Existing research on dynamically capable legged robots, particularly those based on spring-mass models, generally considers improving in isolation either the stability and control accuracy on the rough terrain, or the energetic efficiency in steady state. In this paper, we propose a new method to address both, based on the hierarchical embedding of a simple spring-loaded inverted pendulum (SLIP) template model with a tunable radial damping coefficient into a realistic leg structure with series-elastic actuation. Our approach allows using the entire stance phase to inject/remove energy both for transient steps and in steady state, decreasing the maximum necessary actuator power while eliminating wasteful sources of the negative work. In doing so, we preserve the validity of the existing analytic approximations to the underlying SLIP model, propose improvements to increase the predictive accuracy, and construct accurate, model-based controllers that use the tunable damping coefficient of the template model. We provide extensive comparative simulations to establish the energy and power efficiency advantages of our approach, together with the accuracy of model-based gait control methods.

Widely accepted utility of simple spring-mass models for running behaviors as descriptive tools, as well as literal control targets, motivates accurate analytical approximations to their dynamics. Despite the availability of a number of such analytical predictors in the literature, their validation has mostly been done in simulation, and it is yet unclear how well they perform when applied to physical platforms. In this paper, we extend on one of the most recent approximations in the literature to ensure its accuracy and applicability to a physical monopedal platform. To this end, we present systematic experiments on a well-instrumented planar monopod robot, first to perform careful identification of system parameters and subsequently to assess predictor performance. Our results show that the approximate solutions to the spring-loaded inverted pendulum dynamics are capable of predicting physical robot position and velocity trajectories with average prediction errors of 2% and 7%, respectively. This predictive performance together with the simple analytic nature of the approximations shows their suitability as a basis for both state estimators and locomotion controllers.

In this paper, we introduce a novel logic language and theorem prover for robotic task planning. Our language, which we call Linear Planning Logic (LPL), is a fragment of linear logic whose resource-conscious semantics are well suited for reasoning with dynamic state, while its structure admits efficient theorem provers for automatic plan construction. LPL can be considered as an extension of Linear Hereditary Harrop Formulas (LHHF), whose careful design allows the minimization of nondeterminism in proof search, providing a sufficient basis for the design of linear logic programming languages such as Lolli. Our new language extends on the expressivity of LHHF, while keeping the resulting nondeterminism in proof search to a minimum for efficiency. This paper introduces the LPL language, presents the main ideas behind our theorem prover on a smaller fragment of this language and finally provides an experimental illustration of its operation on the problem of task planning for the hexapod robot RHex.

Mobile robots suffer from sensory data corruption due to body oscillations and disturbances. In particular, information loss on images captured with onboard cameras can be very high, and such loss may become irreversible or computationally costly to undo. In this paper, we propose a novel method to minimize average motion blur captured by such mobile visual sensors. To this end, we derive a motion blur metric (MMBM) that can be computed in real-time by using only inertial sensor measurements and validate it through comparisons with optic flow computations. The applicability of MMBM is illustrated through a motion blur minimizing system implemented on the SensoRHex hexapod robot by externally triggering an onboard camera based on MMBM values computed in real-time while the robot is walking straight on a flat surface. The resulting motion blur is compared to motion blur levels obtained with a regular, fixed frame-rate image acquisition schedule by both qualitative inspection and using a blind blur metric on captured images. MMBM based motion blur minimization system not only reduces average motion blur, but also avoids frames with extreme motion blur before an image gets corrupted by appropriately delaying the triggering of frame acquisition.

Spring-mass models have been very successful both in describing and generating running behaviors. Control of system energy within these models takes different forms, among which the use of a linear actuator in series with the leg spring has been preferred by many recent monopedal and bipedal platform designs due to its relative robustness and simplicity. However, the validity of the well-known Spring-Loaded Inverted Pendulum (SLIP) model of running for such platforms can only preserved under a specific family of control strategies to drive the actuator. In this paper, we propose a novel controller in this family, based on the idea of embedding a lossy SLIP template with a tunable damping coefficient into the linearly actuated compliant leg system. We show that this maximizes energy input within a single stride, allows decreased power requirements on the actuator compared to alternative methods, while preserving the validity and accuracy of analytic solutions and model-based controllers. We present systematic simulations to establish performance gains with respect to the commonly investigated method of modulating leg stiffness. Enabling the most efficient use of actuator power in this manner while preserving analytic tractability will allow efficient and accurate control of running for linearly actuated compliant leg designs.

Mobility through balancing on spherical wheels has recently received some attention in the robotics literature. Unlike traditional wheeled platforms, the operation of such platforms depends heavily on understanding and working with system dynamics, which have so far been approximated with simple planar models and their decoupled extension to three dimensions. Unfortunately, such models cannot capture inherently spatial aspects of motion such as yaw motion arising from the wheel rolling motion or coupled inertial effects for fast maneuvers. In this paper, we describe a novel, fully-coupled 3D model for such spherical wheeled platforms and show that it not only captures relevant spatial aspects of motion, but also provides a basis for controllers better informed by system dynamics. We focus our evaluations to simulations with this model and use circular paths to reveal advantages of this model in dynamically rich situations.

An important motivation for work on legged robots has always been their potential for high-performance locomotion on rough terrain. Nevertheless, most existing control algorithms for such robots either make rigid assumptions about their environments or rely on kinematic planning at low speeds. Moreover, the traditional separation of planning from control often has negative impact on the robustness of the system. In this paper, we introduce a new method for dynamic, fully reactive footstep planning for a planar spring–mass hopper, based on a careful characterization of the model dynamics and the design of an associated deadbeat controller, used within a sequential composition framework. This yields a purely reactive controller with a large domain of attraction that requires no explicit replanning during execution. We show in simulation that plans constructed for a simplified dynamic model can successfully control locomotion of a more complete model across rough terrain. We also characterize the performance of the planner over rough terrain and show that it is robust against both model uncertainty and measurement noise without replanning.

Most legged vertebrates use flexible spines and supporting muscles to provide auxiliary power and dexterity for dynamic behaviors, resulting in higher speeds and additional maneuverability during locomotion. However, most existing legged robots capable of dynamic locomotion incorporate only a single rigid trunk with actuation limited to legs and associated joints. In this paper, we investigate how quadrupedal bounding can be achieved in the presence of an actuated spinal joint and characterize associated performance improvements compared to bounding with a rigid robot body. In the context of both a new controller structure for bounding with a body joint and existing bounding controllers for the rigid trunk, we use optimization methods to identify the highest performance gait parameters and establish that the spinal joint allows increased forward speeds and hopping heights.

Practical realization of model-based dynamic legged behaviors is substantially more challenging than statically stable behaviors due to their heavy dependence on second-order system dynamics. This problem is further aggravated by the difficulty of accurately measuring or estimating dynamic parameters such as spring and damping constants for associated models and the fact that such parameters are prone to change in time due to heavy use and associated material fatigue. In this paper, we present an on-line, model-based adaptive control method for running with a planar spring-mass hopper based on a once-per-step parameter correction scheme. Our method can be used both as a system identification tool to determine possibly time-varying spring and damping constants of a miscalibrated system, or as an adaptive controller that can eliminate steady-state tracking errors through appropriate adjustments on dynamic system parameters. We present systematic simulation studies to show that our method can successfully accomplish both of these tasks.

Pronking (aka. stotting) is a gait in which all legs are used in synchrony, resulting in long flight phases and large jumping heights that may potentially be useful for mobile robots on rough terrain. Robotic instantiations of this gait suffer from severe pitch instability either due to underactuation, or the lack of sufficient feedback. Nevertheless, the dynamic nature of this gait suggests that the Spring-Loaded Inverted Pendulum Model (SLIP), a very successful predictive model for both natural and robotic runners, would be a good basis for more robust and maneuverable robotic pronking. In this paper, we describe how “template-based control”, a controller structure based on the embedding of a simple dynamical “template” within a more complex “anchor” system, can be used to achieve stable and controllable pronking for a planar, underactuated hexapod model. In this context, high-level control of the gait is regulated through speed and height commands to the SLIP template, while the embedding controller based on approximate inverse-dynamics and carefully designed passive dynamics ensures the stability of the remaining degrees of freedom. We show through extensive simulation experiments that unlike existing open-loop alternatives, the resulting control structure provides stability, explicit maneuverability and significant robustness against sensor and actuator noise.

The Spring-Loaded Inverted Pendulum (SLIP) model has long been established as an effective and accurate descriptive model for running animals of widely differing sizes and morphologies, while also serving as a basis for several hopping robot designs. Further research on this model led to the discovery of several analytic approximations to its normally nonintegrable dynamics. However, these approximations mostly focus on steady-state running with symmetric trajectories due to their linearization of gravitational effects, an assumption that is quickly violated for locomotion on more complex terrain wherein transient, non-symmetric trajectories dominate. In this paper, we introduce a novel gravity correction scheme that extends on one of the more recent analytic approximations to the SLIP dynamics and achieves good accuracy even for highly non-symmetric trajectories. Our approach is based on incorporating the total effect of gravity on the angular momentum throughout a single stance phase and allows us to preserve the analytic simplicity of the approximation to support our longer term research on reactive footstep planning for dynamic legged locomotion. We compare the performance of our method in simulation to two other existing analytic approximations and show that it outperforms them for most physically realistic non-symmetric SLIP trajectories while maintaining the same accuracy for symmetric trajectories.

The main driving force behind research on legged robots has always been their potential for high performance locomotion on rough terrain and the outdoors. Nevertheless, most existing control algorithms for such robots either make rigid assumptions about their environments (e.g flat ground), or rely on kinematic planning at low speeds. Moreover, the traditional separation of planning from control often has negative impact on the robustness of the system against model uncertainty and environment noise. In this paper, we introduce a new method for dynamic, fully reactive footstep planning for a simplified planar spring-mass hopper, a frequently used model for running behaviors. Our approach is based on a careful characterization of the model dynamics and an associated deadbeat controller, used within a sequential composition framework. This yields a purely reactive controller with a very large, nearly global domain of attraction that requires no explicit replanning during execution. Finally, we use a simplified hopper in simulation to illustrate the performance of the planner under different rough terrain scenarios and show that it is extremely robust to both model uncertainty and measurement noise.

Synthesis of robot behaviors towards nontrivial goals often requires reasoning about both discrete and continuous aspects of the underlying domain. Existing approaches in building automated tools for such synthesis problems attempt to augment methods from either discrete planning or continuous control with hybrid elements, but largely fail to ensure a uniform treatment of both aspects of the domain. In this paper, we present a new formalism, constrained intuitionistic linear logic (CILL), merging continuous constraint solvers with linear logic to yield a single language in which hybrid properties of robotic behaviors can be expressed and reasoned with. Following a gentle introduction to linear logic, we describe the two new connectives of CILL, introduced to interface the constraint domain with the logical fragment of the language. We then illustrate the application of CILL for robotic planning problems within the balanced blocks world, a "physically realistic" extension of the blocks world domain. Even though some of the formal proofs for the semantic foundations of the language as well as an efficient implementation of a theorem prover are yet to be completed, CILL promises to be a powerful formalism in reasoning within hybrid domains.

In this paper, we introduce a hexapedal locomotion controller that simulation evidence suggests will be capable of driving our RHex robot at speeds exceeding five body lengths per second with reliable stability and rapid maneuverability. We use a low dimensional passively compliant biped as a "template" - a control target for the alternating tripod gait of the physical machine. We impose upon the physical machine an approximate inverse dynamics within-stride controller designed to force the true high dimensional system dynamics down onto the lower dimensional subspace corresponding to the template. Numerical simulations suggest the presence of asymptotically stable running gaits with large basins of attraction. Moreover, this controller improves substantially the maneuverability and dynamic range of RHex's running behaviors relative to the initial prototype open-loop algorithms.

We report on the design and analysis of a controller which can achieve dynamical self-righting of our hexapedal robot, RHex. We present an empirically developed control procedure which works reasonably well on indoor surfaces, using a hybrid energy pumping strategy to overcome torque limitations of its actuators. Subsequent modeling and analysis yields a new controller with a much wider domain of success as well as a preliminary understanding of the necessary hybrid control strategy. Simulation results demonstrate the superiority of the improved control strategy to the first generation empirically designed controller.

We report on our progress in extending the behavioral repertoire of RHex, a compliant leg hexapod robot. We introduce two new controllers, one for climbing constant slope inclinations and one for achieving higher speeds via pronking, a gait that incorporates a, substantial aerial phase. In both cases, we make use of an underlying open-loop control strategy, combined with low bandwidth feedback to modulate its parameters. The inclination behavior arises from our initial alternating tripod walking controller and adjusts the angle offsets of individual leg motion profiles based on inertial sensing of the average surface slope. Similarly, the pronking controller makes use of a "virtual" leg touchdown sensing mechanism to adjust the frequency of the open-loop pronking, effectively synchronizing the controller with the natural oscillations of the mechanical system. Experimental results demonstrate good performance on slopes inclined up to /spl sim/250 and pronking up to speeds approaching 2 body lengths per second (/spl sim/1.0 m/s).

We present the design, modeling and preliminary control of RHex, an autonomous dynamically stable hexapod possessing merely six actuated degrees of freedom (at the hip attachment of each leg). Our design emphasizes mechanical simplicity as well as power and computational autonomy, critical components for legged robotics applications. A compliant hexapod model, used to build a simulation environment closely informed the design and construction of the physical machine and promises to inform, similarly, our future analysis as well. Simulations and experiments show that RHex can achieve dynamically stable walking, running and turning with very simple clock driven open-loop control strategies.

We propose a new family of controllers for multi-jointed planar monoped runners, based on approximate but accurate models of the stance phase dynamics of a two degree of freedom "SLIP" leg. Unlike previous approaches, the new scheme gives control over all parameters of the system including the hopping height, forward speed and duty cycle. The control laws are "deadbeat" in nature, derived by computing the inverse of an approximate return map and corrected by integral compensation. We use the expressions obtained in this way to control the original SLIP leg as well as radically different, more realistic four degree of freedom legs. In each case, the performance of the deadbeat scheme in controlling forward running velocity is compared to a modified Raibert control strategy, whose experimental stability properties have been analyzed carefully in the low degree of freedom setting.