Operational Space Control Research Articles

Optimal robust online tracking control for space manipulator in task space using off-policy reinforcement learning

This study addresses the demands for adaptability, uncertainty management, and high performance in the control of space manipulators, and the inadequacies in achieving optimal control and handling external uncertainty in task space in previous research. Based on off-policy reinforcement learning, a model-free and time-efficient method for online robust tracking control in task space is devised. To address the complexity of dynamic equations in task space, a mixed-variable approach is adopted to transform the multivariable coupled time-varying problem into a single-variable problem. Subsequently, the optimal control policy is derived with the disturbance convergence, stability, and optimality of the control method being demonstrated. This marks the first instance of achieving robust optimal tracking control in task space for space manipulators. The efficacy and superiority of the presented algorithm are validated through simulation.

Intelligent and robust control of space manipulator for sustainable removal of space debris

This study focuses on enhancing the control precision and efficiency of a two-degree-of-freedom (2-DOF) space manipulator used for active space debris removal. The unpredictable space environment introduces large uncertainties, which introduces unique challenges beyond the capabilities of a standalone computed torque controller and degrades control performance. To address this problem, a robust controller is developed, integrating traditional techniques such as sliding mode and computed torque control with a Neural Network framework. This synergy leverages both methods' strengths—conventional controls' accuracy and Neural Network's adaptability. The integration of Neural Network-based sliding mode control complements the robustness of computed torque control by actively mitigating uncertainties and disturbances inherent in the space environment. The 2-DOF manipulator's state variables model the system dynamics, necessitating accurate relative motion estimation between the manipulator and debris. The global asymptotic stability of the developed algorithm is demonstrated through the Lyapunov theorem, guaranteeing error convergence to zero. The convergence, stability, precision, tracking errors, and responsiveness of the controller have been analysed and validated by the MATLAB Simulink simulations. The novel approach's performance effectiveness is substantiated by numerical simulations and a comparative analysis with conventional computed torque control. Outcomes highlight the superior precision and efficiency in manipulator tracking the trajectory, validating the integrated controller's potential for successful active space debris removal.

Adaptive EKF enhanced fault diagnosis and fault tolerant control for space manipulators with position measurements only

Space manipulators play a critical role in the operation of space robots. However, the failure of these manipulators can affect the control performance and even lead to instability. To improve the safety and robustness of space manipulators, this paper presents an efficient fault diagnosis and fault tolerant control method by integrating adaptive extended Kalman filter (AEKF) and sliding mode control (SMC). The proposed method uses AEKF for system estimation, taking into account uncertainties in the process and measurement noise, as well as sensor limitations. By detecting the failure of angle sensors timely, the trajectory tracking performance can be guaranteed by the robustness of AEKF. In cases where a joint experiences free-swinging, the failure can be identified based on the estimated control effectiveness coefficients from AEKF. Then, once the failure is identified, the joint angle can be regulated by exploiting the motion coupling between the joints. Furthermore, SMC is employed to mitigate the effects of unknown disturbances in the joints. The effectiveness of the proposed method is demonstrated through numerical simulation, which illustrates its ability to diagnose failures and maintain control performance under various failure scenarios. In addition, the robustness of the method is verified through Monte Carlo simulation, demonstrating its reliability in dealing with various uncertainties.

Parameter Identification of Space Manipulator's Flexible Joint

It is considered to use a manipulator mounted on a satellite in order to perform active debris removal missions. Space manipulator control system needs to take the dynamic model of the satellite-manipulator system into account because of the influence of the manipulator motion on the position and attitude of the satellite. Therefore, precise modelling of the space manipulator dynamics as well as parameter identification are needed in order to improve the credibility of the simulation tools. In this paper we presented the identification of the flexible-joint space manipulator model based on dynamic equations of motion. Experiments were performed in emulated microgravity environment using planar air bearings. The arbitrarily selected joint-space trajectory was performed by the manipulator’s control system. The experiments were repeated multiple times in order to analyze the identification method sensitivity. The identification is based on Simulink SimMechanics model. Thus, the procedure can be used for any space manipulator without the need of obtaining analytical relations for dynamic equations each time. Including joint flexibility and spring viscous damping in the dynamic model allowed to reflect the experimental measurements better than the reference model could. Identified parameters of the flexible joint have values of the same magnitude as corresponding real system parameters.

Appointed-time velocity-free prescribed performance control for space manipulators

This paper investigates the appointed-time velocity-free prescribed performance control for the space manipulators. A novel exponential-modified tracking differentiator is developed for estimating differential signals to address missing velocity information measurements. The original tracking problem is converted into the boundedness control, achieved through the bidirectional constraint-free mapping, which incorporates a novel performance function characterized by appointed-time convergence property. The coordinated control law is contributed with the designed velocity-free reference stable schemes. Ultimately, we achieve effective tracking of time-varying trajectories, ensuring simultaneous tracking of the desired values for the base and the manipulator. The tracking errors are constrained by the performance functions and convergence to the steady values at an appointed time. Simulation results validate the effectiveness of the proposed control scheme.

Hierarchical jumping optimization for hydraulic biped wheel-legged robots

This paper addresses the challenging task of implementing dynamic jumping motions for biped wheel-legged robots, a motion mode that significantly enhances their mobility and adaptability to complex terrains. However, due to the under-actuation and dynamic instability nature of this type of robots, executing high-dynamic motions remains difficult. To tackle this issue, this paper proposes a novel Hierarchical Jumping Optimization (HJO) framework specifically designed for hydraulic biped wheel-legged robots. The framework involves an upper layer center of mass (CoM) trajectory optimization based on the dynamic properties of a dual-mass spring loaded inverted pendulum (DM-SLIP) model, along with the CoM dynamic coupling relationship introduced by the under-actuated nature of two-wheel self-balancing robots. This leads to a reduction in the dimensionality of optimization variables, facilitating effective CoM trajectory generation. Subsequently, the CoM motions of the robot in the Cartesian space are mapped into the joint space in real-time by using the middle layer hierarchical operational space control (HOSC). By incorporating centroid angular momentum as a task objective, the stability of the robot in highly dynamic motions can be enhanced. Finally, the proposed HJO framework is experimentally validated through jumping experiments on an actual robot. The experimental results demonstrate that the framework optimally utilizes the robot’s under-actuated characteristics, significantly reducing computational costs associated with planning and tracking, while simultaneously preserving motion accuracy and robust.

Adaptive coordinated control for space manipulators with input saturation

This paper presents a concurrent learning command filtering control scheme for space manipulators in the post-capture phase. Due to the complex space environment and inherent model characteristics, space manipulators are subject to parameter uncertainties, non-conserved momentum and input saturation, which will degrade the control performance. To this end, a novel fixed-time concurrent learning law is developed in the presence of the non-conserved linear and angular momentum, where the convergence rate of the estimated parameters is determined by the control coefficients rather than the unpredictable excitation level. Then, a fixed-time command filtering strategy with the error compensation and saturation compensation is designed, to cope with input saturation and avoid the derivation operation of Jacobi matrices and inertial matrices simultaneously. By means of the proposed control scheme, the spacecraft attitude regulation error and the end-of-arm trajectory tracking error can converge to the small neighborhood of zeros within a fixed time. Simulation results demonstrate the effectiveness of the proposed control scheme.

A Non-Prehensile Object Transportation Framework With Adaptive Tilting Based on Quadratic Programming

This work proposes an operational space control framework for non-prehensile object transportation using a robot arm. The control actions for the manipulator are computed by solving a quadratic programming problem considering the object's and manipulator's kinematic and dynamic constraints. Given the desired transportation trajectory, the proposed controller generates control commands for the robot to achieve the desired motion whilst preventing object slippage. In particular, the controller minimizes the occurrence of object slippage by adaptively regulating the tray orientation. The proposed approach has been extensively evaluated numerically with a 7-degree-of-freedom manipulator, and it is also verified and validated with a real experimental setup.

An adaptive continuous sliding mode feedback linearization task space control for robot manipulators

Two main domains have been followed; joint space control and operational (task) space control for robot manipulators. Task space control is simpler than joint space control as it avoids tackling the robot inverse kinematics which is very complex and challenging. However, in order to design robust and accurate controllers in operational space, both kinematics and dynamics uncertainties must be considered. Additionally, singularities that may occur while mapping between joint space and task space should be addressed. To tackle these issues, a new adaptive task space control approach is developed in this paper. The developed approach is able to overcome uncertainties and mitigate the chattering that commonly occur during the control process. The introduced control system has been proven to be globally stable using a designed Lyapunov function. The simulation results show that the suggested model is able to control the robot manipulators efficiently even in the existence of external disturbances.

Singularity-robust full-pose workspace control of space manipulators with non-zero momentum

We address the end-effector full-pose tracking control problem in free-floating space manipulators, experiencing constant non-zero linear and angular momentum. The aim is to develop an output-tracking (workspace) control law free of singularities due to parameterizing the end-effector motion and being robust against singularities of the input–output decoupling matrix (generalized Jacobian matrix). Space manipulators are modeled as open-chain multi-body systems with single- and multi-degree-of-freedom joints, whose kinematics and dynamics are formulated on the Special Euclidean group SE(3). Such systems exhibit conserved (not necessarily zero) total momentum when operating in the free-floating regime, which we use to systematically reduce their dynamical equations by eliminating the base spacecraft’s motion. To avoid parameterizing the end-effector motion, we consider its full pose as the system output and develop a novel feedback linearization technique on the matrix Lie group SE(3) in the reduced phase space of the space manipulator. We then propose an intrinsic feedforward, feedback proportional–integral–derivative workspace controller involving a coordinate-free pose error function on SE(3) and velocity error on its Lie algebra. Using a Lyapunov candidate, this controller is proven to stabilize the end-effector pose to a feasible desired trajectory. The input–output decoupling matrix in the proposed control law can lose rank at some regions of the configuration space; hence, we implement a singularity-robust inverse, derived from the damped least squares method, to avoid impractical joint torques in these regions. The developed controller is implemented on a 7-degree-of-freedom manipulator onboard a spacecraft and its efficacy and robustness are demonstrated through a series of simulations.

Neuromorphic control of a simulated 7-DOF arm using Loihi

In this paper, we present a fully spiking neural network running on Intel’s Loihi chip for operational space control of a simulated 7-DOF arm. Our approach uniquely combines neural engineering and deep learning methods to successfully implement position and orientation control of the end effector. The development process involved four stages: (1) Designing a node-based network architecture implementing an analytical solution; (2) developing rate neuron networks to replace the nodes; (3) retraining the network to handle spiking neurons and temporal dynamics; and finally (4) adapting the network for the specific hardware constraints of the Loihi. We benchmark the controller on a center-out reaching task, using the deviation of the end effector from the ideal trajectory as our evaluation metric. The RMSE of the final neuromorphic controller running on Loihi is only slightly worse than the analytic solution, with 4.13% more deviation from the ideal trajectory, and uses two orders of magnitude less energy per inference than standard hardware solutions. While qualitative discrepancies remain, we find these results support both our approach and the potential of neuromorphic controllers. To the best of our knowledge, this work represents the most advanced neuromorphic implementation of neurorobotics developed to date.

Task-Priority Operational Space Control for Vehicle-Manipulator Systems with Modelling Errors

The dynamics of underwater vehicle-manipulator systems (UVMSs) are very hard to model, which reduces the feasibility of model-based control approaches. Even so, such strategies prove useful in redundancy resolution. In this paper, higher-order sliding mode control is combined with task-priority operational space control (OSC) in order to handle and utilize the redundancy of UVMSs despite the presence of dynamic model errors. At each task level, the generalized super-twisting algorithm is implemented to reject effects caused by model errors while maintaining a continuous control signal. The general problem of OSC with uncertain models is analyzed, and some of its challenges are highlighted, including an algebraic loop. We conduct a simulation study on a highly redundant UVMS, where we compare task-level higher-order sliding mode control to proportional-derivative control. Though this paper is motivated by challenges specific to UVMSs, the results also hold for other vehicle-manipulator systems.

Task-space control for industrial robot manipulators with unknown inner loop control architecture

The operational space control of a robot manipulator using external sensors requires stabilizing the compound system {external sensors - outer controller - inner controller - robot manipulator}. The user must access the inner controller to reshape it to achieve this stabilization. Due to intellectual property protection purposes, most industrial robots have an unknown or inaccessible inner controller. Therefore, it is tricky to design a stable control scheme. To solve this problem, an adaptive radial basis function neural network (RBF NN) outer controller is proposed, which approximates the inner controller’s dynamics to eliminate its effect in the closed-loop. An inherent property for RBF NN is used to reduce the number of adaptive parameters. Since this technique introduces approximation errors, it is included in the control scheme, a term that constrains the system to converge rapidly to the performances prescribed by the user. It is proved that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB) through Lyapunov theory. The effectiveness of the proposed approach is verified through simulation comparisons and experimental studies.

Operational Space Iterative Learning Control of Coupled Active/Passive Multilink Cable-Driven Hyper-Redundant Robots

Abstract The operational space control (OSC) of multilink cable-driven hyper-redundant robots (MCDHRs) is required to perform tasks in many applications. As a new coupled active-passive (CAP) MCDHR system, due to the multiple couplings between the active cables, the passive cables, the joints, and the end-effector, the OSC becomes more and more complicated. However, there is currently no robust and effective control method to solve the OSC problem of such types MCDHRs. In this paper, an OSC framework of CAP-MCDHRs using a dynamics-based iterative-learning-control (ILC) method is proposed, considering multivariate optimization. First, the multi-coupling kinematics and the series-parallel coupling dynamics equation (i.e., cable-joint-end) of the CAP-MCDHR are derived. Then, a dynamics-based trajectory tracking framework was constructed. Moreover, an OSC accuracy evaluation model based on a high-precision laser tracker was also designed. The framework allows the tracking of operational space trajectories (OSTs) online with the feasible cable tension and the joint angle. It is also shown that the tracking performance can be improved through the ILC when the desired trajectory is repeatedly performed. Finally, a simulation and an experimental hardware system are built. The results show that the proposed control framework can be easily and effectively applied to the CAP-MCDHR used in real-time.

Humanoid Motion Control by Compliance Optimization Explicitly Considering its Positive Definiteness

This article discusses a compliance optimization approach that satisfies positive definiteness. Physical human–robot interactions are an important topic in robotics, for which force or compliance control is a key technology. Operational space control (OSC) is one of the most common approaches for robot force control with redundant degrees of freedom. By linearizing OSC, we can derive joint stiffness and viscosity matrices equivalent to the OSC. For an appropriate control, it is important that these matrices are positive definite. However, the stiffness matrix equivalent to the OSC is not always positive definite. In this case, a high kinetic energy is required, which is a problem in terms of the control performance. Therefore, the control performance can be improved by explicitly considering the positive definiteness of the stiffness or compliance. In this article, the authors derive a dynamically consistent compliance formulation and propose a compliance optimization that satisfies positive definiteness. The space of the symmetric positive definite matrix is a Riemannian manifold. We show that minimizing the Riemaniann geodesic distance results in a better performance compared with using OSC. The proposed method is validated via forward dynamics simulations and experiments using a hydrostatically driven humanoid Hydra.

Time delay estimation-based reactionless augmented adaptive sliding mode control of a space manipulator’s pregrasping a target

AbstractReaction null space (RNS) planning and control of a planar three-link space manipulator’s pregrasping a spinning target are studied. First, the Lagrange dynamic model of the manipulator was established. Second, the RNS motion planning algorithm was derived, and the vector norm constraint algorithm of RNS planning was addressed to ensure certain joint angular acceleration constraints were satisfied. Furthermore, an augmented adaptive sliding mode controller based on time delay estimation (TDE) was proposed. This controller estimated the unknowns of the system by TDE technology, in which accurate and complete dynamics were not required, and an adaptive TDE was introduced to decrease the estimation errors and avoid serious chattering. Finally, numerical simulations were carried out to verify the effectiveness of the proposed RNS planning and control algorithm.

Fault tolerant motion planning and control of space manipulators with free-swinging joint failure based on controllable degree

Space manipulators are usually used to assist or replace the astronaut to execute on-orbit tasks. However, due to the burdensome tasks and harsh space environment, free-swinging joint failure is prone to happen, causing the task to be unable to continue. Once the joint failure occurs, the base and free-swinging joint belong to underactuated units, so their trajectories have to be controlled by the active joint. To execute on-orbit tasks successfully after the joint failure occurs, a fault tolerant motion planning and control method (FTMPC) of the space manipulator based on controllable degree is proposed. First, based on the dynamics model of space manipulators, the dynamics coupling relationship between the active joint and the underactuated unit is established. Second, according to the inertia matrix, Coriolis and centrifugal terms of the dynamics model, a controllable degree index of the active joint over the underactuated unit is constructed. Third, according to the specific task requirement and controlled object, the FTMPC based on the controllable degree is designed. The FTMPC is applied according to the number of active joints and underactuated units and whether there is a dynamic singularity during the task execution. The simulation is carried out with a 7-DOF space manipulator, verifying the correctness and effectiveness of the FTMPC. The method has two advantages: 1) Coriolis and centrifugal terms are both considered for the first time in evaluating the control ability of active joints, making the evaluation result more in line with the motion characteristics of space manipulators; 2) A FTMPC based on the controllable degree is proposed, completing the task without dynamic singularity or huge torque on the active joint.

Hierarchical Task-Space Optimal Covariance Control With Chance Constraints

This letter presents a new control paradigm applicable to nonlinear systems such as robots subject to chance and covariance assignment constraints which we refer to as hierarchical optimal covariance control. To the best of our knowledge, this is the first study to formulate the hierarchical optimal covariance control problem involving multiple operational tasks. The framework is defined as a multi-stage optimization problem considering multiple hierarchical tasks specified in lexicographic order. Towards this goal, we first approximate the nonlinear dynamic model of a robot into multiple linear stochastic systems by linearizing the model along given trajectories. We then project these stochastic models onto the null-space of the previous task models for efficiently solving lexicographical optimization. In addition, we specify probability functions to account for chance constraints using the Whittacker M function. We formulate the chance constraints as a positive semi-definite matrix constraint and solve the hierarchical optimal covariance control problem using sequential semi-definite programming. We demonstrate that this procedure yields higher accuracy for multiple hierarchical tasks than employing deterministic operational space control models.

A modified forward and backward reaching inverse kinematics based incremental control for space manipulators

Forward and backward reaching inverse kinematics (FABRIK) is an efficient two-stage iterative solver for inverse kinematics of spherical-joint manipulator without the calculation of Jacobian matrix. Based on FABRIK, this paper presents an incremental control scheme for a free-floating space manipulator consists of revolute joints and rigid links with the consideration of joint constraints and dynamic coupling effect. Due to the characteristics of FABRIK, it can induce large angular movements on specific joints. Apart from that, FABRIK maps three dimensional (3D) problem into two dimensional (2D) problem by a simple geometric projection. This operation can cause infinite loops in some cases. In order to overcome these issues and apply FABRIK on space manipulators, an increments allocation method is developed to constrain the angular movements as well as to re-orient the end-effector. The manipulator is re-positioned based on the momentum conservation law. Instead of pure target position tracking, the orientation control of the end-effector is also considered. Numerical simulation is performed to testify and demonstrate the effectiveness and reliability of the proposed incremental control approach.

A Riemannian metric for geometry-aware singularity avoidance by articulated robots

Articulated robots such as manipulators increasingly must operate in uncertain and dynamic environments where interaction (with human coworkers, for example) is necessary. In these situations, the capacity to quickly adapt to unexpected changes in operational space constraints is essential. At certain points in a manipulator’s configuration space, termed singularities, the robot loses one or more degrees of freedom (DoF) and is unable to move in specific operational space directions. The inability to move in arbitrary directions in operational space compromises adaptivity and, potentially, safety. We introduce a geometry-aware singularity index, defined using a Riemannian metric on the manifold of symmetric positive definite matrices, to provide a measure of proximity to singular configurations. We demonstrate that our index avoids some of the failure modes and difficulties inherent to other common indices. Further, we show that our index can be differentiated easily, making it compatible with local optimization approaches used for operational space control. Our experimental results establish that, for reaching and path following tasks, optimization based on our index outperforms a common manipulability maximization technique and ensures singularity-robust motions.