With the increasing demand for safe and efficient human-robot interaction in industrial applications, robotic manipulators with mixed rigid-elastic joints have gained significant attention, yet their control remains challenging due to inherent parameter uncertainties and complex dynamics. In this paper, an adaptive Cartesian position control for robotic manipulators with mixed rigid-elastic joints is presented. Adaptive controllers are designed to deal with uncertainties in the parameters of the motors, while robust control signals effectively cope with uncertainties of the links and stiffness of the elastic joints. Furthermore, a switching strategy between Cartesian space position control and joint space position control when the end-effector comes into the vicinity of the target point is proposed. This switching strategy helps to keep the pose of the robotic manipulator stable when the end-effector has approached the target point. Simulation results on a 6-DOF robotic manipulator demonstrate that the proposed control scheme can achieve the desired accuracy in position and maintain a stable pose when the end-effector reaches the target.

Traditional large Earth observation satellites (EOSs) are designed with simple imaging strategies. However, small satellites can satisfy immediate user needs through agile imaging modes. In this article, we model several agile imaging mode concepts and test them experimentally on the push-broom hyperspectral imaging cubesat HYPerspectral Smallsat for Ocean observation satellite 1 (HYPSO-1). Six imaging modes are tested: slewing, multitarget, dual-angle, wide swath, on-board processing, and dynamic pointing. The results show that the slewing and multiangle mode increased estimated signal-to-noise ratio (SNR) by$1.4\times $to$1.7\times $, the on-board processing mode decreased data latency, and the multitarget, wide swath, and dynamic pointing modes enhanced spatial coverage.

Modeling complex physical processes such as the extraction of aluminum is mainly done using pure physics-based models derived from first principles. However, the accuracy of these models can often suffer due to a partial understanding of the process, uncertainty in the input parameters, and numerous modeling assumptions. More recently, with the ever-increasing availability of data, there has been an explosion of interest in applying modern machine learning methods because of their ability to learn complex mappings directly from data. Unfortunately, these models tend to be black boxes, require an enormous amount of data, and do not utilize existing domain knowledge. In this work, we develop a novel approach combining physics-based and data-driven modeling approaches while eliminating some weaknesses. We use a data-driven model to correct a misspecified physics-based model of the Hall–Héroult process in an aluminum electrolysis cell using a corrective source term added to the set of governing ordinary differential equations. Our approach ensures that the existing knowledge is utilized to the maximum extent possible while relying on the data-driven models only to model those aspects which the physics-based model does not represent well. We compare this approach with an end-to-end learning approach and an ablated physics-based model, showing that the proposed hybrid method is more accurate, consistent, and stable for long-term predictions.

Model-based reinforcement learning promises to be an effective way to bring reinforcement learning to real-world robotic systems by offering a sample efficient learning approach compared to model-free reinforcement learning. However, model-based reinforcement learning approaches at present struggle to match the performance of model-free ones. This work attempts to fill this gap by improving the performance of model-based reinforcement learning while further improving its sample efficiency. To improve the sample efficiency, an exploration strategy is formulated which maximizes the information gain. The asymptotic performance is improved by compensating for the model-bias using a model-free critic. We have evaluated our proposed approach on four reinforcement learning benchmarking tasks in the openAI gym framework.

Sporadic ocean color events with characteristic spectra, in particular algal blooms, call for quick delivery of high-resolution remote sensing data for further analysis. Motivated by this, we present the mission design for HYPerspectral Smallsat for Ocean observation (HYPSO-1), a 6U CubeSat at 500 km orbital altitude hosting a custom-built pushbroom hyperspectral imager with wavelengths 387–801 nm at 3.33 nm bandpass and a swath width of 70 km. The imager’s expected signal-to-noise ratio is characterized for typical open ocean water-leaving radiance which can be flexibly increased by binning pixels. Using geometric principles, the satellite shall execute a slew maneuver during a scan to induce greater overlap in the pixels with a goal to enable better than 100 m spatial resolution. Since high-dimensional hyperspectral data need to be transmitted over limited space-to-ground communications, we have designed a modular FPGA-based onboard image processing architecture that significantly reduces the data size without losing important spatial-spectral information. We justify the concept with a simulated scenario where HYPSO-1 first collects numerous hyperspectral images of a 40 km by 40 km coastal area in Norway and aims to immediately transfer these to nearby ground stations. Using CCSDS123 lossless compression, it takes about one orbital revolution to obtain the complete data product when considering overhead in satellite bus communications and less than 10 min without the overhead. It is shown that even better latency can be achieved with more advanced onboard processing algorithms.

In this paper, a method is presented for lowering the energy consumption and/or increasing the speed of a standard manipulator spray painting a surface. The approach is based on the observation that a small angle between the spray direction and the surface normal does not affect the quality of the paint job. Recent results in set-based kinematic control are utilized to develop a switched control system, where this angle is defined as a set-based task with a maximum allowed limit. Four different set-based methods are implemented and tested on a UR5 manipulator from Universal Robots. Experimental results verify the correctness of the method, and demonstrate that the set-based approaches can substantially lower the paint time and energy consumption compared to the current standard solution.

For the last decades, additive manufacturing (AM) has become an ever increasing part of the development of new technology and devices. However, it is still challenging to use this technology on a larger scale. This paper presents the state-of-the-art of large-scale AM, looking into some of the projects that have come furthest in utilising AM technology on large structures such as buildings or sculptures. The background for this research is to consider the possibility of large-scale AM by robot manipulator using the welding method cold metal transfer (CMT). After outlining the the necessary algorithms and components for such an AM system, a proof-of-concept experiment using a UR5 robot is presented. This initial experiment will clarify some of the challenges that need to be addressed in future work.

This paper proposes and experimentally validates a straight line path following controller for underwater snake robots in the presence of constant irrotational currents of unknown direction and magnitude. An integral line-of-sight guidance law is presented, which is combined with a sinusoidal gait pattern and a directional controller that steers the robot toward and along the desired path. The stability of the proposed control scheme in the presence of ocean currents is investigated by using Poincaré map analysis. Simulation results are presented to illustrate the performance of the proposed path following controller for both lateral undulation and eel-like motion. In addition, the performance of the path following controller is investigated through experiments with a physical underwater snake robot. The experimental results show that the proposed control strategy successfully steers the robot toward and along the desired path in the presence of an unknown constant irrotational current in the inertial frame.

Drop-on-demand weed control is a field of research within Precision Agriculture, where the herbicide application is controlled down to individual droplets. This paper focuses on the fluid dynamics and electronics design of the droplet dispensing. The droplets are formed through an array of nozzles, controlled by two-way solenoid valves. A much used control circuit for opening and closing a solenoid valve is a spike and hold circuit, where the solenoid current finally is discharged over a Schottky diode on closing. This paper presents a PWM design, where the discharge is done by reversing the polarity of the voltage. This demands an accurate timing of the reverse spike not to recharge and reopen the valve. The PWM design gives flexibility in choosing the spike and hold voltage arbitrarily, and may use fewer components. Calculations combined with laboratory experiments verify this valve control strategy. In early flight the stability of the tail, or filament, is described in theory by the Ohnesorge number. In later flight, when a droplet shape has formed, the droplet stability is governed by the Weber number. These two considerations have opposite implications on the desired surface tension of the fluid. The Weber number is more important for longer distances, as the filament satelites normally catch up and join the main droplet in flight.

Increasing efficiency by improving the locomotion methods is a key issue for underwater robots. Hence, an accurate dynamic model is important for both controller design and efficient locomotion methods. This paper presents a model of the kinematics and dynamics of a planar, underwater snake robot aimed at control design. Fluid contact forces and torques are modeled using analytical fluid dynamics. The model is derived in a closed form and can be utilized in modern model-based control schemes. The proposed model is easily implemented and simulated, regardless of the number of robot links. Simulation results with a ten link robotic system are presented.

This paper presents a general motion planning framework for body shape control of snake robots. We demonstrate the applicability of the framework for straight line path following control, and for implementing body shape compliance in environments with obstacles. Compliance is achieved by assigning mass-spring-damper dynamics to the shape curve defining the motion of the robot. The performance of the control strategies is illustrated with simulation results.

This paper considers straight line path following control of wheel-less planar snake robots using sliding mode techniques. We first derive the Poincaré representation of the equations of motion of the robot using the techniques of differential geometry. Furthermore, we use partial feedback linearization to linearize the directly actuated part of the system dynamics. Subsequently, we propose an analytical solution to the robust path following control problem in two steps. In the first step, we use sliding mode techniques to design a robust tracking controller for the joints of the robot to track a desired gait pattern. In the second step, we stabilize an appropriately defined sliding manifold for the underactuated configuration variables of the robot, thereby guaranteeing convergence of the robot to the desired straight path. The paper presents simulation results which validate the theoretical results.

Snake robots are biomimetic robots highly suited for traversing challenging terrain where traditional robots have difficulty moving. A key aspect is obstacle-aided locomotion, where the snake pushes against the environment to achieve the desired propulsion. The main focus of this work is to optimally determine how to use the motor torque inputs that result in obstacle forces suitable to achieve some user-defined desired path for the snake. To this end, we present a new dynamical snake model, an explicit algebraic relationship between input and obstacle forces, and formulate an optimization problem that seeks to minimize energy consumption while achieving propulsion along the desired path.

Increasing efficiency by improving the locomotion methods is a key issue for underwater robots. Consequently, an accurate dynamic model is important for both controller design and for the development of efficient locomotion methods. This paper presents a model of the kinematics and dynamics of an underwater snake robot moving in a vertical plane in 3D. The fluid contact forces (hydrodynamic forces) and torques (fluid moments) are modeled using analytical fluid dynamics. Hydrodynamic forces and torques, i.e. linear and nonlinear drag forces, current effects, added mass and fluid torque effects, are considered. In addition, this modeling approach also takes into account the hydrostatic forces (gravitational forces and buoyancy). The model is given in a closed form and is thus in a form that is well-suited for modern model-based control schemes. The proposed model is easily implemented and simulated, regardless of the number of robot links. Simulation results for lateral undulation and eel-like motion with a ten link robotic system are presented.

This paper presents a motion planning framework for three-dimensional body shape control of snake robots. Whereas conventional motion planning approaches define the body shape of snake robots in terms of their individual joint angles, the proposed framework allows the body shape to be specified in terms of Cartesian coordinates in the environment of the robot. This approach simplifies motion planning since Cartesian coordinates are more intuitively mapped to the overall body shape of the snake robot. The paper demonstrates the applicability of the framework for realizing different types of three-dimensional motion patterns.

This paper presents the snake robot Mamba, which is a modular, reconfigurable, and waterproof experimental platform developed to support the ongoing research on snake robot locomotion, including underwater locomotion. A novel contribution of the snake robot is its ability to measure environment contact forces acting along its body, which is achieved by isolating the actuator inside each joint module with a custom-designed force/torque sensor. The paper describes the design of this sensor and presents experimental results which illustrate its performance.

In this work, the Mixed-Integer (MIP) formulation for unit commitment problem (UC) for power systems is discussed. A new formulation for the start-up cost is suggested as well. This new formulation of the start-up cost exploits the transformation of the conditional statements into inequalities that comprise linear combination of binary variables. Solutions of the suggested optimization problem were obtained. A comparison between these solutions and those of a strategy common in literature is held to show that the new strategy gives same results with less number of constraints and tighter capture of the start-up cost.

This paper presents a control framework for shape control of snake robots for the purpose of locomotion. An advantage of the framework is that it allows the macroscopic shape of a snake robot to be controlled explicitly and intuitively. The framework is based on specifying the desired shape of the snake robot as a continuous shape curve defined by a set of shape control points interconnected by Bézier curves. We propose a novel approach for motion generation in which the shape curve is repeatedly extended according to a desired gait pattern while a virtual snake robot is progressed along the shape curve to retrieve joint reference angles for the physical snake robot. Practical applications of the proposed control framework are exemplified along with simulation results.

This paper presents the design of a waterproof and mechanically robust joint module for the snake robot Mamba. The main contribution of the module is a custom-designed force/torque sensor based on strain gauges, which enables the module to measure forces and torques acting on its joint shaft. The ability to measure joint constraint forces and torques enables a snake robot to estimate the external contact forces from its environment, which is important for intelligent and adaptive snake robot locomotion. The paper presents experimental results which illustrate the performance of the force/torque sensor.

As a step towards enabling snake robots to move in unstructured environments, this paper considers control strategies where environment adaptation is combined with directional control of snake robot locomotion. The first contribution of the paper is a general framework for motion control of snake robots, which allows the motion to be specified in terms of a body wave component, an environment adaptation component, and a heading control component. As a second contribution, we employ the controller framework to propose a control law for straight line path following control of snake robots in environments with obstacles. The paper presents simulation results where the path following controller is combined with a waypoint guidance strategy in order to steer the snake robot between waypoints in an obstacle environment.

In this paper, we present the experimental results of a new spray paint algorithm presented in previous publications. Both theory and simulations indicate that the proposed method allows a robotic manipulator to paint a given surface using substantially lower joint torques than with conventional approaches. In this paper, we confirm this by implementing the algorithm on an ABB robot and we find that the joint torques needed to follow the trajectory are substantially lower than for the conventional approach. The approach presented is based on the observation that a small error in the orientation of the end effector does not affect the quality of the paint job. It is far more important to maintain constant velocity for the entire trajectory. We thus propose to allow a small error in the specification of the end-effector orientation, and we show how this allows us to obtain a higher constant speed throughout the trajectory. In addition, to improve the uniformity of the paint coating we are also able perform the paint job in less time.

In a recent paper, the authors have proposed a control strategy for a snake robot during obstacle-aided locomotion. In this paper, experimental results are presented where the controller is shown to successfully maintain the forward propulsion of a physical snake robot in a course with different obstacle configurations.

This paper derives and experimentally investigates fundamental properties of the velocity of a snake robot conducting lateral undulation. In particular, the derived properties state that the average forward velocity of the snake robot 1) is proportional to the squared amplitude of the sinusoidal motion of each joint of the robot, 2) is proportional to the angular frequency of the sinusoidal motion of each joint, 3) is proportional to a particular function of the constant phase shift between the joints, and 4) is maximized by the phase shift between the joints that also maximizes the particular phase shift function. The paper presents an experimental investigation of the validity of these derived properties by measuring the forward velocity of a physical snake robot during lateral undulation. The experimental results support the theoretical findings.

Robotic manipulators on non-inertial platforms, such as ships, have to endure large inertial forces due to the non-inertial motion of the platform. When the non-inertial platform's motion is known, motion planning and control algorithms can eliminate these perturbations-in fact, in some situations the motion planning algorithms can even leverage the inertial forces to more cheaply move to a target point. However, for many non-inertial platforms, the motion is unknown. In this paper we investigate how prediction errors and the choice of the prediction horizon affect the motion planning and control of robots mounted on a non-inertial base with a particular focus on seaborne platforms. We study the following three aspects: (i) We study prediction of ship motion and how prediction errors affect the motion planning and control of the manipulator. (ii) We evaluate the relationship between prediction accuracy and control. In particular, we study what prediction horizon length is useful for motion planning and control. We also consider how uncertainties in the ship motion predictions map to uncertainties in the future state of the robot and how to include the variance in the cost function to increase the optimal horizon length. (iii) Finally, we study a receding horizon approach, which re-solves the optimal control problem on-line over a horizon as determined to be meaningful from (ii). Several simulations are presented and, to our knowledge, for the first time experiments of ship-manipulator systems based on real ship motion data are presented.

A snake can traverse cluttered and irregular environments by using irregularities around its body as push-points to aid the propulsion. This characteristic feature of biological snake locomotion, denoted obstacle-aided locomotion, is investigated for snake robot locomotion purposes in this paper. The paper presents a hybrid model of the dynamics of a planar snake robot interacting with obstacles in its environment. Obstacle contact forces are calculated by formulating and solving a linear complementarity problem (LCP). The existence and uniqueness properties of the state evolution of the hybrid model are investigated. Simulation results validate the hybrid modelling approach.

This paper presents a model of the kinematics and dynamics of a planar, wheelless snake robot aimed at control design and stability analysis purposes. The proposed model is significantly less complex than existing models of planar snake robot locomotion. The paper presents an analysis of an existing complex snake robot model which reveals a set of essential properties that characterize the overall motion of a planar snake robot. The proposed model is developed to capture only these essential properties of snake locomotion, thereby significantly reducing the complexity compared to the original model used in the analysis. The paper presents simulation results that indicate that the qualitative behaviour of the proposed model and the original complex model are similar, and that a quantitative similarity is achieved with a proper choice of numerical values of the friction coefficients in the two models.

This paper presents a set of fundamental properties of the velocity of a snake robot conducting lateral undulation on a planar surface. In particular, the derived properties state that the average forward velocity of the snake robot 1) is proportional to the squared amplitude of the sinusoidal motion of each joint of the robot, 2) is proportional to the angular frequency of the sinusoidal motion of each joint, 3) is proportional to a particular function of the constant phase shift between the joints, and 4) is maximized by the phase shift between the joints that also maximizes the particular phase shift function. The paper presents simulation results that support the validity of the derived properties.

In this paper, we present a method for increasing the speed at which a standard industrial manipulator can paint a surface. The approach is based on the observation that a small error in the orientation of the end effector does not affect the quality of the paint job. It is far more important to maintain constant velocity throughout the trajectory. We consider the freedom in the end-effector orientation as functional redundancy and represent the restriction on the orientation error as barrier functions or linear matrix inequalities. In doing this, we cast the problem of finding the optimal orientation at every time step into a convex optimization problem that can be solved very efficiently and in real time. We show that the approach allows the end effector to maintain a higher constant velocity throughout the trajectory guaranteeing uniform paint coating and substantially reducing the time needed to paint the object.

A snake can traverse cluttered and irregular environments by using irregularities around its body as push points to aid the propulsion. This characteristic feature of biological snake locomotion, which is denoted as obstacle-aided locomotion, is investigated for snake robot locomotion purposes in this paper. The paper presents a hybrid model of the dynamics of a planar snake robot interacting with obstacles in its environment. Obstacle contact forces are calculated by formulating and solving a linear complementarity problem (LCP). The existence and uniqueness properties of the state evolution of the hybrid model are investigated. The paper also presents a hybrid control strategy employing measured contact forces to maintain propulsion while simultaneously preventing the snake robot from being jammed between obstacles in its path. The simulation results validate the hybrid modelling approach and the effectiveness of the proposed control strategy.

Robotic manipulators on ships and platforms suffer from large inertial forces due to the non-inertial motion of the ship or platform. When operating in high sea state, operation of such manipulators can be made more efficient and robust if these non-inertial effects are taken into account in the motion planning and control systems. Motivated by this application, we present a rigorous and singularity-free formulation of the dynamics of a robotic manipulator mounted on a non-inertial base. We extend the classical dynamics equations for a serial manipulator to include the 6-DoF motion of the non-inertial base. Then, we show two examples of a 1-DoF and a 4-DoF manipulator to illustrate how these non-inertial effects can be taken into account in the motion planning.

In a wide range of applications the orientation of a rigid body does not need to be restricted to one given orientation, but can be given as a continuous set of frames. We address the problem of defining such sets and to find simple tests to verify if an orientation lies within a given set. The unit quaternion is used to represent the orientation of the rigid body and we develop three different sets of orientations that can easily be described by simple constraints in quaternion space. The three sets discussed can also be described as convex cones in Ropf3defined by different norms. By describing the sets as convex cones and using certain properties of dual cones, we are able find simpler representations for the set of orientations and computationally faster and more accurate tests to verify if a quaternion lies within the given set.

This paper investigates the controllability properties of planar snake robots influenced by viscous ground friction forces. The paper provides three contributions: 1) A partially feedback linearized model of a planar snake robot is developed. 2) A stabilizability analysis is presented proving that any asymptotically stabilizable control law for a planar snake robot to an equilibrium point must be time-varying. 3) A controllability analysis is presented proving that planar snake robots are not controllable when the viscous ground friction is uniform, but that a snake robot becomes strongly accessible when the viscous ground friction is non-uniform. The analysis also shows that the snake robot does not satisfy sufficient conditions for small-time local controllability (STLC).

This paper presents an analysis of snake locomotion that explains how non-uniform viscous ground friction conditions enable snake robots to locomote forward on a planar surface. The explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion. From this analysis, a controller for a snake robot is proposed. A Poincare¿ map is employed to prove that all state variables of the snake robot, except for the position in the forward direction, trace out an exponentially stable periodic orbit.

In this paper we show how a continuous set of orientations can be represented as a positive definiteness test on a given matrix. When this continuous set is restricted by the maximum allowed orientation error in some or all directions it is shown that the requirement for an orientation to satisfy these restrictions is equivalent to positive definiteness for a certain matrix. The problem of finding the optimal orientation that satisfies these restrictions is hence transformed into an optimisation problem on the Riemannian manifold of linearly constrained symmetric positive definite matrices. Thus, the problem of finding the optimal orientation can be solved as a standard optimisation problem with the constraints written in the form of linear matrix inequalities or barrier functions. Linear matrix inequalities have been extensively studied in the optimisation communities and good and efficient algorithms are available.