Partial Contact Force Controllability in Active Wheeled Vehicles

1998 ◽  
Vol 123 (2) ◽  
pp. 169-175 ◽  
Author(s):  
B. J. Choi ◽  
S. V. Sreenivasan
Keyword(s):  
Contact Force ◽  
Geometric Approach ◽  
Contact Forces ◽  
Force Distribution ◽  
Distribution Problem ◽  
Passive Components ◽  
Uneven Terrain ◽  
Partial Contact ◽  
Force Components ◽  
Wheeled Vehicles

This paper presents a geometric approach for solving the force distribution problem in active wheeled vehicles (AWVs) moving on uneven surfaces. Here an active vehicle is defined as a system that includes independent actuators for all its internal joints. In general, AWVs do not possess omni-directional mobility, and they possess fewer actuators than the number of wheel-ground contact force components. This article presents an approach for separating the contact force vectors into active and passive components such that there exists an invertible square matrix that maps the active contact forces to the actuator efforts. An appropriate force allocation algorithm can then be developed for these systems. The concepts introduced in this article are demonstrated via an example of AWVs on uneven terrain. An example of force distribution in active legged vehicles (ALVs) that possess the same number of actuators as contact forces is also provided for comparison.

Partial Contact Force Controllability in Active Wheeled Vehicles

1998 ◽  
Author(s):  
B. J. Choi ◽  
S. V. Sreenivasan
Keyword(s):  
Contact Force ◽  
Geometric Approach ◽  
Contact Forces ◽  
Ground Contact ◽  
Distribution Problem ◽  
Passive Components ◽  
Partial Contact ◽  
Interesting Insight ◽  
Wheeled Vehicles ◽  
Insight Into

Abstract This paper presents a geometric approach for solving the force distribution problem in active wheeled vehicles (AWVs) moving on even and uneven surfaces. In general, AWVs do not possess omni-directional mobility and they do not have sufficient actuators to directly control all the components of the wheel-ground contact forces. This situation requires the separation of the contact force vectors into active and passive components. An optimal contact force allocation algorithm can then be developed for these systems. The concepts introduced in this article are demonstrated via simple planar examples and by using an active off-road vehicle with slip-free motion capability. Off-road kinematic/static simulations of AWVs and force controlled legged vehicles (FCLVs) are presented and a comparison of these results provides interesting insight into partial force controllability characteristics of AWVs.

OPTIMIZING FOOT CENTERS OF PRESSURE THROUGH FORCE DISTRIBUTION IN A HUMANOID ROBOT

2013 ◽  
Vol 10 (03) ◽  
pp. 1350027 ◽  
Author(s):  
PATRICK M. WENSING ◽  
GHASSAN BIN HAMMAM ◽  
BEHZAD DARIUSH ◽  
DAVID E. ORIN
Keyword(s):  
Contact Forces ◽  
Whole Body ◽  
Force Distribution ◽  
Objective Functions ◽  
Distribution Problem ◽  
Double Support ◽  
Uneven Terrain ◽  
Analytical Approaches ◽  
Convex Formulation

The force distribution problem (FDP) in robotics requires the determination of multiple contact forces to match a desired net contact wrench. For the double support case encountered in humanoids, this problem is underspecified, and provides the opportunity to optimize desired foot centers of pressure (CoPs) and forces. In different contexts, we may seek CoPs and contact forces that optimize actuator effort or decrease the tendency for foot roll. In this work, we present two formulations of the FDP for humanoids in double support, and propose objective functions within a general framework to address the variety of competing requirements for the realization of balance. As a key feature, the framework is capable to optimize contact forces for motions on uneven terrain. Solutions for the formulations developed are obtained with a commercial nonlinear optimization package and through analytical approaches on a simplified problem. Results are shown for a highly dynamic whole-body humanoid reaching motion performed on even terrain and on a ramp. A convex formulation of the FDP provides real-time solutions with computation times of a few milliseconds. While the convex formulation does not include CoPs explicitly as optimization variables, a novel objective function is developed which penalizes foot CoP solutions that approach the foot boundaries.

Feasible Contact Forces in Semi-Active Vehicles

1999 ◽  
Author(s):  
S. V. Sreenivasan ◽  
B. J. Choi
Keyword(s):  
Contact Force ◽  
Screw Theory ◽  
Geometric Approach ◽  
Integrated Approach ◽  
Contact Forces ◽  
Force Distribution ◽  
Contact Conditions ◽  
Vehicle System ◽  
Directional Motion ◽  
Contact Force Distribution

Abstract This article provides an integrated approach for identifying the feasible contact force distribution in various classes of semi-active vehicles including (a) vehicles with and without omni-directional motion capability, (b) vehicles with varying levels of actuated, unactuated, and spring joints, and (c) vehicles in singular kinematic configurations. The emphasis is on studying systems that have some level of overactuation which is defined as the number of actuators minus the mobility of the vehicle system. It is well known in the active vehicles and biomechanics literature that such overactuation can be used to optimize contact conditions to enhance locomotion capability. Once appropriate contact forces are computed, the desired actuator efforts can then be obtained. A geometric approach based on screw theory that leads to invariant analytical results has been used.

Force Distribution Characteristics of Actively Reconfigurable Wheeled Vehicle Systems

1996 ◽  
Author(s):  
S. V. Sreenivasan ◽  
P. Nanua
Keyword(s):  
Geometric Approach ◽  
Companion Paper ◽  
Internal Force ◽  
Force Distribution ◽  
Partial Control ◽  
Uneven Terrain ◽  
Redundantly Actuated ◽  
Singular Configuration ◽  
Actuation Scheme ◽  
Wheeled Vehicles

Abstract This paper addresses the force distribution issues associated with redundantly actuated wheeled vehicles that are suited for operation on uneven terrain. Basic results relating to the partitioning of motion and force variables in these mechanisms are developed. The redundant actuation scheme allows for the control of force distribution in the system, in addition to motion control. The unique kinematic characteristics of wheeled systems, that makes these vehicles ‘singular’ on even terrain, and ‘near-singular’ on uneven terrain; and the presence of ‘kinematic slipping’ when these vehicles move on uneven terrain make their force distribution mathematics distinct from other systems considered in the literature. In a singular configuration, it is shown here that these active wheeled vehicles possess only a partial control over their internal force distribution. A procedure to partition the ‘force space’ into controllable and uncontrollable spaces is provided based on a geometric approach. Closed-form force space results are included for an actively articulated multi-module system (a generalization of a passive, articulated mobile robot that has been studied extensively in literature). The force distribution in actively reconfigurable wheeled vehicles is closely related to their rate kinematics. Rate kinematics of these vehicles has been studied in a companion paper [SN96].

Kinematic Geometry of Wheeled Vehicle Systems

1996 ◽  
Author(s):  
S. V. Sreenivasan ◽  
P. Nanua
Keyword(s):  
Geometric Approach ◽  
Companion Paper ◽  
Kinematic Chains ◽  
Uneven Terrain ◽  
Geometric Conditions ◽  
Kinematic Study ◽  
Vehicle Systems ◽  
Motion Characteristics ◽  
The One ◽  
Wheeled Vehicles

Abstract This paper addresses instantaneous motion characteristics of wheeled vehicles systems on even and uneven terrain. A thorough kinematic geometric approach which utilizes screw system theory is used to investigate vehicle-terrain combinations as spatial mechanisms that possess multiple closed kinematic chains. It is shown that if the vehicle-terrain combination satisfies certain geometric conditions, for instance when the vehicle operates on even terrain, the system becomes singular or non-Kutzbachian — it possesses finite range mobility that is different from the one obtained using Kutzbach criterion. An application of this geometric approach to the study of rate kinematics of various classes of wheeled vehicles is also included. This approach provides an integrated framework to study the kinematic effects of varying the vehicle and/or terrain geometric parameters from their nominal values. In addition, design enhancements of existing vehicles are suggested using this approach. This kinematic study is closely related to the force distribution characteristics of wheeled vehicles which is the subject of the companion paper [SN96].

Choosing the Optimal Contact Force Distribution for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
Normal Vector ◽  
Optimization Criteria ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The optimal solution is found using a two-step approach: first finding the description of the entire solution space for the contact force distribution for a statically stable stance under friction constraints, and then choosing an optimal solution in this solution space which maximizes the objectives given by the chosen optimization criteria. An incremental strategy of opening up the friction cones is developed to produce the optimal solution which is defined as the one whose foot contact force vector is closest to the surface normal vector for robustness against slipping. The procedure is aided by using the “force space graph” which indicates where this solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point for the case when one foot is more critical than the other. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

Analysis and Visualization of the Contact Force Solution Space for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Solution Process ◽  
Solution Space ◽  
Contact Forces ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Force Components ◽  
The Relationship

A new analytical method for determining, describing, and visualizing the solution space for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The foot contact forces are first resolved into strategically defined foot contact force components to decouple them for simplifying the solution process, and then the static equilibrium equations are applied to find certain contact force components and the relationship between the others. Using the friction cone equation at each foot contact point and the known contact force components, the problem is transformed into a geometrical one to find the ranges of contact forces and the relationship between them that satisfy the friction constraint. Using geometric properties of the friction cones and by simple manipulation of their conic sections, the whole solution space which satisfies the static equilibrium and friction constraints at each contact point can be found. Two representation schemes, the “force space graph” and the “solution volume representation,” are developed for describing and visualizing the solution space which gives an intuitive visual map of how well the solution space is formed for the given conditions of the system.

Optimal Contact Force Distribution for Multi-Limbed Robots

2005 ◽  
Vol 128 (3) ◽  
pp. 566-573 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Solution Space ◽  
Contact Forces ◽  
Force Distribution ◽  
New Strategy ◽  
Contact Force Distribution

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The incremental strategy of opening up the friction cones is aided by using the “force space graph” which indicates where the solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

Fast Equilibrium Test and Force Distribution for Multicontact Robotic Systems

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
Yu Zheng ◽  
Chee-Meng Chew
Keyword(s):  
Contact Force ◽  
Time Complexity ◽  
Linear Time ◽  
Optimization Technique ◽  
Contact Forces ◽  
The Other ◽  
Robotic Systems ◽  
Force Distribution ◽  
Contact Force Distribution ◽  
Equilibrium Test

In the research of multicontact robotic systems, the equilibrium test and contact force distribution are two fundamental problems, which need to determine the existence of feasible contact forces subject to the friction constraint, and their optimal values for counterbalancing the other wrenches applied on the system and maintaining the system in equilibrium. All the wrenches, except those generated by the contact forces, can be treated as a whole, called the external wrench. The external wrench is time-varying in a dynamic system and both problems usually must be solved in real time. This paper presents an efficient procedure for solving the two problems. Using the linearized friction model, the resultant wrenches that can be produced by all contacts constitute a polyhedral convex cone in six-dimensional wrench space. Given an external wrench, the procedure computes the minimum distance between the wrench cone and the required equilibrating wrench, which is equal but opposite to the external wrench. The zero distance implies that the equilibrating wrench lies in the wrench cone, and that the external wrench can be resisted by contacts. Then, a set of linearly independent wrench vectors in the wrench cone are also determined, such that the equilibrating wrench can be written as their positive combination. This procedure always terminates in finite iterations and runs very fast, even in six-dimensional wrench space. Based on it, two contact force distribution methods are provided. One combines the procedure with the linear programming technique, yielding optimal contact forces with linear time complexity. The other directly utilizes the procedure without the aid of any general optimization technique, yielding suboptimal contact forces with nearly constant time complexity. Effective strategies are suggested to ensure the solution continuity.

The Joint Distribution Problem With Multiple Articular Contact Forces

1990 ◽  
Vol 112 (3) ◽  
pp. 364-366
Author(s):  
J. G. Andrews ◽  
C. K. Cheng
Keyword(s):  
Joint Distribution ◽  
Ad Hoc ◽  
Muscle Force ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Contact Forces ◽  
Equality Constraint ◽  
Distribution Problem ◽  
Straight Line ◽  
Force Components

The single joint distribution problem with two or more unknown bony contact forces is considered, and an optimal solution procedure free of ad hoc assumptions is described. If two bony contact forces are present, a strictly muscle force dependent equality constraint exists that allows for initial independent estimation of muscle forces, followed by unique estimation of all bony contact force components perpendicular to the straight line connecting their known points of application. However, if three or more bony contact forces are present, no strictly muscle force dependent equality constraint exists, solution separability is lost, and optimal muscle and bony contact forces are obtained simultaneously.

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