Directory Functions  219

18.1 Library Maybe  192

Though many research efforts have been devoted to developing robot controllers with uncertainties in the robot dynamics, most research so far has assumed that the model of actuator is known exactly. In implementing the robot controllers, calibration is necessary to identify the exact parameters of the actuator model. When there is an error in calibrating or modeling, it is unknown whether the stability of the system could still be guaranteed. In addition, the actuator model could change as the temperature varies due to overheating of the motor or changes in the ambient temperature. To overcome this problem, we propose in this paper, a task-space controller for the regulation of the robot with an approximate actuator model. We consider second-order dynamics of electric actuators with negligible armature inductances. Sufficient conditions for choosing the feedback gains are presented to guarantee stability.

The sizes of the cycles and unicyclic components in the random graph $G(n, n/2\pm s)$, where $n^{2/3}\ll s \ll n$, are studied using the language of point processes. This refines several earlier results by different authors. Asymptotic distributions of various random variables are given: these distributions include the gamma distributions with parameters 1/4, 1/2 and 3/4, as well as the Poisson–Dirichlet and GEM distributions with parameters 1/4 and 1/2.

17.1 Indexing Lists  181

17.2 “Set” Operations  181

17.3 List Transformations  182

17.4 unfoldr  182

17.5 Predicates  183

17.6 The “By” Operations  183

17.7 The “generic” Operations  184

17.8 Further “zip” Operations  184

17.9 Library List  184

27.1 The RandomGen class, and the StdGen generator  236

27.2 The Random class  239

27.3 The global random number generator  240

The bond percolation critical probability of the Kagomé lattice is greater than 0.5209 and less than 0.5291. The proof of these bounds uses the substitution method, comparing the percolative behaviour of the Kagomé lattice bond model with that of the exactly solved hexagonal lattice bond model via stochastic ordering.

20.1 Naming Conventions  200

20.2 Class MonadPlus  200

20.3 Functions  201

20.4 Library Monad  202

We are developing robotic devices for locomotion training after spinal cord injury. In this paper, we compare two approaches to controlling and quantifying bipedal stepping of spinal rats with robots. In the first approach, the rats stepped on a physical treadmill with robot arms attached to their lower shanks. In the second, the rats stepped on a virtual treadmill generated by the robots. The rats could step on the virtual treadmill, but stepping was more consistent, step height greater, and interlimb coordination improved on the physical treadmill. Implications for the role of sensory input in the control of locomotion and the design robotic of step trainers are discussed.

 Contents  i

 Preface  vii

1.1 Program Structure  3

1.2 The Haskell Kernel  4

1.3 Values and Types  4

1.4 Namespaces  5

A proper vertex coloring of a graph is called equitable if the sizes of colour classes differ by at most 1. In this paper, we find the minimum number l=l(d, Δ) such that every d-degenerate graph with maximum degree at most Δ admits an equitable t-colouring for every t[ges ]l when Δ[ges ]27d.

11.1 Inlining  145

11.2 Specialization  145

12.1 Library Ratio  150

4.1 Overview of Types and Classes  40

4.2 User-Defined datatypes  45

4.3 Type Classes and Overloading  49

4.4 Nested Declarations  55

4.5 Static Semantics of Function and Pattern Bindings  60

4.6 Kind Inference  66

6.1 Standard Haskell Types  81

6.2 Strict Evaluation  84

6.3 Standard Haskell Classes  84

6.4 Numbers  91

 Bibliography  241

 Index  243

Robot-aids or Rehabilitators are our chosen neologism to name a new class of robotic devices that represent a substantially departure from prior applications of robotics in rehabilitation. Rather than use robotics as an assistive technology for a disabled individual, we envision robots and computers as supporting and enhancing the productivity of clinicians in their efforts to facilitate a disabled individual's recovery. In this paper, we attempt a brief overview of our work in what promises to be a ground breaking field. We discuss the concept of robot-aided neuro-rehabilitation as a means to deliver therapy, measure patient performance, and also as a design tool. To illustrate the broad spectrum of neurological diseases that this technology might impact, we will illustrate each case with a different pathology, namely cerebral vascular accident (CVA – also known as stroke), Parkinson's disease (PD), and cerebral palsy (CP).

Hemiplegia, affecting approximately 75% of all stroke survivors, is a common neurological impairment that results in upper and lower limb sensory and motor deficits. Recovery of coordinated movement of both upper limbs is important for bilateral function and promotes personal independence. This paper describes the philosophy and design of Driver's Simulation Environment for Arm Therapy, a one-degree-of-freedom robotic device that uses a modified Constraint-Induced therapy paradigm to promote coordinated bilateral movement in the upper limbs. Baseline force and tracking data for four neurologically unimpaired subjects who completed bilateral and unilateral steering with the impaired arm using the device are presented.

13.1 Library Complex  154