Understanding how dexterity improves with practice is a fundamental challenge of motor control and neurorehabilitation. Here we investigate a ball and beam implementation of a dexterity puzzle in which subjects stabilize a ball at the mid-point of a beam by manipulating the angular position of the beam. Stabilizability analysis of different biomechanical models for the ball and beam task with time-delayed proportional-derivative feedback identified the angular position of the beam as the manipulated variable. Consequently, we monitored the changes in the dynamics with learning by measuring changes in the control parameters. Two types of stable motion are possible: node type (nonoscillatory) and spiral type (oscillatory). Both types of motion are observed experimentally and correspond to well-defined regions in the parameter space of the control gains. With practice the control gains for each subject move close to or on the portion of the boundary which separates the node-type and spiral-type solutions and which is associated with the rightmost characteristic exponent of smallest real part. These observations suggest that with learning the control gains for ball and beam balancing change in such a way that minimizes overshoot and the settling time. This study provides an example of how mathematical analysis together with careful experimental observations can shed light onto the early stages of skill acquisition. Since the difficulty of this task depends on the length of the beam, ball and beam balancing tasks may be useful for the rehabilitation of children with dyspraxia and those recovering from a stroke.

The tracking control of underactuated systems is a challenging problem due to the structural differences compared to fully actuated systems. Contrarily to fully actuated systems, resolving the inverse kinematics problem of underactuated systems is not possible independently from the dynamic equations. Instead, the inverse dynamics must be addressed. It is common to extend the computed torque control (CTC) technique with servoconstraints. Besides the CTC's clearness, the stability of the system cannot be always guaranteed. A novel predictive controller (PC) is presented in this paper. Our PC applies the variational principle to design the motion of the system in order to achieve a stable motion with the lowest possible tracking error. To demonstrate the applicability and the performance of the PC method, a numerical study is presented for a planar manipulator resulting in about 20% RMS error compared to the CTC method from the literature.

Model-based control methods such as inverse dynamics control and computed torque control encounter difficulties if actuator saturation occurs. However, saturation is a common phenomenon in robotics leading to significant nonlinearity in system behavior. In this study, the saturation of the actuator torques is considered as a temporary reduction of the number of independent control inputs. The reduction of the number of actuators leads to an underactuated control problem which typically involves the handling of differential algebraic equation systems. The saturated system may become especially complex when intricate combinations of the actuator saturations appear. A servoconstraint-based inverse dynamics control method for underactuated multibody systems is applied for the treatment of actuator torque saturation. In case of human-friendly robots, the problem of saturation cannot be avoided on the level of trajectory planning because unexpected human perturbations may take place, which result in such abrupt changes in the desired trajectory that lead to saturation at some actuators. A case study for the service robot Acroboter shows the applicability of the proposed approach.

Robotics is undergoing dynamic progression with the spread of soft robots and compliant mechanisms. The mechanical models describing these systems are underactuated, having more degrees-of-freedom than inputs. The trajectory tracking control of underactuated systems is not straightforward. The solution of the inverse dynamics is not stable in all cases, as it only considers the actual state of the system. Therefore employing the advances of optimal control theory is a reasonable choice. However, the real-time application of these is challenging as the solution to the discretized optimization problems is numerically expensive. This paper presents a novel iterative approach to solving nonlinear optimal control problems. The authors first define the iteration formula after which the obtained equations are discretized to prepare the numerical solution, contrarily to the accessible works in the literature having reverse order. The main idea is to approximate the cost functional with a second-order expansion in each iteration step, which is then extremized to get the subsequent approximation of the optimum. In the case of nonlinear optimal control problems, the process leads to a sequence of time-variant linear–quadratic regulator (LQR) problems. The proposed technique was effectively applied to the trajectory tracking control of a flexible rotational-rotational joint (RR) manipulator. The case study showed that the initialization of the iteration is simple, and the convergence is rapid.

Saturation is an undesired event in trajectory tracking control of mechanical systems. When the actuators of a robotic device saturate, the solution of the inverse dynamics problem cannot fully be realized, which results in deviations from the desired trajectory and loss of performance. It is generally hard to consider the limited actuator torques and the corresponding nonlinear effects in the control design. The most common way to handle the problem is recalculating the control forces and trying to adjust the desired trajectory such that saturation will not happen. In contrast we propose a switched control approach, where, upon saturation, different sets of inputs are varied periodically to keep the reference point of the robot on the desired trajectory. For this, the desired motion is formulated by means of servo-constraints, and the periodic switching of these constraints is adjusted according to the variation of a new, manipulability type performance measure. It is demonstrated that the proposed controller can effectively reduce the trajectory following error due to actuator saturation. A typical robotic benchmark example is provided to show the application of the method, and to compare it with other approaches taken from the literature.