C. J. B. Macnab

Robust neural network control of a quadrotor helicopter

This paper proposes a new adaptive neural network control to stabilize a quadrotor helicopter against modeling error and considerable wind disturbance. The new method is compared to both deadzone and e-modification adaptive techniques and through simulation demonstrates a clear improvement in terms of achieving a desired attitude and reducing weight drift.

The dynamic optimization approach to locomotion dynamics: human-like gaits from a minimally-constrained biped model

Abstract This work presents a unifying framework to study energy-efficient optimal gaits for a bipedal model without elastic elements. The model includes a torso, flat feet, and telescoping legs, equipped with rotational hip and ankle joints. Two general types of gaits are studied: with and without a flight phase. The support surface can be level ground, sloped, or staircase. The algorithm achieves the optimum within the admissible space by using a minimal set of realistic physical constraints, and avoiding a priori assumptions on kinetic and kinematic parameters such as extended or instantaneous double-support, collisional or collisionless foot-ground contact, step length, step period, etc. The gait optimization for this simple model predicts many features of human locomotion including the optimality of pendular walking and impulsive running at slow and fast progression speeds, ankle push-off prior to touch-down, swing leg retraction, landing on a near vertical leg in gaits with flight phase, and burst hip torques at both ends of the swing phase.

CMAC adaptive control of flexible-joint robots using backstepping with tuning functions

A neural network used in a direct-adaptive control scheme can achieve trajectory tracking of a (highly) flexible joint robot holding an unknown payload without need for many learning repetitions. A modification of the Lyapunov stable nonlinear control method known as backstepping with tuning functions is derived to achieve this. Specifically, the introduction of appropriate weightings of the different tuning-function terms results in high performance. Also, a robust redesign of the tuning function method is presented to account for the uniform approximation (modeling) error of the neural network. This computationally burdensome method is made practical by taking advantage of the efficient structure of the CMAC neural network. Simulations with a (highly) flexible-joint robot show immediate compensation for a payload with performance nearly recovered after five seconds.

Adaptive Haptic Control for Telerobotics Transitioning Between Free, Soft, and Hard Environments

This paper presents an adaptive haptic control for a one degree-of-freedom master-slave teleoperated device. The aim is to reduce excessive collision forces that occur when there are significant time delays in master-slave communication. The control design also allows the operator to move the slave in free space and in a soft medium. Previous approaches to haptic teleoperation typically design for either movement in a medium or constrained contact with a solid surface; then, it is up to the operator to avoid collisions or precisely anticipate collisions. The proposed control runs on the slave side inner loop, with no time delay, and tracks commanded forces from the outer loop. A Lyapunov-stable backstepping-with-tuning-functions design provides a way to ensure smooth forces are applied that guarantee stability in the presence of unmodeled environmental stiffness and viscosity. Experiments using a Phantom hand controller interacting with simulated environment show that collision forces are substantially reduced compared to two other control methods. In collision-free operation, the performance is comparable to other methods.

Preventing bursting in adaptive control using an introspective neural network algorithm

Abstract This paper presents a solution to the problem of weight drift, and associated bursting phenomenon, found in direct adaptive control. Bursting is especially likely to occur when systems are nonminimum phase or open-loop unstable. Standard methods in the literature, including leakage, e-modification, dead-zone, and weight projection, all trade off performance to prevent bursting. The solution presented here uses a novel introspective algorithm operating within a Cerebellar Model Arithmetic Computer (CMAC) neural network framework. The introspective algorithm determines an estimate of the derivative of error with respect to each weight in the CMAC. The local nature of the CMAC cell domains enables this technique, since this derivative can be calculated at the moment a cell is deactivated – based on the error within the cell׳s domain. If the derivative looks significant, the resulting weight change (due to a Lyapunov-stable adaptive update law) remains in the cell׳s memory. An insignificant derivative results in the weight change being discarded before the cell׳s next activation. The algorithm can prevent bursting without sacrificing performance, verified through an experiment with a (nonminimum phase) flexible-joint robot and a simulation of an (open-loop unstable) quadrotor helicopter.

Optimal relative timing of stance push-off and swing leg retraction

Swing leg retraction, the backward rotation of the swing leg prior to heel-strike, is known to have several advantages in legged locomotion. To achieve this motion, a hip torque is required at the end of the swing phase to brake the forward rotation of the leg and/or accelerate its backward motion. In walking, pre-emptive push-off of the stance leg also occurs at the end of the swing, so its relative timing with late-swing retracting torque influences gait energetics. To find the best relative timing between the stance legs push-off force and the swing leg retraction torque, we calculate their work-based energetics in a simple bipedal model using impulsive approximations and with the aid of the so-called overlap parameter that quantifies the relative order and the percentage overlap of the push-off and retraction impulses. By minimizing the energetic cost of the gait, we found that it is energetically favorable to start with the push-off force, and postpone braking the leg swing until completely after the push-off (impulsive force/torque). The implication for the more realistic non-impulsive cases is to apply the retraction torque at the very end of the push-off before heel-strike. We show that the results are valid for many other bipedal models, for both periodic and aperiodic gaits, and regardless of the actuator efficiencies for positive and negative work.

Discrete-time weight updates in neural-adaptive control

Typical neural-adaptive control approaches update neural-network weights as though they were adaptive parameters in a continuous-time adaptive control. However, requiring fast digital rates usually restricts the size of the neural network. In this paper we analyze a delta-rule update for the weights, applied at a relatively slow digital rate. We show that digital weight update causes the neural network to estimate a discrete-time model of the system, assuming that state feedback is still applied in continuous time. A Lyapunov analysis shows uniformly ultimately bounded signals. Furthermore, slowing the update frequency and using the extra computational time to increase the size/accuracy of the neural network results in better performance. Experimental results achieving link tracking of a two-link flexible-joint robot verify the improved performance.

Stable active running of a planar biped robot using Poincare map control

This work formulates the active limit cycles of bipedal running gaits for a compliant leg structure as the fixed point of an active Poincare map. Two types of proposed controllers stabilize the Poincare map around its active fixed point. The first one is a discrete linear state feedback controller designed with appropriate pole placement. The discrete-time control first uses purely constant torques during stance and flight phase, then discretizes each phase into smaller constant-torque intervals. The other controller is an invariant manifold based chaos controller: a generalized Ott, Grebogi and Yorke controller having a linear form and a nonlinear form. Both controllers can stabilize active running gaits on either even or sloped terrains. The efficiency of these controllers for bipedal running applications are compared and discussed. Graphical Abstract

Direct adaptive force feedback for haptic control with time delay

Haptic devices convey force measurement to a human operator, who closes the control loop by moving the haptic hand controller. In surgical robotics, haptics dramatically improve the quality of the teleoperation. However, time delays can accumulate in the closed loop when haptic hand controllers are located in a different room (or even a different city) than the robot. When puncturing through tissue or hitting a solid surface, the commanded movement or force will be too large during the time delay, until the surgeon feels the effect and can pull back on the control. This paper proposes using a nonlinear adaptive inner-loop control scheme for haptic master/slave systems, to reduce effects of time delay. A Lyapunov analysis ensures stability. Simulation results show the improved response for a one-degree-of-freedom system in a highly nonlinear environment.

Hopping on Even Ground and Up Stairs with a Single Articulated Leg

This paper presents a method for generating gaits for a one-legged articulated hopping robot. A static optimization procedure produces the initial joint velocities for the flight phase, using the principle of conservation of angular momentum and assuming (nearly) passive flight. Two novel objective functions for this static optimization enable one to choose different gaits by simply changing a few parameters. A dynamic optimization procedure yields a solution for the flight trajectory that minimizes control effort. The stance phase (when the foot is touching the ground) becomes a standard two point boundary value problem, also solved with a dynamic optimization procedure. During the stance phase, the physical joint limitations, ground reaction forces, and the trajectory of the zero-moment point all constrain the solution. After these single-phase optimizations, a complete-cycle optimization procedure, incorporating both flight and stance phases, further reduces the control effort and balances the motion phases. In simulation, the leg hops on even ground and up stairs, exhibiting energy-efficient and intuitively satisfying gaits.