Control of Force Distribution in Robotic Mechanisms Containing Closed Kinematic Chains

1981 ◽  
Vol 103 (2) ◽  
pp. 134-141 ◽  
Author(s):  
D. E. Orin ◽  
S. Y. Oh
Keyword(s):  
Linear Programming ◽  
Basic Problem ◽  
Inequality Constraints ◽  
Force Distribution ◽  
Joint Torques ◽  
Kinematic Chains ◽  
System Trajectory ◽  
Reaction Forces ◽  
Tripod Gait ◽  
Weighted Combination

Control of the force distribution in locomotion and manipulation systems containing closed kinematic chains is an important problem since many tasks such as walking or grasping depend upon it. The basic problem is to solve for the input joint torques for a particular system trajectory and is usually underspecified. As such, linear programming has been used to obtain a solution which optimizes a weighted combination of energy consumption and load balancings. Inequality constraints on the maximum actuator torques and reaction forces at the tip of each chain of the system are imposed, in addition to equality constraints which specify movement in a desired system trajectory. An example is given in which the joint torques to drive a hexapod locomotion vehicle in a tripod gait are computed.

scholarly journals Upper-Limb Isometric Force Feasible Set: Evaluation of Joint Torque-Based Models

Biomechanics ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 102-117
Author(s):  
Nasser Rezzoug ◽  
Vincent Hernandez ◽  
Philippe Gorce
Keyword(s):  
Upper Limb ◽  
Isometric Force ◽  
Joint Torque ◽  
Force Distribution ◽  
Prediction Errors ◽  
Feasible Set ◽  
Joint Torques ◽  
Motor Abilities ◽  
Capacity Evaluation ◽  
Measured Force

A force capacity evaluation for a given posture may provide better understanding of human motor abilities for applications in sport sciences, rehabilitation and ergonomics. From data on posture and maximum isometric joint torques, the upper-limb force feasible set of the hand was predicted by four models called force ellipsoid, scaled force ellipsoid, force polytope and scaled force polytope, which were compared with a measured force polytope. The volume, shape and force prediction errors were assessed. The scaled ellipsoid underestimated the maximal mean force, and the scaled polytope overestimated it. The scaled force ellipsoid underestimated the volume of the measured force distribution, whereas that of the scaled polytope was not significantly different from the measured distribution but exhibited larger variability. All the models characterized well the elongated shape of the measured force distribution. The angles between the main axes of the modelled ellipsoids and polytopes and that of the measured polytope were compared. The values ranged from 7.3° to 14.3°. Over the entire surface of the force ellipsoid, 39.7% of the points had prediction errors less than 50 N; 33.6% had errors between 50 and 100 N; and 26.8% had errors greater than 100N. For the force polytope, the percentages were 56.2%, 28.3% and 15.4%, respectively.

scholarly journals Simulation of Stand-to-Sit Biomechanics for Design of Lower-Limb Exoskeletons and Prostheses with Energy Regeneration

2019 ◽  
Author(s):  
Brock Laschowski ◽  
Reza Sharif Razavian ◽  
John McPhee
Keyword(s):  
Lower Limb ◽  
Electrical Energy ◽  
Mechanical Power ◽  
Future Research ◽  
Ground Reaction Forces ◽  
Dynamic Simulations ◽  
Inverse Dynamic ◽  
Joint Torques ◽  
Reaction Forces ◽  
Body Segment Parameters

AbstractAlthough regenerative actuators can extend the operating durations of robotic lower-limb exoskeletons and prostheses, these energy-efficient powertrains have been exclusively designed and evaluated for continuous level-ground walking.ObjectiveHere we analyzed the lower-limb joint mechanical power during stand-to-sit movements using inverse dynamic simulations to estimate the biomechanical energy available for electrical regeneration.MethodsNine subjects performed 20 sitting and standing movements while lower-limb kinematics and ground reaction forces were measured. Subject-specific body segment parameters were estimated using parameter identification, whereby differences in ground reaction forces and moments between the experimental measurements and inverse dynamic simulations were minimized. Joint mechanical power was calculated from net joint torques and rotational velocities and numerically integrated over time to determine joint biomechanical energy.ResultsThe hip produced the largest peak negative mechanical power (1.8 ± 0.5 W/kg), followed by the knee (0.8 ± 0.3 W/kg) and ankle (0.2 ± 0.1 W/kg). Negative mechanical work from the hip, knee, and ankle joints per stand-to-sit movement were 0.35 ± 0.06 J/kg, 0.15 ± 0.08 J/kg, and 0.02 ± 0.01 J/kg, respectively.Conclusion and SignificanceAssuming an 80-kg person and previously published regenerative actuator efficiencies (i.e., maximum 63%), robotic lower-limb exoskeletons and prostheses could theoretically regenerate ~26 Joules of total electrical energy while sitting down, compared to ~19 Joules per walking stride. Given that these regeneration performance calculations are based on healthy young adults, future research should include seniors and/or rehabilitation patients to better estimate the biomechanical energy available for electrical regeneration among individuals with mobility impairments.

A New Dynamic Basis Algorithm for Solving Linear Programming Problems for Engineering Design

1988 ◽  
Author(s):  
Y. Wang ◽  
E. Sandgren
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Inequality Constraints ◽  
Upper And Lower Bounds ◽  
Programming Algorithm ◽  
Active Constraint ◽  
Design Variables ◽  
Artificial Variable ◽  
Linear Programming Problems ◽  
Revised Simplex Method

Abstract A new linear programming algorithm is proposed which has significant advantages compared to the traditional simplex method. The search direction generated which is always along a common edge of the active constraint set, is used to locate candidate constraints, and can be used to modify the current basis. The dimension of the basis begins at one and dynamically increases but remains less than or equal to the number of design variables. This is true regardless of the number of inequality constraints present including upper and lower bounds. The proposed method can operate equally well from a feasible or infeasible point. The pivot operation and artificial variable strategy of the simplex method are not used. Examples are presented and results are compared with a traditional revised simplex method.

scholarly journals A Comparative Study of Redundant Constraints Identification Methods in Linear Programming Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Paulraj S. ◽  
Sumathi P.
Keyword(s):  
Linear Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Computational Effort ◽  
Linear Functions ◽  
Redundant Constraints ◽  
Computer Scientists ◽  
Constraints Solving ◽  
Linear Programming Problems

The objective function and the constraints can be formulated as linear functions of independent variables in most of the real-world optimization problems. Linear Programming (LP) is the process of optimizing a linear function subject to a finite number of linear equality and inequality constraints. Solving linear programming problems efficiently has always been a fascinating pursuit for computer scientists and mathematicians. The computational complexity of any linear programming problem depends on the number of constraints and variables of the LP problem. Quite often large-scale LP problems may contain many constraints which are redundant or cause infeasibility on account of inefficient formulation or some errors in data input. The presence of redundant constraints does not alter the optimal solutions(s). Nevertheless, they may consume extra computational effort. Many researchers have proposed different approaches for identifying the redundant constraints in linear programming problems. This paper compares five of such methods and discusses the efficiency of each method by solving various size LP problems and netlib problems. The algorithms of each method are coded by using a computer programming language C. The computational results are presented and analyzed in this paper.

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