Advances in Robot Control

On the celebration of my seventieth birthday, I would like to ask you to allow me to introduce my present dream: human robotics. Before explicating what is human robotics, it is important for me to spell out why such dream has been incubated in my mind during the past decade.

Numerous robotic tasks require the solution of the inverse problem, known to be ill-conditioned in the neighborhood of kinematic singularities. The problem is addressed here via a non-linear, differential-geometric approach. A “natural motion” component is identified thereby at the velocity level. Dynamic analysis reveals that the essence of this component is nondissipative motion along the prescribed end-effector path, with nonstationary initial condition. A kinematic feedback controller and a dynamic feedback controller are introduced and shown to ensure stable motion initialization from kinematic singularities, as well as tracking of prescribed paths that pass through such singularities.

Most research so far in robot control has assumed either kinematics or Jacobian matrix of the robots from joint space to task space is known exactly. Unfortunately, no physical parameters can be derived exactly. In addition, when the robot picks up objects of uncertain lengths, orientations or gripping points, the kinematics and dynamics become uncertain and change according to different tasks. This paper presents several approximate Jacobian control laws for robots with uncertainties in kinematics and dynamics. Lyapunov functions are presented for stability analysis of feedback control problems with uncertain kinematics. We shall show that the end-effector’s position converges to a desired position even when the kinematics and Jacobian matrix are uncertain.

A novel adaptive controller is presented in this Chapter for image-based dynamic control of a robot manipulator when the intrinsic and extrinsic parameters of the camera and the position coordinates of the feature points are unknown. Both the fixed camera and eye-in-hand camera configurations are considered. The key idea lies in the use of a depth-independent image Jacobian matrix to map the visual signals onto the joint space of the robot manipulator. By virtue of the depthindependent image Jacobian matrix, it is possible to linearly parameterize the closed loop dynamics of the system by the uncalibrated camera parameters and the unknown feature coordinates. A new adaptive algorithm, different from the Slotine and Li algorithm, has been proposed to estimate the unknown parameters and coordinates on-line. The asymptotic stability of the system under the control of the proposed method is rigorously proved by the Lyapunov theory with the nonlinear robot dynamics fully taken into account.

In this paper we study passivity-based control for the problem of coordination and synchronization of multi-agent systems. We treat agents described by affine nonlinear systems that are input-output passive and that exchange information over a network described by an interconnection graph. We treat both linear interconnections on balanced, directed graphs and nonlinear interconnections on undirected graphs. We present synchronization results for both fixed and switching graphs. Finally, we treat the realistic case of time delay in the communication of information among agents. Our results unify several existing results from the literature on multi-agent systems.

In this review we explore the possibility of adapting first order hybrid feedback controllers for nonholonomically constrained systems to their dynamical counterparts. For specific instances of first order models of such systems, we have developed gradient based hybrid controllers that use Navigation functions to reach point goals while avoiding obstacle sets along the way. Just as gradient controllers for standard quasi-static mechanical systems give rise to generalized “PD-style” controllers for dynamical versions of those standard systems, so we believe it will be possible to construct similar “lifts” in the presence of non-holonomic constraints notwithstanding the necessary absence of point attractors.

In this paper, we discuss control scheme design methods of a complex system that comprises many elements. To control such a system, we assert the importance of a control scheme design based on the structure, which is physically characterized. As examples of the control scheme design method, iterative learning control and time-scale transformation are introduced. This paper particularly describes that the dynamics of a robot and a contact environment are physically characterized by time-scale transformation. The effectiveness of the time-sale transformation is shown in cases where a robot moves in air and in water. It is difficult to model the hydrodynamic effect in the neighborhood of the robot when it moves in water. It is claimed that the difficulty on modeling is overcome if timescale transformation is applied. Finally, the usefulness of time-scale transformation is demonstrated through examination of some experimental results.

Although neurons as computational elements are 7 orders of magnitude slower than their artificial counterparts, the primate brain grossly outperforms robotic algorithms in all but the most structured tasks. Parallelism alone is a poor explanation, and much recent functional modeling of the central nervous system focuses on its modular, heavily feedback-based architecture, the result of accumulation of subsystems throughout evolution. In our earlier work, we have extensively discussed this architecture from a global stability and convergence point of view. In this article, we describe recent work which extends these ideas to synchronization as a model of computations at different scales in the nervous system. We also describe a simple condition for a general dynamical system to globally converge to a polyrhythm, i.e., a regime where multiple groups of fully synchronized elements coexist. Applications to some classical questions in robotics and systems neuroscience are discussed.

The advantages and challenges of producing and controlling force with a mechanism like the human skeleton driven by actuators like mammalian muscles are considered. Some counter-intuitive subtleties of musculo-skeletal biomechanics are discovered: despite the energetic cost of isometric muscle activation, exerting forces that do no work may reduce metabolic energy consumption; in some circumstances, anatomical antagonist muscles may become functional synergists; and muscle tension acts to make skeletal posture statically unstable. The latter effect can be counteracted by muscle mechanical impedance, which emerges as an essential adjunct to muscle force production.

This chapter deals with modeling of human-like reaching and pinching movements. For the reaching movements, we construct a two-link planar arm model with six redundant muscles. A simple task-space feedback control scheme, taking into account internal forces induced by the redundant and nonlinear muscles, is proposed for this model. Numerical simulations show that our sensory-motor control can realize human-like reaching movements. The effect of gravity is also studied here and a method for the gravity compensation on the muscle input signal level is introduced. The stability of this method is proved and its effectiveness is shown through numerical simulations. For the pinching movements, realized by the index finger and the thumb, the co-contraction between the flexor and extensor digitorum muscles is analyzed. It is shown that an internal force term can be generated by the redundant muscles to modulate a damping factor in the joint space. Numerical simulations show that the co-contraction of each digitorums makes it possible to realize human-like pinching movements. Our results suggest that the central nervous system (CNS) does not need to calculate complex mathematical models based on the inverse dynamics or on the planning of optimal trajectories. Conversely, the human motor functions can be realized through the sensory-motor control by exploiting the passivity, nonlinearity and the redundancy of the musculo-skeletal systems.

The principle of superposition introduced by Prof. S. Arimoto and his colleagues for the control of robotic hand has been shown to be applicable to the control of prehensile actions by humans. In particular, experiments have shown that static human hand actions can be viewed as a superposition of two independent synergies controlling the grasping force and the orientation of the object. Studies of elderly persons have shown that they are impaired in both synergies and show worse stabilization of the grasping force and of the total moment of forces applied by the digits to a hand-held object. Recent studies have also shown that the principle of superposition holds with respect to reactions to expected and unexpected mechanical perturbations applied to a hand-held object. Indices of the two synergies have shown different changes following a perturbation. Generalization of the principle of superposition to human prehension is an important step towards understanding the principles of control of the human hand.

The paper deals with modeling of human-like reaching movements in dynamic environments. A simple but not trivial example of reaching in a dynamic environment is the rest-to-rest manipulation of a multi-mass flexible object (underactuated system) with the elimination of residual vibrations. This a complex, sport-like movement task where the hand velocity profiles can be quite different from the classical bell shape and may feature multiple phases. First, we establish the Beta function as a model of unconstrained reaching movements and analyze it properties. Based on this analysis, we construct a model where the motion of the most distal link of the object is specified by the lowest order polynomial, which is not uncommon in the control literature. Our experimental results, however, do not support this model. To plan the motion of the system under consideration, we develop a minimum hand jerk model that takes into account the dynamics of the flexible object and show that it gives a satisfactory prediction of human movements.

We report the development, implementation, and evaluation of a novel application of robot force control called position based force scaling. Force scaling employs position based force control algorithms to augment human haptic feedback during human-robot co-manipulation tasks.

We propose a method of controlling a paddle so as to return the ball to a desired point on the table with specified flight duration. The proposed method consists of the following three input-output maps implemented by means of Locally Weighted Regression (LWR): (1) A map for predicting the impact time of the ball hit by the paddle and the ball position and velocity at that moment according to input vectors describing the state of the incoming ball; (2) A map representing a change in ball velocities before and after impact; and (3) A map giving the relation between the ball velocity just after impact and the landing point and time of the returned ball. We also propose a feed-forward control scheme based on iterative learning control to accurately achieve the stroke movement of the paddle as determined by using these maps.