Execution of Voluntary Bipedal Movement with a Simple Afferent Processor

Abstract It is generally agreed upon (Llinas, 1975; Eccles, 1977; Thach, 1978; 1980; Marsden, 1980) that the central nervous system is involved in the three stages of planning, programming, and execution of voluntary movement. The planning and programming are understood to take place at higher centers of the central nervous system than where the execution takes place. This chapter is concerned with the formulation of a physiologically compatible approach to the execution of voluntary movement in bipedal systems. The approach involves the use of an afferent system and a simple processor to project the influence of all internal and external forces acting on the musculoskeletal system onto the motor system. Computer simulations of a voluntary movement and a postural adjustment movement are presented to support the physical viability and technical feasibility of the formulation. In the engineering and robotic disciplines, the three stages of planning, programming, and execution of movement have been grossly simplified. The practice has been to assume the existence of a trajectory planner and an inverse system. The trajectory planner, as a model of the planning and programming stages, produces the trajectories of the desired motion as functions of time. With the desired trajectories as input, the inverse system produces the necessary feedforward torques needed at the joints of the biped to execute the movement. A computational requirement of the inverse system is that the positive definite symmetric moment of inertia matrix has to be continuously inverted along the trajectory. The size of the matrix of inertia to be inverted is task-dependent and depends on the number of body segments involved in the movement. In robotic applications, this is not a hindrance since present day robots are limited in movement, and fast and computationally efficient algorithms exist for on-line inversion of matrices. For natural systems, there is no evidence for such an inversion scheme. At the same time, natural systems enjoy a rich and extensive afferent sensory multi-modal network. The obvious question concerns how the sensory system, with the assistance of some simple computations, can produce the input forces to the musculoskeletal system of natural systems. The natural scheme would obviate the inverse system as we have known it so far. The formulation proposed here is one attempt to address the above question and entails the following hypothesis: A combined measurement-computation unit, referred to as a simple afferent processor here, that can compute the physical effects of all external and internal forces acting on all the segments of the skeletal system simplifies execution of voluntary movements and obviates inversion of matrices both for robotic and natural systems. The requirement of the synthesis of the desired trajectories remains the same, i.e. the higher control centers generate the desired position, velocity, and acceleration trajectories of all the body segments and make them available for execution of the movement. Furthermore, this processor can assist with the execution of certain position and/or velocity constraints that result from the imposition of postural adjustment conditions on the system. One example of such postural adjustment constraint is the maintaining of balance - the center of pressure must lie between the feet. Another example is the widening the base of support for not falling as a result of external disturbances. Implementing any other desirable regulatory feedback loop, such as the vestibulo-ocular reflex, is analogous to the regulation of postural adjustments in the sense that position or velocity related variables are regulated. All such regulatory loops can be assisted by the above processor as will be shown.