Long-term Motion Research Articles

The Role of the Yarkovsky Effect in the Long-term Dynamics of Asteroid (469219) Kamo’oalewa

Abstract The Near-Earth asteroid (469219) Kamo’oalewa (aka 2016 HO3) is an Earth coorbital and a potential space mission target. Its short-term dynamics are characterized by a periodic switching between quasisatellite and horseshoe configurations. Due to its small diameter of only about 36 m, the Yarkovsky effect may play a significant role in the long-term dynamics. In this work, we addressed this issue by studying the changes in the long-term motion of Kamo’oalewa caused by the Yarkovsky effect. We used an estimation of the magnitude of the Yarkovsky effect assuming different surface compositions and introduced the semimajor axis drift by propagating orbits of test particles representing the clones of the nominal orbit. Our simulations showed that the Yarkovsky effect may cause Kamo’oalewa to exit from the Earth coorbital region a bit faster when compared to a purely gravitational model. Nevertheless, it still could remain an Earth companion for at least 0.5 My in the future. Our results imply that Kamo’oalewa is the most stable Earth’s coorbital object known so far, not only from a short-term perspective but also on long timescales.

TMF: Temporal Motion and Fusion for action recognition

Temporal motion information plays an important role in video understanding, human action recognition and other fields. Optical flow, which contains rich temporal motion information, has been widely used in many visual tasks and has achieved superior performance. However, the extraction of optical flow is time-consuming and laborious. In this paper, we propose a Temporal Motion and Fusion (TMF) module, including a motion extraction (ME) module and a temporal crossing fusion (TCF) module. The ME module can replace the traditional optical flow, establish the matching relationship between adjacent frames on the convoluted feature maps. And then extract simple and effective short-term motion information. TCF module crosses adjacent frames and fuse the information of nonadjacent video frames to realize long-term motion information modeling. Finally, the extracted motion information is fused with the appearance information captured by 2D convolution for final recognition. The experiment proved that with only a few additional parameters and calculation costs increased, our proposed lightweight model achieves state-of-the-art results on Something-Something-V1&V2 and Diving-48, and obtains competitive results on HMDB-51 and UCF-101 among the single models.

Bidirectional LSTM with saliency-aware 3D-CNN features for human action recognition

Deep convolutional neural network (DCNN) and recurrent neural network (RNN) have been proved as an imperious research area in multimedia understanding and obtained remarkable action recognition performance. However, videos contain rich motion information with varying dimensions. Existing recurrent based pipelines fail to capture long-term motion dynamics in videos with various motion scales and complex actions performed by multiple actors. Consideration of contextual and salient features is more important than mapping a video frame into a static video representation. This research work provides a novel pipeline by analyzing and processing the video information using a 3D convolution (C3D) network and newly introduced deep bidirectional LSTM. Like popular two-stream convent, we also introduce a two-stream framework with one modification; that is, we replace the optical flow stream by saliency-aware stream to avoid the computational complexity. First, we generate a saliency-aware video stream by applying the saliency-aware method. Secondly, a two-stream 3D-convolutional network (C3D) is utilized with two different types of streams, i.e., RGB stream and saliency-aware video stream, to collect both spatial and semantic temporal features. Next, a deep bidirectional LSTM network is used to learn sequential deep temporal dynamics. Finally, time-series-pooling-layer and softmax-layers classify human activity and behavior. The introduced system can learn long-term temporal dependencies and can predict complex human actions. Experimental results demonstrate the significant improvement in action recognition accuracy on different benchmark datasets.

The stepovers of the Central Dead Sea Fault: What can we learn from the confining vertical axis rotations?

The geometry of stepovers along strike-slip faults dictates the deformational field and topography induced around the faults. Stepover geometry also impacts the ability of a fault rupture to propagate from one fault segment to another and therefore acts as a major controlling factor in the size of earthquakes. However, the geometry of stepovers is often poorly resolved, as they tend to underlie young sedimentary successions. Yet, although mostly ignored, the accumulated long-term relative plate motions accommodated by the stepping faults generate permanent rotational deformation in the crust surrounding them. Here we present the results from a combined mechanical and paleomagnetic investigation of the vertical axis rotational pattern confining stepovers. We focus our investigation on the central Dead Sea Fault, where two prominent stepovers are located at the Kinneret and Hula depressions. To better understand their still somewhat elusive geometric settings, we mapped the crustal rotational field by studying the magnetization of the confining volcanic rocks. Remanent magnetization directions reveal localized zones of anomalously high vertical axis rotations in the vicinity of the stepovers that evolve to negligible rotations elsewhere. We then constructed a series of elastic and elasto-plastic slip models aiming to cover possible plate boundary architectures. Comparable patterns between the observed and predicted rotations were achieved when the Dead Sea Fault motion was concentrated along the eastern margins of both the Kinneret and Hula Basins. Our best-fit model suggests that the along-strike under-lapping distance for the Kinneret Stepover is ~8 km whereas for the Hula Stepover is only ~2 km. Our results, supported by historic and paleoseismic records that show no evidence of an earthquake that ruptured through the Kinneret Stepover, imply an enhanced deformation zone in the center of Lake Kinneret, which acts as a major barrier to rupture propagation. Our combined paleomagnetic and modeling analysis approach provides a new avenue for the study of the geometries of plate boundaries.

Guest Editorial: Introduction to the Special Issue on Long-Term Human Motion Prediction

The articles in this special section focus on long term human motion prediction. This represents a key ability for advanced autonomous systems, especially if they operate in densely crowded and highly dynamic environments. In those settings understanding and anticipating human movements is fundamental for robust long-term operation of robotic systems and safe human-robot collaboration. Foreseeing how a scene with multiple agents evolves over time and incorporating predictions in a proactive manner allows for novel ways of planning and control, active perception, or humanrobot interaction. Recent planning and control approaches use predictive techniques to better cope with the dynamics of the environment, thus allowing the generation of smoother and more legible robot motion. Predictions can be provided as input to the planning or optimization algorithm (e.g. as a cost term or heuristic function), or as additional dimension to consider in the problem formulation (leading to an increased computational complexity). Recent perception techniques deeply interconnect prediction modules with detection, segmentation and tracking, to generally increase the accuracy of different inference tasks, i.e. filtering, predicting. As also indicated by some of the scientific works accepted in this special issue, novel deep learning architectures allow better interleaving of the aforementioned units.

Seasonal and long-term vertical land motion in Southwest China determined using GPS, GRACE, and surface loading model

Owing to the intense tectonic activity and significant seasonal surface mass change, Southwest China is characterized by noticeable vertical land movement. We determined the vertical movement of Southwest China using 10 years of data from 41 continuous global positioning system (GPS) stations, gravity recovery and climate experiment (GRACE), and surface loading model (SLM). The annual variation in hydrological loading is the main factor causing the seasonal oscillation of surface deformation in Southwest China. Seasonal deformations captured by GPS, GRACE, and SLM are consistent to a certain extent, and the correlation coefficients between GPS/GRACE, and GPS/SLM are 0.82 and 0.81, respectively. After deducting the results yielded by GRACE and SLM from the GPS time series, the average reductions in root mean square were 41.3% and 38.0%, respectively. However, some systematic differences were observed among the annual amplitudes and phases of the seasonal deformations among the three products. For example, the average amplitudes estimated by GRACE and SLM were 7.4 mm and 6.1 mm, respectively, which were smaller than the amplitude deduced from GPS (9.7 mm). Furthermore, mean phase delays of 16, 22, and 6 days were observed between GPS/GRACE, GPS/SLM, and GRACE/SLM. The data processing errors and local geophysical signals in GPS and the underestimation of land water storage in GRACE and SLM were jointly responsible for the systemic differences. The simulated data show that the misestimating of hydrological loading can explain approximately 50%, 64%, and 83% of the phase delays between GPS/GRACE, GPS/SLM, and GRACE/SLM, respectively. In addition, we obtained long-term vertical crustal motion rates by subtracting the loading deformation rates estimated by GRACE from the linear rates of the GPS. The vertical crustal motion in this region is block-dependent. The Central Yunnan block and its eastern boundary are uplifted; meanwhile, the Southwest Yunnan block, which features stretching in the horizontal direction, appears to be subsiding. The aforementioned results can provide data support for the study of water resource utilization and geodynamics in Southwest China.

The Hipparcos–Gaia Catalog of Accelerations: Gaia EDR3 Edition

Abstract We present a cross-calibration of Hipparcos and Gaia EDR3 intended to identify astrometrically accelerating stars and to fit orbits to stars with faint, massive companions. The resulting catalog, the EDR3 edition of the Hipparcos–Gaia Catalog of Accelerations (HGCA), provides three proper motions with calibrated uncertainties on the EDR3 reference frame: the Hipparcos proper motion, the Gaia EDR3 proper motion, and the long-term proper motion given by the difference in position between Hipparcos and Gaia EDR3. Our approach is similar to that for the Gaia DR2 edition of the HGCA but offers a factor of ∼3 improvement in precision thanks to the longer time baseline and improved data processing of Gaia EDR3. We again find that a 60/40 mixture of the two Hipparcos reductions outperforms either reduction individually, and we find strong evidence for locally variable frame rotations between all pairs of proper motion measurements. The substantial global frame rotation seen in DR2 proper motions has been removed in EDR3. We also correct for color- and magnitude-dependent frame rotations at a level of up to ∼50 μas yr−1 in Gaia EDR3. We calibrate the Gaia EDR3 uncertainties using a sample of radial velocity standard stars without binary companions; we find an error inflation factor (a ratio of total to formal uncertainty) of 1.37. This is substantially lower than the position-dependent factor of ∼1.7 found for Gaia DR2 and reflects the improved data processing in EDR3. While the catalog should be used with caution, its proper motion residuals provide a powerful tool to measure the masses and orbits of faint, massive companions to nearby stars.

An Action Recognition Algorithm for Sprinters Using Machine Learning

The advancements in modern science and technology have greatly promoted the progress of sports science. Advanced technological methods have been widely used in sports training, which have not only improved the scientific level of training but also promoted the continuous growth of sports technology and competition results. With the development of sports science and the gradual deepening of sport practices, the use of scientific training methods and monitoring approaches has improved the effect of sports training and athletes’ performance. This paper takes sprint as the research problem and constructs the image of sprinter’s action recognition based on machine learning. In view of the shortcomings of traditional dual-stream convolutional neural network for processing long-term video information, the time-segmented dual-stream network, based on sparse sampling, is used to better express the characteristics of long-term motion. First, the continuous video frame data is divided into multiple segments, and a short sequence of data containing user actions is formed by randomly sampling each segment of the video frame sequence. Next, it is applied to the dual-stream network for feature extraction. The optical flow image extraction involved in the dual-stream network is implemented by the system using the Lucas–Kanade algorithm. The system in this paper has been tested in actual scenarios, and the results show that the system design meets the expected requirements of the sprinters.

Towards automated ultrasound imaging—robotic image acquisition in liver and prostate for long-term motion monitoring

Real-time volumetric (4D) ultrasound has shown high potential for diagnostic and therapy guidance tasks. One of the main drawbacks of ultrasound imaging to date is the reliance on manual probe positioning and the resulting user dependence. Robotic assistance could help overcome this issue and facilitate the acquisition of long-term image data to observe dynamic processes in vivo over time. The aim of this study is to assess the feasibility of robotic probe manipulation and organ motion quantification during extended imaging sessions. The system consists of a collaborative robot and a 4D ultrasound system providing real-time data access. Five healthy volunteers received liver and prostate scans during free breathing over 30 min. Initial probe placement was performed with real-time remote control with a predefined contact force of 10 N. During scan acquisition, the probe position was continuously adjusted to the body surface motion using impedance control. Ultrasound volumes, the pose of the end-effector and the estimated contact forces were recorded. For motion analysis, one anatomical landmark was manually annotated in a subset of ultrasound frames for each experiment. Probe contact was uninterrupted over the entire scan duration in all ten sessions. Organ drift and imaging artefacts were successfully compensated using remote control. The median contact force along the probe’s longitudinal axis was 10.0 N with maximum values of 13.2 and 21.3 N for liver and prostate, respectively. Forces exceeding 11 N only occurred in 0.3% of the time. Probe and landmark motion were more pronounced in the liver, with median interquartile ranges of 1.5 and 9.6 mm, compared to 0.6 and 2.7 mm in the prostate. The results show that robotic ultrasound imaging with dynamic force control can be used for stable, long-term imaging of anatomical regions affected by motion. The system facilitates the acquisition of 4D image data in vivo over extended scanning periods for the first time and holds the potential to be used for motion monitoring for therapy guidance as well as diagnostic tasks.

Circulating, eccentric periodic orbits at the Moon

Loosely captured orbits with circulating and pulsating eccentricity vectors have a variety of attractive mission design properties, including low insertion costs, near-circular and highly eccentric phases, mid- to high inclinations, long-term stability, and spatially distributed close approaches. Such orbits are the known result of averaging third-body perturbations over the spacecraft and system motions. Unfortunately, the doubly averaged model does not match long-term unaveraged motion well at high altitudes. Singly averaged dynamics are accurate for orbits with much higher semimajor axis values, providing a mechanism to predict and characterize high-altitude motion in the unaveraged model. In this work, singly averaged circulating, eccentric orbits are surveyed in the specific context of the dimensioned Earth–Moon system, where high-altitude orbits are expected to have the most useful applications. A global search is performed over non-impacting system resonances, and families of periodic orbits are used as a framework to map the feasible space. The resulting database of periodic orbits is provided as an online supplement. The singly averaged families are shown to provide a reliable bridge between the analytic results of the doubly averaged system and initial guesses that converge to periodic orbits in the unaveraged model. Non-impacting circulating, eccentric orbits are demonstrated to maintain their structure for multiple years in a high-fidelity force model. These circulating, eccentric, lunar orbits may be useful for human-crewed space stations, dedicated science orbits, extended missions, loitering orbits, or transfers between the Lagrange points and low-lunar orbits.

Frequency-Aware SVD Decomposition and its Application to Color Magnification and Motion Denoising

Videos are full of dynamic changes along both the spatial and temporal dimensions. Large, jerky short-term motions make it difficult to extract significant changes from videos such as subtle color changes and long-term motions occurring in time-lapse sequences. In this paper, we introduce two singular value decomposition (SVD)-based video decomposition schemes to clearly reveal such changes. The first scheme involves enhancing the visual characteristics of small subtle color changes in the presence of a wide variety of motion patterns by magnifying their pixel intensities. The second scheme removes short-term motions that visually distract attention from the underlying content of video sequences such as time-lapse videos, snowing scene, and maritime surveillance. Both schemes involve the decomposition of videos into spatiotemporal slices in which each slice is further decomposed into several singular components. The low-rank components that primarily represent background and color intensity information are then temporally processed to magnify the magnitude of the signal at the subtle color change target frequency. At the same time, an approach similar to that used in denoising time-lapse sequences is applied to temporally filter the singular components representing sparse information, thereby removing jittery short-term motions while preserving long-term motions, which are represented by both low-rank and unfiltered sparse components. We demonstrate promising color magnification and motion denoising results that can be obtained much faster than results estimated using state-of-the-art techniques.

Dynamic Analysis and Libration Control of Electrodynamic Tether for Reboost Applications

Electrodynamic tethers can be employed as an immensely promising propulsion system for boosting the altitude of spacecraft, cite instance space stations, satellites, and the like, which ameliorates the expenditure of fuel and minimizes detrimental spacecraft impacts. This paper analyzes the libration dynamics and stability of reboost spacecraft with insulation electrodynamic tethers. A key aspect of spacecraft reboost with an electrodynamic tether is how to keep the tether aligned with the local vertical and stabilized in the context of external disturbances. It has been shown in the current research that the librational instability results in the tether slackness and swings in long-term motion without effective control. Moreover, electrodynamic force (Ampere force) is regarded as a distributed load acting on the tether causing tether deformations which may be detrimental if severe. Aiming at the problem, an optimal control method and PID are given to stabilize the libration motion by modulating the tether current. The dynamical model of the electrodynamic tether system is established using Lagrange equations of the second kind under considering tether deformation and control laws are proposed based on the model. The effectiveness of libration stability control is validated through numerical results in which a current regulation law with appropriate control parameters is used for the libration motion of electrodynamic tether system.

Motion Generation Using Bilateral Control-Based Imitation Learning With Autoregressive Learning

Imitation learning has been studied as an efficient and high-performance method to generate robot motion. Specifically, bilateral control-based imitation learning has been proposed as a method of realizing fast motion. However, the learning approach of this method leads to the accumulation of prediction errors during the prediction process and may not generate desirable long-term behavior. Therefore, in this paper, we propose a method of autoregressive learning for bilateral control-based imitation learning to reduce the accumulation of prediction errors. A new neural network model for implementing autoregressive learning is also proposed. Three types of experiments are conducted to verify the effectiveness of the proposed method, where the method is shown to have improved performance over those of conventional approaches. Due to the structure and method of autoregressive learning employed by the developed model, the proposed method can generate desirable long-term motion for successful tasks and has a high generalization ability for environmental changes based on the human demonstrations of tasks.

Multiscale Spatio-Temporal Graph Neural Networks for 3D Skeleton-Based Motion Prediction.

We propose a multiscale spatio-temporal graph neural network (MST-GNN) to predict the future 3D skeleton-based human poses in an action-category-agnostic manner. The core of MST-GNN is a multiscale spatio-temporal graph that explicitly models the relations in motions at various spatial and temporal scales. Different from many previous hierarchical structures, our multiscale spatio-temporal graph is built in a data-adaptive fashion, which captures nonphysical, yet motion-based relations. The key module of MST-GNN is a multiscale spatio-temporal graph computational unit (MST-GCU) based on the trainable graph structure. MST-GCU embeds underlying features at individual scales and then fuses features across scales to obtain a comprehensive representation. The overall architecture of MST-GNN follows an encoder-decoder framework, where the encoder consists of a sequence of MST-GCUs to learn the spatial and temporal features of motions, and the decoder uses a graph-based attention gate recurrent unit (GA-GRU) to generate future poses. Extensive experiments are conducted to show that the proposed MST-GNN outperforms state-of-the-art methods in both short and long-term motion prediction on the datasets of Human 3.6M, CMU Mocap and 3DPW, where MST-GNN outperforms previous works by 5.33% and 3.67% of mean angle errors in average for short-term and long-term prediction on Human 3.6M, and by 11.84% and 4.71% of mean angle errors for short-term and long-term prediction on CMU Mocap, and by 1.13% of mean angle errors on 3DPW in average, respectively. We further investigate the learned multiscale graphs for interpretability.

Experimental Study on Ramp Shock Wave Control in Ma3 Supersonic Flow Using Two-Electrode SparkJet Actuator

The control of a shock wave produced by a ramp (ramp shock) in Ma3 supersonic flow using a two-electrode SparkJet (SPJ) actuator in a single-pulse mode is studied experimentally. Except for schlieren images of the interaction process of SPJ with the flow field, a dynamic pressure measurement method is also used in the analysis of shock wave control. In a typical experimental case, under the control of single-pulsed SPJ, the characteristic of ramp shock changes from “short-term local upstream motion” in the initial stage to “long-term whole downstream motion” in the later stage. The angle and position of the ramp shock changes significantly in the whole control process. In addition, the dynamic pressure measurement result shows that the ramp pressure is reduced by a maximum of 79% compared to that in the base flow field, which indicates that the ramp shock is significantly weakened by SPJ. The effects of some parameters on the control effect of SPJ on the ramp shock are investigated and analyzed in detail. The increase in discharge capacitance helps to improve the control effect of SPJ on the ramp shock. However, the control effect of the SPJ actuator with medium exit diameter is better than that with a too small or too large one. In addition, when the SPJ exit is located in the separation zone and outside, the change in the ramp shock shows significant differences, but the control effect in the case of medium ramp distance is better when the SPJ exit is located outside the separation zone.

Periodic dike intrusions at Kı-lauea volcano, Hawai’i

AbstractForecasting heightened magmatic activity is key to assessing and mitigating global volcanic hazards, including eruptions from lateral rift zones at basaltic volcanoes. At Kı-lauea volcano, Hawai’i (United States), planar dikes intrude its east rift zone (ERZ) and repeatedly affect the same segments. Here we show that Kı-lauea’s upper and middle ERZ dikes in the last four decades intruded at regular intervals of ∼8 or ∼14 yr. Segments with shorter recurrence intervals are adjacent to faster-moving parts of the flank, and ∼1–5 MPa of tension accumulates from flank spreading in the time between dike events. Intrusion frequency was neither advanced nor delayed during magma supply variations, supporting the role of long-term flank motion on the timing of dike intrusions. Although fewer historical dikes have occurred near the 2018 CE eruption site in the lower ERZ and the adjacent slowly sliding lower eastern flank, similar tension accumulated between the 1955 and 2018 eruptions. Regular dike intrusion recurrence intervals indicate the importance of including both extrusive and (commonly neglected) intrusive activity in eruption hazard analyses.

Mapping the age of ice of Gauligletscher combining surface radionuclide contamination and ice flow modeling

Abstract. In the 1950s and 1960s, specific radionuclides were released into the atmosphere as a result of nuclear weapons testing. This radioactive fallout left its signature on the accumulated layers of glaciers worldwide, thus providing a tracer for ice particles traveling within the gravitational ice flow and being released into the ablation zone. For surface ice dating purposes, we analyze here the activity of 239Pu, 240Pu and 236U radionuclides derived from more than 200 ice samples collected along five flowlines at the surface of Gauligletscher, Switzerland. It was found that contaminations appear band-wise along most of the sampled lines, revealing a V-shaped profile consistent with the ice flow field already observed. Similarities to activities found in ice cores permit the isochronal lines at the glacier from 1960 and 1963 to be identified. Hence this information is used to fine-tune an ice flow/mass balance model, and to accurately map the age of the entire glacier ice. Our results indicate the strong potential for combining radionuclide contamination and ice flow modeling in two different ways. First, such tracers provide unique information on the long-term ice motion of the entire glacier (and not only at its surface), and on the long-term mass balance, and therefore offer an extremely valuable data tool for calibrating ice flows within a model. Second, the dating of surface ice is highly relevant when conducting “horizontal ice core sampling”, i.e., when taking chronological samples of surface ice from the distant past, without having to perform expensive and logistically complex deep ice-core drilling. In conclusion, our results show that an airplane which crash-landed on the Gauligletscher in 1946 will likely soon be released from the ice close to the place where pieces have emerged in recent years, thus permitting the prognosis given in an earlier model to be revised considerably.

Online generation and control of quasi-static multi-contact motion by PWT Jacobian matrix with contact wrench estimation and joint load reduction*

In this paper, we propose a generic method of online motion generation and control that realizes quasi-static multi-contact motion for real position-controlled humanoids. The proposed system calculates command joint angle online by prioritized inverse kinematics that realizes the target contact states and the target position/orientation of interaction end-effectors feasibly. In order to enable control of contact wrench and joint torque with position-controlled robots, Jacobian matrixes (PWT Jacobian matrix) focusing on relationships between command joint angle and actual joint position, contact wrench, and joint torque are introduced. In addition, contact wrench is estimated at the body parts where force sensors are not mounted to enable contacts there, and joint load reduction based on the motor temperature is taken into account to enable long-term motions with real humanoids. The proposed method was verified by a real life-size position-controlled humanoid HRP2-JSKNTS, and various multi-contact motions such as desk climbing using the right knee and both arms were realized.

Computer-Aided Recognition and Analysis of Abnormal Behavior in Video

In intelligent computer-aided video abnormal behavior recognition, pedestrian behavior analysis technology can detect and handle abnormal behaviors in time, which has great practical value in ensuring social safety. We analyze a deep learning video behavior recognition network that has advantages in current research. The network first sparsely sampled the input video to obtain the video frame of each video segment, and then used a two-dimensional convolutional network to extract the characteristics of each video frame, then used a three-dimensional network to fuse them. The method realizes the recognition of long-term and short-term actions in the video at the same time. In order to overcome the shortcoming of the large amount of calculation in the 3D convolution part of the network, this paper proposes an improvement to this module in the network, and proposes a mobile 3D convolution network structure. Aiming at the problem of low utilization of long-term motion features in video sequences, this paper constructs a deep residual module by introducing long and short-term memory networks, residual connection design, etc., to fully and effectively utilize the long-term dynamic features in video sequences. Aiming at the problem of large differences in similar actions and small differences between classes in abnormal behavior videos, this paper proposes a 2CSoftmax function based on double center loss to optimize the network model, which is beneficial to maximize the distance between classes and minimize the distance between classes, so as to realize the classification and recognition of similar actions and improve the recognition accuracy.

Keyframe-based multi-contact motion synthesis

Most of the human daily activities include acyclic multi-contact motions. Yet, generating such motions is challenging because of its high-dimensional and nonlinear solution space made by combinations of individual movements of body parts. In this paper, we present a novel keyframe-based framework to automatically generate multi-contact character motions. Our system consists of two components: key-pose planning and interpolation. Given initial and goal poses in which each contact can be repositioned at most one time during the transition, our key-pose planning step generates intermediate key-poses that represent contact changes, taking into account a set of principles for goal-directed movements. Next, the key-poses of each joint are independently interpolated to generate an acyclic multi-contact motion. We demonstrate that our framework can synthesize plausible interaction motions with a number of man-made objects, such as chairs and bicycles, without using any motion data. In addition, we show the scalability of our method by creating a long-term motion of climbing a ladder.