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Model predictive control (MPC) has become increasingly popular for the control of robot manipulators due to its improved performance compared to instantaneous control approaches. However, tuning these controllers remains a considerable hurdle. To address this hurdle, we propose a practical MPC formulation which retains the more interpretable tuning parameters of the instantaneous control approach while enhancing the performance through a prediction horizon. The formulation is motivated at hand of a simple example, highlighting the practical tuning challenges associated with typical MPC approaches and showing how the proposed formulation alleviates these challenges. Furthermore, the formulation is validated on a surface-following task, illustrating its applicability to industrially relevant scenarios. Although the research is presented in the context of robot manipulator control, we anticipate that the formulation is more broadly applicable., Comment: Accepted for the IEEE Robotics and Automation Letters

Measuring the similarity between motions and established motion models is crucial for motion analysis, recognition, generation, and adaptation. To enhance similarity measurement across diverse contexts, invariant motion descriptors have been proposed. However, for rigid-body motion, few invariant descriptors exist that are bi-invariant, meaning invariant to both the body and world reference frames used to describe the motion. Moreover, their robustness to singularities is limited. This paper introduces a novel Bi-Invariant Local Trajectory-Shape descriptor (BILTS) and a corresponding dissimilarity measure. Mathematical relationships between BILTS and existing descriptors are derived, providing new insights into their properties. The paper also includes an algorithm to reproduce the motion from the BILTS descriptor, demonstrating its bidirectionality and usefulness for trajectory generation. Experimental validation using datasets of daily-life activities shows the higher robustness of the BILTS descriptor compared to the bi-invariant ISA descriptor. This higher robustness supports the further application of bi-invariant descriptors for motion recognition and generalization., Comment: This work has been submitted as a regular research paper for consideration in the IEEE Transactions on Robotics

In previous work on learning and controlling contact-rich tasks, the procedure for choosing a proper reference frame to express learned signals for the motion and the interaction wrench is often implicit, requires expert insight, or starts from proposed frame candidates. This article presents an automatic method to derive the optimal reference frame, referred to as optimal task frame, directly from the recorded motion and wrench data of the demonstration. Using screw theory, several origin and orientation candidates are generated that maximize decoupling in the data. These candidates are then processed probabilistically, without needing hyperparameters, to obtain the optimal task frame. Its origin and orientation are independently fixed to either the world or the robot tool. The method works regardless of whether the task involves translation, rotation, force, or moment, or any combination thereof. The method was validated for various tasks, including surface following and manipulation of articulated objects, showing good agreement between derived and assumed expert task frames. To validate the robot's performance, a constraint-based controller was designed based on the data expressed in the derived task frames. These experiments demonstrated the approach's effectiveness and versatility. The automatic task frame derivation approach supports learning methods to design controllers for a wide range of contact-rich tasks.

Trajectory segmentation refers to dividing a trajectory into meaningful consecutive sub-trajectories. This paper focuses on trajectory segmentation for 3D rigid-body motions. Most segmentation approaches in the literature represent the body's trajectory as a point trajectory, considering only its translation and neglecting its rotation. We propose a novel trajectory representation for rigid-body motions that incorporates both translation and rotation, and additionally exhibits several invariant properties. This representation consists of a geometric progress rate and a third-order trajectory-shape descriptor. Concepts from screw theory were used to make this representation time-invariant and also invariant to the choice of body reference point. This new representation is validated for a self-supervised segmentation approach, both in simulation and using real recordings of human-demonstrated pouring motions. The results show a more robust detection of consecutive submotions with distinct features and a more consistent segmentation compared to conventional representations. We believe that other existing segmentation methods may benefit from using this trajectory representation to improve their invariance., Comment: This work has been submitted to the IEEE International Conference on Robotics and Automation (ICRA) for possible publication

Invariant descriptors of point and rigid-body motion trajectories have been proposed in the past as representative task models for motion recognition and generalization. Currently, no invariant descriptor exists for representing force trajectories, which appear in contact tasks. This paper introduces invariant descriptors for force trajectories by exploiting the duality between motion and force. Two types of invariant descriptors are presented depending on whether the trajectories consist of screw or vector coordinates. Methods and software are provided for robustly calculating the invariant descriptors from noisy measurements using optimal control. Using experimental human demonstrations of 3D contour following and peg-on-hole alignment tasks, invariant descriptors are shown to result in task representations that do not depend on the calibration of reference frames or sensor locations. The tuning process for the optimal control problems is shown to be fast and intuitive. Similar to motions in free space, the proposed invariant descriptors for motion and force trajectories may prove useful for the recognition and generalization of constrained motions, such as during object manipulation in contact., Comment: 20 pages, 14 figures. Accepted for Publication in IEEE Transactions on Robotics (July 25, 2023)

This paper compares three controllers for quasi-passive exoskeletons. The Utility Maximizing Controller (UMC) uses intent estimation to recognize user motions and decision theory to activate the support mechanism. The intent estimation algorithm requires demonstrations for each motion to be recognized. Depending on what motion is recognized, different control signals are sent to the exoskeleton. The Extended UMC (E-UMC) adds a calibration step and a velocity module to trigger the UMC. As a benchmark, and to compare the behavior of the controllers irrespective of the hardware, a Passive Exoskeleton Controller (PEC) is developed as well. The controllers were implemented on a hip exoskeleton and evaluated in a user study consisting of two phases. First, demonstrations of three motions were recorded: squat, stoop left and stoop right. Afterwards, the controllers were evaluated. The E-UMC combines benefits from the UMC and the PEC, confirming the need for the two extensions. The E-UMC discriminates between the three motions and does not generate false positives for previously unseen motions such as stair walking. The proposed methods can also be applied to support other motions., Comment: 15 pages, 12 figures. This work has been submitted to IEEE Transactions in Robotics for possible publication

Trajectory optimization is a powerful tool for robot motion planning and control. State-of-the-art general-purpose nonlinear programming solvers are versatile, handle constraints effectively and provide a high numerical robustness, but they are slow because they do not fully exploit the optimal control problem structure at hand. Existing structure-exploiting solvers are fast, but they often lack techniques to deal with nonlinearity or rely on penalty methods to enforce (equality or inequality) path constraints. This work presents Fatrop: a trajectory optimization solver that is fast and benefits from the salient features of general-purpose nonlinear optimization solvers. The speed-up is mainly achieved through the integration of a specialized linear solver, based on a Riccati recursion that is generalized to also support stagewise equality constraints. To demonstrate the algorithm's potential, it is benchmarked on a set of robot problems that are challenging from a numerical perspective, including problems with a minimum-time objective and no-collision constraints. The solver is shown to solve problems for trajectory generation of a quadrotor, a robot manipulator and a truck-trailer problem in a few tens of milliseconds. The algorithm's C++-code implementation accompanies this work as open source software, released under the GNU Lesser General Public License (LGPL). This software framework may encourage and enable the robotics community to use trajectory optimization in more challenging applications.

This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal feedback control policies. Unlike other tailored approaches for this problem class, the proposed method does not require restrictive regularity conditions on the problem. This allows its use in nonlinear optimal control problem solvers that use exact Lagrangian Hessian information. We demonstrate that our approach can be implemented in a highly efficient algorithm that scales linearly with the horizon length. Numerical tests show a significant speed-up of up to two orders of magnitude with respect to state-of-the-art general-purpose sparse linear solvers. Based on the proposed approach, faster nonlinear optimal control problem solvers can be developed that are suitable for more complex applications or for implementations on low-cost or low-power computational platforms. The implementation of the proposed algorithm is made available as open-source software.

This paper proposes and experimentally validates a Bayesian network model of a range finder adapted to dynamic environments. All modeling assumptions are rigorously explained, and all model parameters have a physical interpretation. This approach results in a transparent and intuitive model. With respect to the state of the art beam model this paper: (i) proposes a different functional form for the probability of range measurements caused by unmodeled objects, (ii) intuitively explains the discontinuity encountered in te state of the art beam model, and (iii) reduces the number of model parameters, while maintaining the same representational power for experimental data. The proposed beam model is called RBBM, short for Rigorously Bayesian Beam Model. A maximum likelihood and a variational Bayesian estimator (both based on expectation-maximization) are proposed to learn the model parameters. Furthermore, the RBBM is extended to a full scan model in two steps: first, to a full scan model for static environments and next, to a full scan model for general, dynamic environments. The full scan model accounts for the dependency between beams and adapts to the local sample density when using a particle filter. In contrast to Gaussian-based state of the art models, the proposed full scan model uses a sample-based approximation. This sample-based approximation enables handling dynamic environments and capturing multi-modality, which occurs even in simple static environments.