This paper explores the formation and control of optimal trajectories in voluntary, human multijoint arm movements. The authors, Y. Uno, M. Kawato, and R. Suzuki, from Osaka University, propose a minimum torque-change model to explain how the central nervous system (CNS) selects specific trajectories among an infinite number of possible paths to reach a target. They observe that skilled movements often exhibit common invariant features, such as straight hand paths with bell-shaped speed profiles when moving between two targets. The model is formulated using a mathematical objective function, \( C_T \), which measures the performance of any movement by integrating the square of the rate of change of torque over the entire movement. This function is defined as: \[ C_T = \frac{1}{2} \frac{t_f}{t} \sum_{i=1}^{n} ( \frac{d z_i}{d t} )^2 dt, \] where \( z_i \) is the torque generated by the \( i \)-th actuator (muscle), and \( t_f \) is the movement time. The model is challenging to solve due to the complex nonlinear dynamics of the musculoskeletal system, so an iterative scheme is developed to simultaneously compute the optimal trajectory and motor commands. The authors evaluate their model by measuring human hand trajectories under various conditions, finding that the human hand trajectory is indeed planned and controlled according to the minimum torque-change criterion. The paper also discusses the computational aspects of voluntary movement, proposing a model that addresses the determination of desired trajectories, transformation of visual coordinates to body coordinates, and generation of motor commands. The model suggests that these tasks can be solved simultaneously, rather than in a step-by-step manner.This paper explores the formation and control of optimal trajectories in voluntary, human multijoint arm movements. The authors, Y. Uno, M. Kawato, and R. Suzuki, from Osaka University, propose a minimum torque-change model to explain how the central nervous system (CNS) selects specific trajectories among an infinite number of possible paths to reach a target. They observe that skilled movements often exhibit common invariant features, such as straight hand paths with bell-shaped speed profiles when moving between two targets. The model is formulated using a mathematical objective function, \( C_T \), which measures the performance of any movement by integrating the square of the rate of change of torque over the entire movement. This function is defined as: \[ C_T = \frac{1}{2} \frac{t_f}{t} \sum_{i=1}^{n} ( \frac{d z_i}{d t} )^2 dt, \] where \( z_i \) is the torque generated by the \( i \)-th actuator (muscle), and \( t_f \) is the movement time. The model is challenging to solve due to the complex nonlinear dynamics of the musculoskeletal system, so an iterative scheme is developed to simultaneously compute the optimal trajectory and motor commands. The authors evaluate their model by measuring human hand trajectories under various conditions, finding that the human hand trajectory is indeed planned and controlled according to the minimum torque-change criterion. The paper also discusses the computational aspects of voluntary movement, proposing a model that addresses the determination of desired trajectories, transformation of visual coordinates to body coordinates, and generation of motor commands. The model suggests that these tasks can be solved simultaneously, rather than in a step-by-step manner.