Schaffner, G., Newman, D.J. and S. Robinson, "Inverse Dynamic Simulation and Computer Animation of EVA," AIAA paper 97-0232, Annual Conference, Reno, NV, January, 1997.
Computational multi-body dynamics were used to simulate astronaut motions during extravehicular activity (EVA). The application of computational dynamic simulation to EVA was prompted by the realization that physical microgravity simulators have inherent limitations: viscosity in neutral buoyancy tanks; friction in air bearing floors; short duration for parabolic aircraft; and inertia and friction in suspension systems. This research effort fills a current gap in quantitative analysis of EVA dynamics by employing computational dynamics, with emphasis on Kane's method, to solve the equations of motion for EVA tasks involving a multi-body model. Two specific EVAs performed on Space Shuttle missions STS-63 in February, 1995, and STS-49 in May, 1992 were simulated. The EVA performed on STS-63 involved the manipulation of the 1,200 kg Spartan astronomy payload as practise for large mass handling during future Space Station assembly tasks. The STS-49 EVA involved various attempts at capturing a stranded Intelsat VI satellite using a specially designed capture bar. Since the original attempts using the capture bar were unsuccessful, simulation of the Intelsat EVA provided an opportunity for exploring dynamic effects that might have been masked by the limitations of physical simulators.
Our dynamic simulation approach comprises several phases, all of which are performed on a Silicon Graphics Indigo 2 computer. In the Spartan simulation these are: system description, equation formulation, inverse kinematics, inverse dynamics, and data display with animation. The Spartan simulation model consists of seven segments with an additional eighth segment representing the Spartan payload being manipulated. It is assumed that the astronaut's feet are clamped to a rigid body of large mass, as represented by the portable foot restraint and Space Shuttle Orbiter in real life. Relevant geometry and mass properties of the dynamic system serve as inputs to a commercial dynamics analysis software package and are specified in a system description file. The output consists of C code subroutines that implicitly represent the equations of motion for the particular system as derived using Kane's method. Execution and control of the simulation is accomplished by code written by the authors. During the inverse kinematics phase the position, velocity, and acceleration of the center of mass of the hand are prescribed for a circular trajectory followed at constant speed. At each time step, the position, velocity, and acceleration values for each joint are calculated by solving the inverse Jacobian matrix and recorded in a two-dimensional state-time array. In cases where there is redundancy in the number of degrees of freedom, the solution is found by means of a linearized least squares method, subject to the constraints imposed on the system. These joint kinematic values are recalled for the inverse dynamics phase where the amount of torque required in each joint to bring about the motion is calculated. Finally, an animation program has been developed to graphically represent the astronaut model and display the simulation results. Since the animation is synchronized with plots of relevant system parameters, the interpretation of simulation results is greatly facilitated. The Intelsat simulation which was performed after the Spartan simulation, makes use of a more complex 12 segment astronaut model plus separate capture bar and satellite objects. Furthermore, this model implicitly incorporates the range of motion constraints for the human and the space suit as well as the mass properties of the space suit. Again it is assumed that the astronaut's feet are clamped to a massive object. The interaction between the capture bar and the satellite was modeled using a combination of sliding and rotation jointsInverse kinetics and motion integration phases replace the inverse kinematics and inverse dynamics phases used forthe Spartan simulation. For the inverse kinetics phase, the force applied by each hand is prescribed and the required joint torques to achieve this are calculated. The resulting motion of the system, in particular that of the satellite, is calculated by integrating the equations of motion over time subject to the applied forces and constraints.
Results and Conclusions:
Two dynamic simulations were carried out for EVA tasks involving manipulation of the Spartan payload. The initial configuration of the astronaut's lower body (trunk, upper leg, and lower leg) was set to a neutral microgravity posture. In the first simulation the lower body assumes a rigid posture with fixed joint angles while the arms manipulate the payload around a circular trajectory of 0.15 m radius in 10 seconds. It was found that the wrist joint theoretically exceeded its ulnar deviation limit by as much as 40 degrees and was required to exert torques as high as 26 N-m to accomplish the task, well in excess of the wrist physiological limit of 12 N-m. The largest torque in the first simulation, 52 N-m, occurred in the ankle joint. To avoid these problems, the second simulation placed the arm in a more comfortable initial position, reduced the radius and velocity of the circular trajectory by half, and more realistically modeled the passive behavior of muscle groups in the lower body by applying torsional springs and dampers at the hip, knee, and ankle joints. As a result, the joint angles and torques were reduced to values well within their physiological limits. In particular, the maximum wrist torque for the second simulation was only 3 N-m and the maximum ankle torque was only 6 N-m. The improvements in the results of the second simulation demonstrate the evolutionary approach to improving realism and accuracy in successive simulations. Three separate simulations were carried out for the Intelsat EVA, representing (1) equal forces applied by each hand, (2) unequal forces, and (3) unequal forces with a frictional counter-rotation torque applied to the satellite. The magnitudes of these forces were estimated from discussions with the EVA astronauts involved. It was found that the third case interaction induced an extreme amount of nutation in the resulting motion of the satellite reaching as much as a 45 degree angular deviation of the satellite spin axis. Furthermore, it was discovered that the satellite translates out of the astronaut's reach envelope within 5 to 10 seconds, thus allowing insufficient time for the latch mechanisms in the capture bar to engage. Computational multi-body dynamics analysis is shown to be a useful complement to existing physical EVA simulators.
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