB) positioning system. The first challenge is increasing the accuracy and robustness of the UWB technology. The range measurements are subject to disturbances, which introduce an unwanted bias. This range bias is measured, characterized and modeled to increase the positioning accuracy to an average of 3 cm. The second challenge is a user-friendly deployment of the system. This is achieved by a semi-automated autocalibration procedure. In the proposed method the mobile device (tag) is moved around in the covered area. Based on all the captured data, the coordinates and a range bias model parameter of the static devices (anchors) are obtained. No additional measurement devices are required during the procedure. The positioning accuracy with the autocalibrated parameters decreases to an acceptable 9 cm on average, compared to the situation with exact parameters.

Factories of the future must be agile to adapt to rapidly changing customer needs, market volatility and shortened product life cycles. This requires flexibility in hardware and software at distinct levels of the factory and manufacturing process: multipurpose machines with fast change-overs, easy to use reconfigurable software and distributed decision-making are key. This paper leverages the new Industry 4.0 design principles to cope with these new manufacturing requirements: (i) distributed auction-based coordination allows local decision-making and task allocation, (ii) distributed model predictive control-based transportation enables free space collision avoidance of automated guided vehicles (AGVs), and (iii) distributed vision-based localisation provides scalable and dynamic position information of key resources on the factory floor. Furthermore, these contributions are brought together in a lab-scale reconfigurable manufacturing system to showcase modularity and distributed decision-making at several levels of a manufacturing process' logistics.

In pursuit of the time-optimal motion of an industrial robot along a desired path, a previously identified model is typically used to calculate the required inputs for perfect tracking. An inevitable model-plant mismatch, however, causes the obtained inputs to be suboptimal-resulting in poor tracking performance-or even be infeasible by exceeding given limits. This paper, at hand, presents a two-step iterative learning algorithm that compensates for such model-plant mismatch and finds the time-optimal motion, improving tracking performance, and ensuring feasibility. Due to an efficient solution of the path tracking problem using a sequential convex log barrier method, the delay between consecutive task executions is eliminated. To show the effectiveness of the proposed algorithm, an experimental validation on a standard industrial manipulator is performed, illustrating that the developed approach is capable of reducing the execution time while at the same time improving the tracking performance.

This paper presents a generalized iterative learning control (ILC) design in the frequency domain with experimental validation. The optimal ILC learning function and robustness filter function are simultaneously optimized by solving a linear programming problem using frequency response functions. Moreover, the design realizes an optimal trade-off between robust convergence, converged tracking performance, convergence speed, and input constraints. The proposed ILC method is experimentally validated on a lab scale overhead crane system. The results demonstrate the advantages of the approach as an automation design with optimal solutions, efficient computation, robustness and intuitive tuning for trade-off analyses between multiple ILC specifications.

This paper explores a combined global and local identification approach for linear parameter-varying systems. Ideally, the combined approach retains advantages of its two extremes - global and local - with the possibility to emphasize one or the other. Practically, it is prone to overfitting. This paper proposes a remedy based on the ℓ2,1-norm regularization, describes its implementation within the nonlinear least squares framework, and gives an experimental validation. The results show a substantial decrease in the Euclidean norm of the model parameters, which resulted in a significantly smoother frequency response function surface and in overall, less-deviating model behavior.

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.

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.

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 paper investigates and demonstrates the feasibility of identifying contact dynamics parameters forstiffroboticpayloadsusing a robotic system. The contact dynamics model for stiff payloads is motivated, and theoretical parameter values and bounds are provided. Then, the effect of nonidealities such as surface roughness and plastic deformation on the theoretical values is demonstrated. A row-wise-scaled total least-squares parameter estimation algorithm is proposed and applied to experimental data measured using the special purpose dexterous manipulator task verification facility manipulator at the Canadian Space Agency. The experimental results are compared to a separate set of experiments with a material testing machine as well as finite-element modeling results. Finally, the experimental findings are generalized by providing guidelines for the maximum identifiable payload stiffness as a function of the position resolution, the maximum exertable force, and the structural stiffness of the robotic system.

Robots are increasingly used to perform complex tasks, which often involve interaction and contact with unstructured environments. By identifying geometric uncertainties and the dynamic behavior of the environment on-line, the autonomy of intelligent robot systems can be considerably improved. This paper considers the 2D case of an industrial robot equipped with a probe to explore an unknown environment. The goal is to estimate from the measured end-effector position, velocity and forces not only the environmental contact dynamics parameters, but also geometric parameters such as the environment position and orientation, and the position of the probe end-point with respect to the robot end-effector. To this end, a Kalman filter based algorithm is proposed, which enforces physical constraints and which is executed in an event-triggered way to improve convergence and robustness. Experimental results illustrate the viability of the proposed algorithm.

This paper presents a method to improve the path tracking accuracy of an industrial robot without replacing the standard industrial controller. By calculating off-line an appropriate trajectory pre-compensation, the effects of the nonlinear dynamics are compensated. This is realized by filtering the desired trajectory with the inverse dynamic model of the robot and its velocity controller. This compensation is applied as a velocity feedforward in the standard industrial controller avoiding the need for a torque control interface. The method presented is validated experimentally on a KUKA IR 361 industrial robot. The results show clearly an improved path tracking accuracy on circular trajectories.

Experimental robot identification techniques can principally be divided into two categories, based on the type of models they use: internal or external. Internal models relate the joint torques or forces and the motion of the robot; external models relate the reaction forces and torques on the bedplate and the motion data. This paper describes how internal and external robot models can be combined into one identifiable minimal model. This model allows to combine joint torque/force and reaction torque/force measurements in one parameter estimation scheme. This combined model estimation will yield more accurate parameter estimates, and consequently better actuator torque predictions, which is shown experimentally on an industrial robot (KUKA IR 361).

The paper discusses the experimental identification of dynamic robot models for their application in model based robot control, e.g., computed torque control. The accuracy of these controllers relies highly on the ability of the robot model to accurately predict the required actuator torques. The paper shows how this application reflects on the choices that have to be made in the different steps of the identification procedure, and consequently on the accuracy of the obtained model parameters and actuator torque prediction.

This paper discusses experimental robot identification based on a statistical framework. It presents a new approach toward the design of optimal robot excitation trajectories, and formulates the maximum-likelihood estimation of dynamic robot model parameters. The differences between the new design approach and the existing approaches lie in the parameterization of the excitation trajectory and in the optimization criterion. The excitation trajectory for each joint is a finite Fourier series. This approach guarantees periodic excitation which is advantageous because it allows: 1) time-domain data averaging; 2) estimation of the characteristics of the measurement noise, which is valuable in the case of maximum-likelihood parameter estimation. In addition, the use of finite Fourier series allows calculation of the joint velocities and acceleration in an analytic way from the measured position response, and allows specification of the bandwidth of the excitation trajectories. The optimization criterion is the uncertainty on the estimated parameters or a lower bound for it, instead of the often used condition of the parameter estimation problem. Simulations show that this criterion yields parameter estimates with smaller uncertainty bounds than trajectories optimized according to the classical criterion. Experiments on an industrial robot show that the presented trajectory design and maximum-likelihood parameter estimation approaches complement each other to make a practicable robot identification technique which yields accurate robot models.