Vision-based object detectors are a crucial basis for robotics applications as they provide valuable information about object localization in the environment. These need to ensure high reliability in different lighting conditions, occlusions, and visual artifacts, all while running in real-time. Collecting and annotating real-world data for these networks is prohibitively time consuming and costly, especially for custom assets, such as industrial objects, making it untenable for generalization to in-the-wild scenarios. To this end, we present Synthetica, a method for large-scale synthetic data generation for training robust state estimators. This paper focuses on the task of object detection, an important problem which can serve as the front-end for most state estimation problems, such as pose estimation. Leveraging data from a photorealistic ray-tracing renderer, we scale up data generation, generating 2.7 million images, to train highly accurate real-time detection transformers. We present a collection of rendering randomization and training-time data augmentation techniques conducive to robust sim-to-real performance for vision tasks. We demonstrate state-of-the-art performance on the task of object detection while having detectors that run at 50–100Hz which is 9 times faster than the prior state-of-the-art (SOTA). We further demonstrate the usefulness of our training methodology for robotics applications by showcasing a pipeline for use in the real world with custom objects for which there do not exist prior datasets. Our work highlights the importance of scaling synthetic data generation for robust sim-to-real transfer while achieving the fastest real-time inference speeds. Videos and supplementary information can be found at https://sites.google.com/view/synthetica-vision

Robotics policies are always subjected to complex, second order dynamics that entangle their actions with resulting states. In reinforcement learning (RL) contexts, policies have the burden of deciphering these complicated interactions over massive amounts of experience and complex reward functions to learn how to accomplish tasks. Moreover, policies typically issue actions directly to controllers like Operational Space Control (OSC) or joint PD control, which induces straightline motion towards these action targets in task or joint space. However, straightline motion in these spaces for the most part do not capture the rich, nonlinear behavior our robots need to exhibit, shifting the burden of discovering these behaviors more completely to the agent. Unlike these simpler controllers, geometric fabrics capture a much richer and desirable set of behaviors via artificial, second order dynamics grounded in nonlinear geometry. These artificial dynamics shift the uncontrolled dynamics of a robot via an appropriate control law to form behavioral dynamics. Behavioral dynamics unlock a new action space and safe, guiding behavior over which RL policies are trained. Behavioral dynamics enable bang-bang-like RL policy actions that are still safe for real robots, simplify reward engineering, and help sequence real-world, high-performance policies. We describe the framework more generally and create a specific instantiation for the problem of dexterous, in-hand reorientation of a cube by a highly actuated robot hand.

This paper explores the problem of collision-free motion generation for manipulators by formulating it as a global motion optimization problem. We develop a parallel optimization technique to solve this problem and demonstrate its effectiveness on massively parallel GPUs. We show that combining simple optimization techniques with many parallel seeds leads to solving difficult motion generation problems within 53ms on average, 62x faster than SOTA trajectory optimization methods. We achieve SOTA performance by combining L-BFGS step direction estimation with a novel parallel noisy line search scheme and a particle-based optimization solver. To further aid trajectory optimization, we develop a parallel geometric planner that is atleast 28x faster than SOTA RRTConnect implementations. We also introduce a collision-free IK solver that can solve over 9000 queries/s. We are releasing our GPU accelerated library CuRobo that contains core components for robot motion generation. Additional details are available at sites.google.com/nvidia.com/curobo.

Motion generation seeks to produce safe and feasible robot motion from start to goal. Various tools at different levels of granularity have been developed. On one extreme, sampling-based motion planners focus on completeness - a solution, if it exists, would eventually be found. However, produced paths are often of low quality, and contain superfluous motion. On the other, reactive methods optimise the immediate cost to obtain the next controls, producing smooth and legible motion that can quickly adapt to perturbations, uncertainties, and changes in the environment. However, reactive methods are highly local, and often produce motion that become trapped in non-convex regions of the environment. This paper contributes, Geometric Fabric Command Sequences, a method that lies in the middle ground. It can produce globally optimal motion that is smooth and intuitive, while being also reactive. We model motion via a reactive Geometric Fabric policy that ingests a sequence of attractor states, or commands, and then apply global optimisation over the space of commands. We postulate that solutions for different problems and scenes are highly transferable when conditioned on environmental features. Therefore, an implicit generative model is trained on solutions from optimisation and environment features in a self-supervised manner. That is, faced with multiple motion generation problems, the learning and optimisation are contained within the same loop: the optimisation generates labels for learning, while the learning improves the optimisation for the next problem, which in turn provides higher quality labels. We empirically validate our method in both simulation and on a real-world 6-DOF JACO arm.

Robotics research has found numerous important applications of Riemannian geometry. Despite that, the concept remain challenging to many roboticists because the background material is complex and strikingly foreign. Beyond Riemannian geometry, there are many natural generalizations in the mathematical literature—areas such as Finsler geometry and spray geometry—but those generalizations are largely inaccessible, and as a result there remain few applications within robotics. This paper presents a re-derivation of spray and Finsler geometries, critical for the development of our recent work on geometric fabrics, which builds the ideas from familiar concepts in advanced calculus and the calculus of variations. We focus on the pragmatic and calculable results, avoiding the use of tensor notation to appeal to a broader audience and emphasizing geometric path consistency over ideas around connections and curvature. We hope that they will contribute to an increased understanding of generalized nonlinear, and even classical Riemannian, geometry within the robotics community and inspire future research into new applications.

Generating robot motion that fulfills multiple tasks simultaneously is challenging due to the geometric constraints imposed on the robot. In this paper, we propose to solve multi-task problems through learning structured policies from human demonstrations. Our structured policy is inspired by RMPflow, a framework for combining subtask policies on different spaces. The policy structure provides the user an interface to 1) specifying the spaces that are directly relevant to the completion of the tasks, and 2) designing policies for certain tasks that do not need to be learned. We derive an end-to-end learning objective that is suitable for the multi-task problem, emphasizing the distance between generated motions and demonstrations measured on task spaces. Furthermore, the motion generated from the learned policy class is guaranteed to be stable. We validate the effectiveness of our proposed learning framework through qualitative and quantitative evaluations on three robotic tasks on a 7-DOF Rethink Sawyer robot.

Generating robot motion for multiple tasks in dynamic environments is challenging, requiring an algorithm to respond reactively while accounting for complex nonlinear relationships between tasks. In this article, we develop a novel policy synthesis algorithm, Riemannian motion policy (RMP)flow, based on geometrically consistent transformations of RMPs. RMPs are a class of reactive motion policies that parameterize non-Euclidean behaviors as dynamical systems in intrinsically nonlinear task spaces. Given a set of RMPs designed for individual tasks, RMPflow can combine these policies to generate an expressive global policy, while simultaneously exploiting sparse structure for computational efficiency. We study the geometric properties of RMPflow and provide sufficient conditions for stability. Finally, we experimentally demonstrate that accounting for the natural Riemannian geometry of task policies can simplify classically difficult problems, such as planning through the clutter on high-degree-of-freedom manipulation systems.Note to Practitioners—Requirements on safety and responsiveness for collaborative robots have driven a need for new ideas in control design that bridge between standard objectives in low-level control (such as trajectory tracking) and high-level behavioral objectives (such as collision avoidance) often relegated to planning systems. Modern results from geometric control, which promise stable controllers that can smoothly and safely transition between many behavioral tasks, therefore, become highly relevant. However, for years, this field has remained inaccessible due to its mathematical complexity. This article aims to: 1) make those ideas accessible to robotics and control experts by recasting them in a concrete algorithmic framework amenable to controller design and 2) to additionally generalize them to better satisfy the specific needs of robotic behavior generation. Our experiments demonstrate that the resulting controllers can engender natural behavior that adapts instantaneously to changing surroundings with zero planning while performing manipulation tasks. The framework is gaining traction within the robotics community, finding increasing application in areas, such as autonomous navigation, tactile servoing, and multi-agent systems. Future research will address learning these controllers from data to simplify that process of design and tuning, which at present can require experience.

Teleoperation offers the possibility of imparting robotic systems with sophisticated reasoning skills, intuition, and creativity to perform tasks. However, teleoperation solutions for high degree-of-actuation (DoA), multi-fingered robots are generally cost-prohibitive, while low-cost offerings usually offer reduced degrees of control. Herein, a low-cost, depth-based teleoperation system, DexPilot, was developed that allows for complete control over the full 23 DoA robotic system by merely observing the bare human hand. DexPilot enabled operators to solve a variety of complex manipulation tasks that go beyond simple pick-and-place operations and performance was measured through speed and reliability metrics. DexPilot cost-effectively enables the production of high dimensional, multi-modality, state-action data that can be leveraged in the future to learn sensorimotor policies for challenging manipulation tasks. The videos of the experiments can be found at https://sites.google.com/view/dex-pilot.

Traditional robotic approaches rely on an accurate model of the environment, a detailed description of how to perform the task, and a robust perception system to keep track of the current state. On the other hand, reinforcement learning approaches can operate directly from raw sensory inputs with only a reward signal to describe the task, but are extremely sampleinefficient and brittle. In this work, we combine the strengths of model-based methods with the flexibility of learning-based methods to obtain a general method that is able to overcome inaccuracies in the robotics perception/actuation pipeline, while requiring minimal interactions with the environment. This is achieved by leveraging uncertainty estimates to divide the space in regions where the given model-based policy is reliable, and regions where it may have flaws or not be well defined. In these uncertain regions, we show that a locally learned-policy can be used directly with raw sensory inputs. We test our algorithm, Guided Uncertainty-Aware Policy Optimization (GUAPO), on a real-world robot performing peg insertion. Videos are available at: https://sites.google.com/view/guapo-rl.

Visual topological navigation has been revitalized recently thanks to the advancement of deep learning that substantially improves robot perception. However, the scalability and reliability issue remain challenging due to the complexity and ambiguity of real world images and mechanical constraints of real robots. We present an intuitive approach to show that by accurately measuring the capability of a local controller, large-scale visual topological navigation can be achieved while being scalable and robust. Our approach achieves state-of-the-art results in trajectory following and planning in large-scale environments. It also generalizes well to real robots and new environments without retraining or finetuning.

Effective human-robot collaboration requires informed anticipation. The robot must anticipate the human's actions, but also react quickly and intuitively when its predictions are wrong. The robot must plan its actions to account for the human's own plan, with the knowledge that the human's behavior will change based on what the robot actually does. This cyclical game of predicting a human's future actions and generating a corresponding motion plan is extremely difficult to model using standard techniques. In this work, we describe a novel Model Predictive Control (MPC)-based framework for finding optimal trajectories in a collaborative, multi-agent setting, in which we simultaneously plan for the robot while predicting the actions of its external collaborators. We use human-robot handovers to demonstrate that with a strong model of the collaborator, our framework produces fluid, reactive human-robot interactions in novel, cluttered environments. Our method efficiently generates coordinated trajectories, and achieves a high success rate in handover, even in the presence of significant sensor noise.

Algorithmic solutions for the motion planning problem have been investigated for five decades. Since the development of A* in 1969 many approaches have been investigated, traditionally classified as either grid decomposition, potential fields or sampling-based. In this work, we focus on using numerical optimization, which is understudied for solving motion planning problems. This lack of interest in the favor of sampling-based methods is largely due to the non-convexity introduced by narrow passages. We address this shortcoming by grounding the solution in differential geometry. We demonstrate through a series of experiments on 3 Dofs and 6 Dofs narrow passage problems, how modeling explicitly the underlying Riemannian manifold leads to an efficient interior point non-linear programming solution.1

We present a predictor-corrector framework, called PicCoLO, that can transform a first-order model-free reinforcement or imitation learning algorithm into a new hybrid method that leverages predictive models to accelerate policy learning. The new “PicCoLOed” algorithm optimizes a policy by recursively repeating two steps: In the Prediction Step, the learner uses a model to predict the unseen future gradient and then applies the predicted estimate to update the policy; in the Correction Step, the learner runs the updated policy in the environment, receives the true gradient, and then corrects the policy using the gradient error. Unlike previous algorithms, PicCoLO corrects for the mistakes of using imperfect predicted gradients and hence does not suffer from model bias. The development of PicCoLO is made possible by a novel reduction from predictable online learning to adversarial online learning, which provides a systematic way to modify existing first-order algorithms to achieve the optimal regret with respect to predictable information. We show, in both theory and simulation, that the convergence rate of several first-order model-free algorithms can be improved by PicCoLO.

We consider the problem of transferring policies to the real world by training on a distribution of simulated scenarios. Rather than manually tuning the randomization of simulations, we adapt the simulation parameter distribution using a few real world roll-outs interleaved with policy training. In doing so, we are able to change the distribution of simulations to improve the policy transfer by matching the policy behavior in simulation and the real world. We show that policies trained with our method are able to reliably transfer to different robots in two real world tasks: swing-peg-in-hole and opening a cabinet drawer. The video of our experiments can be found at https://sites.google.com/view/simopt.

To perform complex tasks, robots must be able to interact with and manipulate their surroundings. One of the key challenges in accomplishing this is robust state estimation during physical interactions, where the state involves not only the robot and the object being manipulated, but also the state of the contact itself. In this work, within the context of planar pushing, we extend previous inference-based approaches to state estimation in several ways. We estimate the robot, object, and the contact state on multiple manipulation platforms configured with a vision-based articulated model tracker, and either a biomimetic tactile sensor or a force-torque sensor. We show how to fuse raw measurements from the tracker and tactile sensors to jointly estimate the trajectory of the kinematic states and the forces in the system via probabilistic inference on factor graphs, in both batch and incremental settings. We perform several benchmarks with our framework and show how performance is affected by incorporating various geometric and physics based constraints, occluding vision sensors, or injecting noise in tactile sensors. We also compare with prior work on multiple datasets and demonstrate that our approach can effectively optimize over multi-modal sensor data and reduce uncertainty to find better state estimates.

End-to-end learning for autonomous navigation has received substantial attention recently as a promising method for reducing modeling error. However, its data complexity, especially around generalization to unseen environments, is high. We introduce a novel image-based autonomous navigation technique that leverages in policy structure using the Riemannian Motion Policy (RMP) framework for deep learning of vehicular control. We design a deep neural network to predict control point RMPs of the vehicle from visual images, from which the optimal control commands can be computed analytically. We show that our network trained in the Gibson environment can be used for indoor obstacle avoidance and navigation on a real RC car, and our RMP representation generalizes better to unseen environments than predicting local geometry or predicting control commands directly.

Current methods for estimating force from tactile sensor signals are either inaccurate analytic models or task-specific learned models. In this paper, we explore learning a robust model that maps tactile sensor signals to force. We specifically explore learning a mapping for the SynTouch BioTac sensor via neural networks. We propose a voxelized input feature layer for spatial signals and leverage information about the sensor surface to regularize the loss function. To learn a robust tactile force model that transfers across tasks, we generate ground truth data from three different sources: (1) the BioTac rigidly mounted to a force torque (FT) sensor, (2) a robot interacting with a ball rigidly attached to the same FT sensor, and (3) through force inference on a planar pushing task by formalizing the mechanics as a system of particles and optimizing over the object motion. A total of 140k samples were collected from the three sources. We achieve a median angular accuracy of 3.5 degrees in predicting force direction (66% improvement over the current state of the art) and a median magnitude accuracy of 0.06 N (93% improvement) on a test dataset. Additionally, we evaluate the learned force model in a force feedback grasp controller performing object lifting and gentle placement. Our results can be found on https: //sites.google.com/view/tactile-force.

To achieve a dexterous robotic manipulation, we need to endow our robot with tactile feedback capability, i.e. the ability to drive action based on tactile sensing. In this paper, we specifically address the challenge of tactile servoing, i.e. given the current tactile sensing and a target/goal tactile sensing - memorized from a successful task execution in the past - what is the action that will bring the current tactile sensing to move closer towards the target tactile sensing at the next time step. We develop a data-driven approach to acquire a dynamics model for tactile servoing by learning from demonstration. Moreover, our method represents the tactile sensing information as to lie on a surface - or a 2D manifold - and perform a manifold learning, making it applicable to any tactile skin geometry. We evaluate our method on a contact point tracking task using a robot equipped with a tactile finger.

It is difficult to create robust, reusable, and reactive behaviors for robots that can be easily extended and combined. Frameworks such as Behavior Trees are flexible but difficult to characterize, especially when designing reactions and recovery behaviors to consistently converge to a desired goal condition. We propose a framework which we call Robust Logical-Dynamical Systems (RLDS), which combines the advantages of task representations like behavior trees with theoretical guarantees on performance. RLDS can also be constructed automatically from simple sequential task plans and will still achieve robust, reactive behavior in dynamic real-world environments. In this work, we describe both our proposed framework and a case study on a simple household manipulation task, with examples for how specific pieces can be implemented to achieve robust behavior. Finally, we show how in the context of these manipulation tasks, a combination of an RLDS with planning can achieve better results under adversarial conditions.

Modern robotics is gravitating toward increasingly collaborative human robot interaction. Tools such as acceleration policies can naturally support the realization of reactive, adaptive, and compliant robots. These tools require us to model the system dynamics accurately - a difficult task. The fundamental problem remains that simulation and reality diverge-we do not know how to accurately change a robot's state. Thus, recent research on improving inverse dynamics models has been focused on making use of machine learning techniques. Traditional learning techniques train on the actual realized accelerations, instead of the policy's desired accelerations, which is an indirect data source. Here we show how an additional training signal - measured at the desired accelerations - can be derived from a feedback control signal. This effectively creates a second data source for learning inverse dynamics models. Furthermore, we show how both the traditional and this new data source, can be used to train task-specific models of the inverse dynamics, when used independently or combined. We analyze the use of both data sources in simulation and demonstrate its effectiveness on a real-world robotic platform. We show that our system incrementally improves the learned inverse dynamics model, and when using both data sources combined converges more consistently and faster.

In this paper we present motion optimization algorithms for computing manipulation motions in presence of obstacles. Our approach builds a geometric representation of the workspace by constructing Riemannian metrics using electric potentials emanating from the workspace obstacles. Velocity of the robot's body is measured with respect to this metric instead of traditional Cartesian velocity. Empirical results demonstrate that Riemannian metrics are better handled by optimizers that leverage objective and constraint functions' second order information. This information encodes how the Riemannian geometry of the modeled workspace pulls back into the configuration space. We also show that despite the additional computational burden of computing the electric-potential based metric, it results in faster overall convergence than reasoning on Euclidean geometry alone. Evaluation is made efficient by cashing the electric potential in voxel grids and using Tri-cubic spline interpolation to assess the potentials gradient.

Learning of inverse dynamics modeling errors is key for compliant or force control when analytical models are only rough approximations. Thus, designing real time capable function approximation algorithms has been a necessary focus towards the goal of online model learning. However, because these approaches learn a mapping from actual state and acceleration to torque, good tracking is required to observe data points on the desired path. Recently it has been shown how online gradient descent on a simple modeling error offset term to minimize tracking at acceleration level can address this issue. However, to adapt to larger errors a high learning rate of the online learner is required, resulting in reduced compliancy. Thus, here we propose to combine both approaches: The online adapted offset term ensures good tracking such that a nonlinear function approximator is able to learn an error model on the desired trajectory. This, in turn, reduces the load on the adaptive feedback, enabling it to use a lower learning rate. Combined this creates a controller with variable feedback and low gains, and a feedforward model that can account for larger modeling errors. We demonstrate the effectiveness of this framework, in simulation and on a real system.

What is it that makes movement around obstacles hard? The answer seems clear: obstacles contort the geometry of the workspace and make it difficult to leverage what we consider easy and intuitive straight-line Cartesian geometry. But is Cartesian motion actually easy? It's certainly well-understood and has numerous applications. But beneath the details of linear algebra and pseudoinverses, lies a non-trivial Riemannian metric driving the solution. Cartesian motion is easy only because the pseudoinverse, our powerhouse tool, correctly represents how Euclidean workspace geometry pulls back into the configuration space. In light of that observation, it reasons that motion through a field of obstacles could be just as easy as long as we correctly account for how those obstacles warp the geometry of the space. This paper explores extending our geometric model of the robot beyond the notion of a Cartesian workspace space to fully model and leverage how geometry changes in the presence of obstacles. Intuitively, impenetrable obstacles form topological holes and geodesics curve around them accordingly. We formalize this intuition and develop a general motion optimization framework called Riemannian Motion Optimization (RieMO) to efficiently find motions using our geometric models. Our experiments demonstrate that, for many problems, obstacle avoidance can be much more natural when placed within the right geometric context.

Efficient manipulation requires contact to reduce uncertainty. The manipulation literature refers to this as funneling: a methodology for increasing reliability and robustness by leveraging haptic feedback and control of environmental interaction. However, there is a fundamental gap between traditional approaches to trajectory optimization and this concept of robustness by funneling: traditional trajectory optimizers do not discover force feedback strategies. From a POMDP perspective, these behaviors could be regarded as explicit observation actions planned to sufficiently reduce uncertainty thereby enabling a task. While we are sympathetic to the full POMDP view, solving full continuous-space POMDPs in high-dimensions is hard. In this paper, we propose an alternative approach in which trajectory optimization objectives are augmented with new terms that reward uncertainty reduction through contacts, explicitly promoting funneling. This augmentation shifts the responsibility of robustness toward the actual execution of the optimized trajectories. Directly tracing trajectories through configuration space would lose all robustness-dual execution achieves robustness by devising force controllers to reproduce the temporal interaction profile encoded in the dual solution of the optimization problem. This work introduces dual execution in depth and analyze its performance through robustness experiments in both simulation and on a real-world robotic platform.

Goal sets are omnipresent in manipulation: picking up objects, placing them on counters or in bins, handing them off - all of these tasks encompass continuous sets of goals. This paper describes how to design optimal trajectories that exploit goal sets. We extend CHOMP (Covariant Hamiltonian Optimization for Motion Planning), a recent trajectory optimizer that has proven effective on high-dimensional problems, to handle trajectory-wide constraints, and relate the solution to the intuition of taking unconstrained steps and subsequently projecting them onto the constraints. We then show how this projection simplifies for goal sets (i.e. constraints that affect only the end-point). Finally, we present experiments on a personal robotics platform that show the importance of exploiting goal sets in trajectory optimization for day-to-day manipulation tasks.

Existing high-dimensional motion planning algorithms are simultaneously overpowered and underpowered. In domains sparsely populated by obstacles, the heuristics used by sampling-based planners to navigate “narrow passages” can be needlessly complex; furthermore, additional post-processing is required to remove the jerky or extraneous motions from the paths that such planners generate. In this paper, we present CHOMP, a novel method for continuous path refinement that uses covariant gradient techniques to improve the quality of sampled trajectories. Our optimization technique both optimizes higher-order dynamics and is able to converge over a wider range of input paths relative to previous path optimization strategies. In particular, we relax the collision-free feasibility prerequisite on input paths required by those strategies. As a result, CHOMP can be used as a standalone motion planner in many real-world planning queries. We demonstrate the effectiveness of our proposed method in manipulation planning for a 6-DOF robotic arm as well as in trajectory generation for a walking quadruped robot.

We present a novel approach for determining robot movements that efficiently accomplish the robot's tasks while not hindering the movements of people within the environment. Our approach models the goal-directed trajectories of pedestrians using maximum entropy inverse optimal control. The advantage of this modeling approach is the generality of its learned cost function to changes in the environment and to entirely different environments. We employ the predictions of this model of pedestrian trajectories in a novel incremental planner and quantitatively show the improvement in hindrance-sensitive robot trajectory planning provided by our approach.

Imitation learning of sequential, goal-directed behavior by standard supervised techniques is often difficult. We frame learning such behaviors as a maximum margin structured prediction problem over a space of policies. In this approach, we learn mappings from features to cost so an optimal policy in an MDP with these cost mimics the expert's behavior. Further, we demonstrate a simple, provably efficient approach to structured maximum margin learning, based on the subgradient method, that leverages existing fast algorithms for inference. Although the technique is general, it is particularly relevant in problems where A* and dynamic programming approaches make learning policies tractable in problems beyond the limitations of a QP formulation. We demonstrate our approach applied to route planning for outdoor mobile robots, where the behavior a designer wishes a planner to execute is often clear, while specifying cost functions that engender this behavior is a much more difficult task.

The Maximum Margin Planning (MMP) (Ratliff et al., 2006) algorithm solves imitation learning problems by learning linear mappings from features to cost functions in a planning domain. The learned policy is the result of minimum-cost planning using these cost functions. These mappings are chosen so that example policies (or trajectories) given by a teacher appear to be lower cost (with a lossscaled margin) than any other policy for a given planning domain. We provide a novel approach, M M P B O O S T , based on the functional gradient descent view of boosting (Mason et al., 1999; Friedman, 1999a) that extends MMP by "boosting" in new features. This approach uses simple binary classification or regression to improve performance of MMP imitation learning, and naturally extends to the class of structured maximum margin prediction problems. (Taskar et al., 2005) Our technique is applied to navigation and planning problems for outdoor mobile robots and robotic legged locomotion.