We derive a family of efficient constrained dynamics algorithms by formulating an equivalent linear quadratic regulator (LQR) problem using Gauss' principle of least constraint and solving it using dynamic programming. Our approach builds upon the pioneering (but largely unknown)$O(n + m^{2}\;d + m^{3})$solver by Popov and Vereshchagin (PV), where$n$,$m$, and$d$are the number of joints, number of constraints, and the kinematic tree depth, respectively. We provide an expository derivation for the original PV solver and extend it to floating-base kinematic trees with constraints allowed on any link. We make new connections between the LQR's dual Hessian and the inverse operational space inertia matrix (OSIM), permitting efficient OSIM computation, which we further accelerate using matrix inversion lemma. By generalizing the elimination ordering and accounting forMuJoCo-type soft constraints, we derive two original$O(n + m)$complexity solvers. Our numerical results indicate that significant simulation speed-up can be achieved for high dimensional robots like quadrupeds and humanoids using our algorithms as they scale better than the widely used$O(nd^{2} + m^{2}\;d + d^{2}\;m)$LTL algorithm of Featherstone. The derivation through the LQR-constrained dynamics connection can make our algorithm accessible to a wider audience and enable cross fertilization of software and research results between the fields.

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

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.

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 presents a novel open-loop shaping approach for robust PID controller design, relying on polynomial spline parameterizations. The proposed approach exploits the generalized Kalman Yakubovic Popov (KYP) lemma to derive parameter-dependent linear matrix inequalities (LMIs) for robust PID synthesis. Multiple finite frequency domain specifications are taken into account to intuitively design practical controllers. By assuming piecewise polynomial parametrizations for the parameter-dependent optimization variables, and subsequently applying B-spline based relaxations, tractable conditions are derived that guarantee feasibility of the parameter-dependent LMIs for all uncertain parameter values. An elegant and effective approach results that solves the robust PID synthesis problem with limited conservatism. Numerical results demonstrate the potential of our approach.

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.