Compliant Frame Research Articles

Cooperative Motion Control and Sensing Architecture in Compliant Framed Modular Mobile Robots

A novel motion control and sensing architecture for a two-axle compliant framed wheeled modular mobile robot (CFMMR) is proposed in this paper. The CFMMR is essentially a cooperative mobile robotic system with complex physical constraints and highly nonlinear interaction forces. The architecture combines a kinematic controller for coordinating motion and providing reference commands, robust dynamic controllers for following these commands and rejecting disturbances, and a sensor fusion system designed to provide accurate relative posture estimates. Requirements for each of these subsystems and their respective interconnections are defined in this paper in order to optimize system performance. Experimental results compare performance of the proposed architecture to sub-optimal configurations. Results derived from seven groups of experiments based upon 35 individual tests validate superiority of the architecture.

Path Manifold-based Kinematic Control of Wheeled Mobile Robots Considering Physical Constraints

This paper presents a time invariant kinematic motion controller for wheeled mobile robots. Actuator capability, mechanical design, and traction forces governed by terrain features provide velocity and curvature limitations that are used in the design of the controller. A novel path manifold that considers curvature limitations is introduced to provide a desired path shape and convergence to the reference posture or trajectory. Lyapunov techniques are then used to derive a control law that asymptotically converges the robot to an arbitrarily small neighborhood of the path manifold. Posture regulation, path following, and trajectory tracking capability to a similarly scaled neighborhood of the target are provided. Controller parameters are optimized and initial conditions are identified that satisfy physical constraints of the robot and provide smooth commands. Curvature boundaries and asymptotic convergence naturally limit allowable initial conditions and are resolved by driving the robot to intermediate goal points within regions of allowable initial conditions. Posture regulation is evaluated in simulation and experiment on a Compliant Framed wheeled Modular Mobile Robot (CFMMR) for two different terrain surfaces. Trajectory tracking and path following of constant curvature references are evaluated in simulation and experiment, respectively.

Instrumentation and Algorithms for Posture Estimation in Compliant Framed Modular Mobile Robots

Posture sensing techniques for Compliant Framed Modular Mobile Robots (CFMMR) are presented in this paper using a new Relative Posture Sensor (RPS) combined with standard sensors in a tiered fusion algorithm. The RPS consists of a compliant frame member instrumented with strain gauges and associated algorithms such that the RPS can predict relative posture. The first tier of the fusion algorithm uses traditional Kalman filters and rigid axle kinematic models to predict the global posture of each axle. In the second tier, a Relative Measurement Stochastic Posture Error Correction (RMSPEC) algorithm is introduced to fuse disparate axle data using the RPS. Experimental results are derived from over 60 trials operating the robot on high traction carpet, low traction sand, and sand with rugged rocky terrain. Results comparing the proposed sensory system with standard sensory systems demonstrate that the proposed techniques yield accurate relative posture estimates and posture regulation even on rugged terrain, which is a vast improvement over previous results.

Simplified motion control of a two-axle compliant framed wheeled mobile robot

Kinematic models and motion control algorithms for a two-axle compliant frame mobile robot are examined. General kinematics describing the compliantly coupled nonholonomic kinematics are derived using velocity constraints that minimize traction forces and consider foreshortening of the frame. Given the complexity of these equations, the steering ratio a is defined to describe the relative heading angles of the front and rear axles. Simplified kinematic models are developed based upon a (Types I, II, and III) and the reference point used to guide the robot. Physical limitations and performance metrics (lateral mobility and maneuverability per unit of traction force) are derived to evaluate the models. Six groups of simulations and 24 experimental tests consisting of 120 trials evaluate the performance of the algorithms on carpet, sand, and sand with rocks. Results indicate that Type I (curvature-based steering) provides superior maneuverability and regulation accuracy, whereas Type II provides excellent lateral mobility at the cost of high traction forces, reduced accuracy, and potential singularities. Both models offer significant reductions in complexity for simplified control using standard curvature-based unicycle control algorithms. These results support expectations derived from performance metrics and physical limitations. Experimental results also demonstrate the efficacy of the robot to adapt to and maneuver over extremely rugged rocky terrain.

Distributed Robust Control of Compliant Framed Wheeled Modular Mobile Robots

A distributed robust controller for Compliant Framed wheeled Modular Mobile Robots (CFMMR) is studied in this paper. This type of wheeled mobile robot uses rigid axles coupled by compliant frame modules to provide both full suspension and enhanced steering capability without additional hardware. In this research, a distributed nonlinear damping controller using backstepping techniques for wheel-torque control is first developed for single-axle unicycle type robots. The controller is then extended to multiple-axle CFMMR configurations and is robust to disturbances created by modeling errors; especially highly nonlinear frame forces caused by axle interaction. In particular, the controller considers time-varying reference velocities and allows the robot to perform posture regulation, path following, or general trajectory tracking. A two-axle scout CFMMR configuration is used to evaluate the controller. Simulation and experimental results verify robust dynamic motion control of path following.

Six-DOF impedance control based on angle/axis representations

A new approach to 6-DOF impedance control is proposed, where the end-effector orientation displacement is derived from the rotation matrix expressing the mutual orientation between the compliant frame and the desired frame. An alternative Euler angles-based description is proposed which mitigates the effects of representation singularities. Then, a class of angle/axis representations are considered to derive the dynamic equation for the rotational part of a 6-DOF impedance at the end effector, using an energy-based argument. The unit quaternion representation is selected to further analyze the properties of the rotational impedance. The resulting impedance controllers are designed according to an inverse dynamics strategy with contact force and moment measurements, where an inner loop acting on the end-effector position and orientation error is adopted to confer robustness to unmodeled dynamics and external disturbances. Experiments on an industrial robot were carried out, and the results of case studies are discussed.

Poroelastic Backus averaging for anisotropic layered fluid‐ and gas‐saturated sediments

A homogeneous anisotropic effective‐medium model for saturated thinly layered sediments is introduced. It is obtained by averaging over many layers with different poroelastic moduli and different saturating fluids. For a medium consisting of a stack of vertically fractured horizontal layers, this effective medium is orthorhombic. We derive the poroelastic constants that define such media in the long‐wavelength limit as well as the effective large‐scale permeability tensor. The permeability shows strong anisotropy for large porosity fluctuations. We observe pronounced effects that do not exist in purely elastic media. At very low frequencies, seismic waves cause interlayer flow of pore fluid across interfaces from more compliant into stiffer layers. For higher frequencies, the layers behave as if they are sealed, and no fluid flow occurs. The effective‐medium velocities of the quasi‐compressional waves are higher in the no‐flow than in the quasi‐static limit. Both are lower than the high‐frequency, i.e., ray‐theory limit. Partial saturation affects the anisotropy of wave propagation. In the no‐flow limit, gas that is accumulated primarily in the stiffer layers reduces the seismic anisotropy; gas that is trapped mainly in layers with a more compliant frame tends to increase the anisotropy. In the quasi‐static limit, local flow keeps the anisotropy constant independent of partial saturation effects. For dry rock, no‐flow and quasi‐static velocities are the same, and the anisotropy caused by layering is controlled only by fluctuations of the layer shear moduli. If the shear stiffness of all layers is the same and only the compressive stiffness or saturation varies, only the ray‐theory velocity exhibits anisotropy.

Constraint Formulation for Invariant Hybrid Position/Force Control of Robots

This paper focuses on the formulation of constraints for hybrid position/force control of robots. Since the noninvariant nature of the classical approach based on orthogonality of some subspaces has recently been demonstrated, alternative methods are proposed in the paper. The geometrical approach is based on the use of an appropriately located compliant frame in which the position and force controlled directions can be clearly identified. Performing the coordinate transformation using sets of curvilinear coordinates is referred to as the analytical approach. The relation between both approaches is described, and their applicability is discussed. It is shown that the analytical approach is more general. The properties of the task space decomposition are analyzed, and the invariant and noninvariant formulations are discussed. The reasons why some previously published approaches produced results with noninvariant terms and some quantities with a misleading physical sense are explained. Two examples illustrate the application of both approaches.

On the invariance of the hybrid position/force control

Recently, the noninvariance nature of the Raibert and Craig hybrid control scheme, based on the work of Mason and others, has been pointed out. In fact, on the basis of the screw theory, Lipkin and Duffy demonstrated that the selection of the position and force controlled degrees of freedom in the Raibert and Craig scheme, may give wrong results if a translation or change in unit length of the coordinate frame is performed. A general theoretical solution to this problem, called ‘kinestatic filtering’, has been given by Lipkin and Duffy. In this paper, the two approaches are summarized and discussed. First, the conditions in which the Mason filtering technique fails are determined and, second, the situations where the Lipkin and Duffy approach cannot be applied owing to degeneracy of the twist and wrench spaces, are reported. As a consequence of this analysis, a new invariant kinestatic filtering method is proposed. The method here presented is based on the original Mason approach and requires the definition of a task-dependent filter based on the knowledge of the position of the compliant frame. Examples are presented and discussed.

Reasoning about nature of contact for planning manipulators tasks

Extracting information about contact between two convex bodies from the measured force vector is a prerequisite for any fine compliant motion control strategy. Contact information contains the direction and orientation of the contact surface normal and its relative location and orientation with respect to the compliant reference frame system.