Experimental Investigation of Human Two-arm Manipulation

We address the trajectory planning problem for a task which requires positioning and orienting an object firmly grasped by two hands at a visually specified goal configuration in the horizontal plane. The motor task involves three degrees of freedom (two translational and one rotational), and the motions of the arms are constrained by the physical coupling through the held object. Experimentally measured trajectories are presented and they are compared with those obtained by minimizing the integral of the rate of change of actuator torques over the trajectory. Good match is shown for a class of manipulation tasks in which the person-to-person variability is small. INTRODUCTION This paper is primarily concerned with the coordination and cooperation of two physically coupled arms in a task which requires positioning and orienting an object firmly grasped by two hands. Although many previous works have investigated the mechanisms that might underlie the generation of single arm trajectories (Soechting and Lacquaniti (1981); Hogan (1984); Atkeson and Hollerbach (1985)), trajectory planning that is involved in generating motions of two arms physically coupled through a held object has received relatively little attention. Motion planning for a manipulation task in general occurs at three levels. First, given the initial configuration of the system and the goal position and orientation of the object, the trajectory of the object must be planned. Second, the appropriate joint trajectories must be chosen for the human arms. Finally, muscle forces must be computed to achieve the desired motion. In a two-arm manipulation task, we will typically encounter kinematic and actuator redundancy. Therefore, at each level a trajectory has to be chosen among infinitely many possible solutions. Based on studies of single arm reaching in humans, Flash and Hogan (1985) have suggested that the central nervous system uses an optimality criterion to plan the trajectory. They observed that medium speed, large amplitude, unconstrained planar motions of a single arm closely follow the trajectories minimizing the integral of the jerk. These minimum-jerk trajectories depend only on the kinematics of the task. According to Garvin et al. (1995), the success of the minimum-jerk model in accounting for two-arm trajectories is limited. Further, the model only predicts trajectories of the object, it offers no mechanism for resolving kinematic and actuator redundancy. In Uno et al. (1989), an alternative cost function is proposed for trajectory generation: the integral of the norm of the vector of derivatives of the actuator torques along the trajectory. This cost function (called minimum torque-change criterion) takes into account the dynamics of the system and its minimization yields object trajectory, joint trajectories and actuator (muscle) torques. In this paper, we consider the minimum torque-change model following the results from Garvin et al. (1995) and Žefran et al. (1994). We present the experimental data for human two-arm manipulation and compare the data with the trajectories predicted by the model. Good match is shown for a class of manipulation tasks in which the person-to-person variability is small. We conclude the paper with a short discussion. EXPERIMENTS Two-arm planar motions of human subjects were recorded using a three degree of freedom planar passive manipulandum (Fig. 1). The apparatus consists of three links, connected by revolute joints. The third link is a handlebar that can rotate around its center. Three optical encoders mounted at each joint are used to record the manipulandum joint angles. Six axis force sensors are mounted underneath each handle, allowing measurement of the forces and torques exerted on the handles by the subject. All the transducers are sampled at 150 Hz. The subject is seated in front of a transparent Plexiglas plate and firmly grasps the two handles of the handlebar (Fig. 1). The plate lies horizontally at the level of the subject’s chin. Four target sets are mounted on the plate. Target 1 is 30cm in front of the subject’s chest, Target 2 (Target 3) is displaced by 8:5cm forward and 15cm to the left (right) of Target 1, and Target 4 is displaced 19:5cm forward with respect to Target 1. Each target set consists of an array of light emitting diodes (LED’s) that can specify target positions and orientations. For detailed description of the experimental setup we refer the reader to Garvin et al. (1995). Four subjects participated in the study: two right-handed, one left-handed and one ambidextrous. Three types of motions were studied: a) motions parallel to the frontal plane (2! 3 and 3! 2 in Fig. 1), b) motions in the sagittal plane (1 ! 4 and 4! 1), and c) oblique motions (1! 2 and 1 ! 3). Velocities and forces exerted on the handles