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Adaptive Locomotion

Animal locomotion is remarkably adaptable, both on short and long timescales. They can immediately change directions and gait patterns based on the substrate conditions or the presence of disturbance to maintain stability. They can also adaptively develop different kinematic modes for different environments. It is generally considered that the behavioral adaptability is a result of the locomotion pattern modified by the sensory feedback signals. The exploration of mechanisms in animals' adaptive locomotion has been adopted in various bio-inspired robot designs. Robotics takes inspiration from biology in terms of morphologies, modes of locomotion, and adaptive control learning mechanisms. In return, many bio-inspired robots have been used as scientific tools to systematically test biology hypothesis in animals' adaptive locomotion. This relevance of locomotion both for biology and robotics has led to increasing interdisciplinary study between the two fields.

Animal
To navigate different environments, an animal must be able to adapt its locomotory gait to its physical surroundings. Adaptation in locomotion is critical to animals' survival, i.e., to avoid predators or look for food.

Mechanisms of instantaneous gait adaptation
Adaptive locomotion is coupled dynamics of the neural system (CPGs (Central pattern generators, responses, reflexes) and the mechanical system (virtual spring-damper system) by interacting with the environment. A CPG receives sensory input and changes the period of its own active phase as responses. The virtual spring–damper system also receives sensory input and outputs torque as reflexes. The states in the virtual spring–damper system are switched based on the phase signal of the CPG. Consequently, adaptive walking is generated through the interaction with environment.

Inherence in the musculoskeletal structure
Muscles and tendons of animals act as a spring–damper system in medium- and high-speed walking and running, and play an important role for stabilization and energy storage. Especially in high-speed running, kinetic energy is dominant, and self-stabilization by a mechanical system with a spring and a damper is more important than adjustments by the neural system. The whole visco-elasticity of a muscle is the sum of its own visco-elasticity as a material and the visco-elasticity as a result of feedback by the stretch reflex and others. The muscle stiffness in the stretch reflex is almost proportional to the muscle tension, high in a stance phase for supporting a body against gravity and low in a swing phase for compliance against the disturbance

Central pattern generator
Animals’ walking is mainly generated at the spinal cord by a combination of a rhythm pattern generator (Central pattern generator, CPG), plus reflexes in response to the peripheral stimulus. Central pattern generators (CPGs) are neural networks that produce rhythmic patterned outputs without sensory feedback. CPGs have been shown to produce rhythmic outputs resembling normal "rhythmic motor pattern production" even in isolation from motor and sensory feedback from limbs and other muscle targets.

Sensory feedback
Adaptation requires the central nervous system appears to be aware of the present position, e.g., state of the system, and its eventual or terminal state. Some sensory stimuli modify CPG activity and reflexive responses to sensory stimuli are phase-dependent under CPG activity. Such interaction between CPG activity and a sensory stimulus is very important for adaptation and corresponds to the necessary conditions.

Visual feedback and tactile feedback both play important role in animals' adaptive locomotion. Stick insects use their antennae as active, tactile near-range sensors in the locomotion, particularly in climbing and negotiation of obstacles. When one of the antennae touches the vertical surface of an obstacle, the animal often initiates climbing behavior. Antennal tactile feedback information about the presence and height of obstacles, direction of turning, gap width of the relative height of a shelf, are used for the control of adaptive locomotion.

It is observed in cockroach locomotion that sensory feedback mechanism is of more importance in slower walking compared to high speed running. American cockroaches ignore sensory input during fast running, and combine the output from CPGs with sensor information during slow or medium walking. The much slower walking stick insects require sensory input at all times, since the centrally generated pattern is either extremely weak or nonexistent.

Interlimb coordination
Animal locomotor patterns must constantly change to accommodate the demands of a complex world. Functional locomotion demands that limb movements be flexible enough to accommodate different terrain, speeds, and trajectories. Achieving this flexibility requires continuous modulation of coordination within (intralimb) or between (interlimb) the legs. Interlimb coordination, particularly the maintenance of reciprocal, out of phase motions of the limbs, is particularly critical for stable human (bipedal) walking. Either sensory or motor information from one limb affects the control of the opposite limb’s movement. Both quadrupeds and bipeds can make basic adjustments in stance and swing times to maintain an alternating pattern with legs moving at different speeds.

Adaptation of the interlimb parameters largely restored symmetry to the gait cycle, and therefore improve the stability. As such, different interlimb coordination patterns are used for various forms of locomotion (e.g., walk, run) and for walking in curved trajectories. For example, to walk in a curved path, the relative motion of the legs must change: the outer leg takes a longer step with a shorter stance time, and the inner leg does the opposite. However, this is accomplished effortlessly and without obvious asymmetries.

kinematic modes switch for different environments
Animals rarely perform steady-state locomotion for long. They tend to superpose, and switch between, multiple motor behaviors. The sandfish lizards can bury themselves into the ground to escape from predators and high temperature. It uses its limbs to crawl on the sand surfaces while performs Undulatory locomotion within the sand. Certain amphibian fish species, like mudskippers (see also walking fish, Flying fish), are able to adapt themselves to both aquatic living and terrestrial habitat,, and travel over land for extended periods of time, and in such way they could get access to broader resources. These adaptations require locomotion mode switch in kinematics, force generation and muscle activation. These animals change their locomotion kinematics to perform an optimal or more efficient locomotion within different environment.

Ground of different stiffness
Tendons and ligaments serve as excellent elastic energy stores during running gaits. They stretch and recoil with each step, reducing the work required from the muscles and lowering the metabolic cost of locomotion The Central nervous system (CNS) coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a spring mass system during ground contact, where the linear spring representing the stance limb and the point mass equivalent to body mass.

In the natural world, animals encounter many surfaces that compress under their feet. These compliant surfaces are like another spring in series with the runner's spring-mass system. Animals are capable of adjusting leg stiffness to accommodate different surface stiffnesses, allowing them to maintain similar running mechanics (e.g., the ground contact time, stride frequency, and vertical displacement of the COM) on different surfaces.

Robots
Nowadays, robots are expected to autonomously explore numerous unknown and challenging environments, which leads to the an increasing need of terrain-adaptive robot design and control. Inspired by organism locomotion adaptability, many robot platforms that can automatically adjust kinematics on different terrains have been developed. Biological concepts of Spring-loaded inverted pendulum (SLIP) model has been incorporated in the development of legged robots, to maximize the dynamic energy stability for the robot in a variety of environments. By adjusting the rotational compliance and damping of the "hip" joints, the robot could better stabilize its gait and have high-speed mobility over irregular terrains.

Posture control
Postural control is initiated by sensory feedback from the feet. The goal of the postural control module is to equalize pressure on the feet by making suitable shifts in trunk position and trunk configuration. The input from the foot pressure sensors on the feet are compared and used to adjust bias of the posture. The idea behind the control scheme is to maintain three degrees of symmetry front to back, side-to-side and diagonal symmetry. Thus sensory signals become references for other signals related by a degree of symmetry; senses are compared to each other. Furthermore, each degree of symmetry is related to a particular 'muscle group' in the robot. Front to back symmetry generates commands for the hip rotation axes. Side-to-side symmetry drives hip adductors. Finally, diagonal symmetry drives twist about the body axis.

This ompensation could be achieved on a slope. Gyro sensors, inclinometers are usually used to obtain sensory information for the body pitch and roll angle, based on which the controller could coordinate the robot posture to balance external forces or the effect of sloping terrain. Also, postural adjustment can be made to compensate for weights placed on the robot. Such weight may mimic a payload dropped onto the robot’s back. It may also mimic constant perturbations such as dangling wires and cables. Thus this scheme achieves postural control in the face of significant outside disturbances.

CPG control
The biological foundation of most natural locomotory systems is the Central pattern generator (CPG). The CPG is a set of neural circuits found in the spinal cord, arranged to produce oscillatory periodic waveforms that activate muscles in a coordinated. The neural system model in a robot usually consists of a central pattern generator and reflexes. A CPG receives sensory input and changes the period of its own active phase. The desired angle and P-gain of each joint in the virtual spring–damper system is then switched based on the phase signal of the CPG. CPGs, the motion of the virtual spring–damper system of each leg, and the rolling motion of the body are mutually entrained through the rolling motion feedback to CPGs, and can generate adaptive walking for the robot.

Leg stiffness adjustment
The use of active-compliance controller could compensate for stability variations in the presence of disturbances. This kind of controller produces a motion similar to that produced by a spring following Hook’s law, connecting a foot directly to the body. This helps the robot recover from small perturbations. However, when walking on inclined ground or troubled by sizeable disturbances, the transient response of the compliant motion can itself cause instability.

Recommended reading
Alexander, R. McNeill (2003) Principles of Animal Locomotion. Princeton University Press, Princeton, N.J. ISBN 0-691-08678-8