Research on motor learning suggests that training with haptic guidance enhances learning of the timing components of motor tasks, whereas error amplification is better for learning the spatial components. We present a novel mixed guidance controller that combines haptic guidance and error amplification to simultaneously promote learning of the timing and spatial components of complex motor tasks. The controller is realized using a force field around the desired position. This force field has a stable manifold tangential to the trajectory that guides subjects in velocity-related aspects. The force field has an unstable manifold perpendicular to the trajectory, which amplifies the perpendicular (spatial) error. We also designed a controller that applies randomly varying, unpredictable disturbing forces to enhance the subjects' active participation by pushing them away from their "comfort zone." We conducted an experiment with thirty-two healthy subjects to evaluate the impact of four different training strategies on motor skill learning and selfreported motivation: (i) No haptics, (ii) mixed guidance, (iii) perpendicular error amplification and tangential haptic guidance provided in sequential order, and (iv) randomly varying disturbing forces. Subjects trained two motor tasks using ARMin IV, a robotic exoskeleton for upper limb rehabilitation: follow circles with an ellipsoidal speed profile, and move along a 3D line following a complex speed profile. Mixed guidance showed no detectable learning advantages over the other groups. Results suggest that the effectiveness of the training strategies depends on the subjects' initial skill level. Mixed guidance seemed to benefit subjects who performed the circle task with smaller errors during baseline (i.e., initially more skilled subjects), while training with no haptics was more beneficial for subjects who created larger errors (i.e., less skilled subjects). Therefore, perhaps the high functional difficulty of the tasks limited the potential benefit of mixed guidance. Adding random disturbing forces during training reduced the learning effect size compared to no haptics. The unanticipated forces also decreased the subjects' feelings of competence while did not increase their effort and interest. Further studies with mildly affected neurologically patients employing easier tasks need to be performed in order to evaluate the applicability of our approaches in rehabilitation.

Problems with differential cross-coupling can arise in mechanical systems when independent external forces are absent in some of the coordinates. Input-output linearization of these systems, in general, leads to unstable internal dynamics. A discrete-time decoupling scheme which circumvents this problem is developed. It is shown that internally-stable decoupling is possible with the proposed method if and only if the sampling interval is larger than a pre-specified value. The design of a stabilizing controller with such a decoupling scheme is also addressed. Simulation results are presented using a helicopter model in which the speed of the propeller is manipulated to control the aerodynamic force.

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Previous results suggest that haptic guidance enhances learning of the timing components of motor tasks, whereas error amplification is better for learning the spatial components. In this paper we evaluate a novel mixed guidance controller that combines haptic guidance and error amplification to simultaneously promote learning of the timing and spatial components. The controller is realized using a saddle-like force field around the desired movement position. This force field has a stable manifold tangential to the trajectory that guides subjects in velocity related aspects. The force field has its unstable manifold perpendicular to the trajectory, which amplifies the normal (spatial) error. We conducted an experiment with twenty nine healthy subjects to test whether training with the mixed guidance controller resulted in better learning than training without guidance or with guidance-as-needed. Subjects trained two tasks: a continuous rhythmic task (circle) and a continuous single task (line). We found that the effectiveness of the training strategy depended on the task. Training with mixed guidance was especially beneficial for learning the timing components of the line, but limited learning of the circle. Perhaps the continuous change in the force directions during training of the circle was too difficult to interpret.

The wheeled inverted pendulum shown in Fig. 1 is a typical nonlinear system that is both nonholonomic and complex in dynamics. In this paper a novel control concept is applied to stabilize a wheeled inverted pendulum. The suggested controller requires no mathematical simplification or linearization of the system. Online identification and feed-forward control are realized by an adapted filtered-x least mean square algorithm (FXLMS). Using discrete wavelet transform (DWT), control can be exerted in both the time and frequency domains simultaneously. The results show that the proposed controller is robust even when the system is perturbed. The system can also be partially stabilized at positions out of the upper equilibrium. In this case the time domain error is small though the system stays broadband in the frequency domain.